TSTP Solution File: ITP252^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP252^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:26:20 EDT 2023
% Result : Timeout 299.86s 300.14s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.59/2.63 % Problem : ITP252^3 : TPTP v8.1.2. Released v8.1.0.
% 2.59/2.64 % Command : do_cvc5 %s %d
% 2.66/2.85 % Computer : n028.cluster.edu
% 2.66/2.85 % Model : x86_64 x86_64
% 2.66/2.85 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.66/2.85 % Memory : 8042.1875MB
% 2.66/2.85 % OS : Linux 3.10.0-693.el7.x86_64
% 2.66/2.85 % CPULimit : 300
% 2.66/2.85 % WCLimit : 300
% 2.66/2.85 % DateTime : Sun Aug 27 13:23:11 EDT 2023
% 2.66/2.85 % CPUTime :
% 5.48/5.69 %----Proving TH0
% 5.48/5.69 %------------------------------------------------------------------------------
% 5.48/5.69 % File : ITP252^3 : TPTP v8.1.2. Released v8.1.0.
% 5.48/5.69 % Domain : Interactive Theorem Proving
% 5.48/5.69 % Problem : Sledgehammer problem VEBT_Bounds 01246_070255
% 5.48/5.69 % Version : [Des22] axioms.
% 5.48/5.69 % English :
% 5.48/5.69
% 5.48/5.69 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.48/5.69 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.48/5.69 % Source : [Des22]
% 5.48/5.69 % Names : 0071_VEBT_Bounds_01246_070255 [Des22]
% 5.48/5.69
% 5.48/5.69 % Status : Theorem
% 5.48/5.69 % Rating : 1.00 v8.1.0
% 5.48/5.69 % Syntax : Number of formulae : 11453 (5925 unt;1191 typ; 0 def)
% 5.48/5.69 % Number of atoms : 28932 (12797 equ; 0 cnn)
% 5.48/5.69 % Maximal formula atoms : 71 ( 2 avg)
% 5.48/5.69 % Number of connectives : 119438 (2799 ~; 477 |;1833 &;103870 @)
% 5.48/5.69 % ( 0 <=>;10459 =>; 0 <=; 0 <~>)
% 5.48/5.69 % Maximal formula depth : 39 ( 6 avg)
% 5.48/5.69 % Number of types : 103 ( 102 usr)
% 5.48/5.69 % Number of type conns : 4865 (4865 >; 0 *; 0 +; 0 <<)
% 5.48/5.69 % Number of symbols : 1092 (1089 usr; 68 con; 0-8 aty)
% 5.48/5.69 % Number of variables : 25989 (2162 ^;22954 !; 873 ?;25989 :)
% 5.48/5.69 % SPC : TH0_THM_EQU_NAR
% 5.48/5.69
% 5.48/5.69 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.48/5.69 % from the van Emde Boas Trees session in the Archive of Formal
% 5.48/5.69 % proofs -
% 5.48/5.69 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.48/5.69 % 2022-02-18 03:33:01.224
% 5.48/5.69 %------------------------------------------------------------------------------
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__Set__Oset_It__List__Olist_I_Eo_J_J,type,
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% 5.48/5.69 thf(ty_n_t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__Filter__Ofilter_It__Real__Oreal_J,type,
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% 5.48/5.69
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% 5.48/5.69
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__Filter__Ofilter_It__Nat__Onat_J,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__List__Olist_It__Real__Oreal_J,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__List__Olist_It__Num__Onum_J,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__VEBT____Definitions__OVEBT,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__Set__Oset_It__Num__Onum_J,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
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% 5.48/5.69 thf(ty_n_t__Code____Numeral__Ointeger,type,
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% 5.48/5.69
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__Complex__Ocomplex,type,
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% 5.48/5.69
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% 5.48/5.69
% 5.48/5.69 thf(ty_n_t__Rat__Orat,type,
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% 5.48/5.69
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% 5.48/5.69 thf(ty_n_t__Int__Oint,type,
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% 5.48/5.69
% 5.48/5.69 % Explicit typings (1089)
% 5.48/5.69 thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
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% 5.48/5.69
% 5.48/5.69 thf(sy_c_Archimedean__Field_Oceiling_001t__Real__Oreal,type,
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% 5.48/5.69
% 5.48/5.69 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
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% 5.48/5.69
% 5.48/5.69 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal,type,
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% 5.48/5.69
% 5.48/5.69 thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
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% 5.48/5.69
% 5.48/5.69 thf(sy_c_Archimedean__Field_Ofrac_001t__Real__Oreal,type,
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% 5.48/5.69
% 5.48/5.69 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
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% 5.48/5.69
% 5.48/5.69 thf(sy_c_Archimedean__Field_Oround_001t__Real__Oreal,type,
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% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLeq,type,
% 5.48/5.69 bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
% 5.48/5.69 bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.48/5.69 bNF_re1962705104956426057at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 5.48/5.69 bNF_re895249473297799549at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_Eo_001_Eo,type,
% 5.48/5.69 bNF_re728719798268516973at_o_o: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( ( nat > rat ) > $o ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J_001_062_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.48/5.69 bNF_re4695409256820837752l_real: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( real > real > real ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_Eo_J_001_062_It__Real__Oreal_M_Eo_J,type,
% 5.48/5.69 bNF_re4521903465945308077real_o: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > $o ) > ( real > $o ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( real > real > $o ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 5.48/5.69 bNF_re3023117138289059399t_real: ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_Eo_001_Eo,type,
% 5.48/5.69 bNF_re4297313714947099218al_o_o: ( ( nat > rat ) > real > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( real > $o ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 5.48/5.69 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.48/5.69 bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 5.48/5.69 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.48/5.69 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 5.48/5.69 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.48/5.69 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 5.48/5.69 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.48/5.69 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.48/5.69 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Rat__Orat,type,
% 5.48/5.69 bNF_re4702136315717946289at_rat: ( nat > nat > $o ) > ( rat > rat > $o ) > ( nat > rat ) > ( nat > rat ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Int__Oint_J,type,
% 5.48/5.69 bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 5.48/5.69 bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 5.48/5.69 bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_Eo_001_Eo,type,
% 5.48/5.69 bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 5.48/5.69 bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.48/5.69 bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 5.48/5.69 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.48/5.69 bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 5.48/5.69 bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.48/5.69 bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 5.48/5.69
% 5.48/5.69 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 5.48/5.69 bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
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% 5.48/5.70 ring_18347121197199848620nteger: int > code_integer ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Complex__Ocomplex,type,
% 5.48/5.70 ring_17405671764205052669omplex: int > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 5.48/5.70 ring_1_of_int_int: int > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 5.48/5.70 ring_1_of_int_rat: int > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 5.48/5.70 ring_1_of_int_real: int > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_Eo_J,type,
% 5.48/5.70 inf_inf_nat_rat_o: ( ( nat > rat ) > $o ) > ( ( nat > rat ) > $o ) > ( nat > rat ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Extended____Nat__Oenat,type,
% 5.48/5.70 inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 5.48/5.70 inf_inf_nat: nat > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.48/5.70 inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Lattices_Osemilattice__neutr_001t__Nat__Onat,type,
% 5.48/5.70 semila9081495762789891438tr_nat: ( nat > nat > nat ) > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 5.48/5.70 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 5.48/5.70 sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 5.48/5.70 sup_sup_nat: nat > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.48/5.70 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Extended____Nat__Oenat,type,
% 5.48/5.70 lattic921264341876707157d_enat: set_Extended_enat > extended_enat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 5.48/5.70 lattic8265883725875713057ax_nat: set_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Lifting_OQuotient_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 5.48/5.70 quotie3684837364556693515t_real: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > real ) > ( real > nat > rat ) > ( ( nat > rat ) > real > $o ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.48/5.70 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 5.48/5.70 append_nat: list_nat > list_nat > list_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 5.48/5.70 drop_nat: nat > list_nat > list_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 5.48/5.70 last_nat: list_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 5.48/5.70 linord2614967742042102400et_nat: set_nat > list_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.48/5.70 cons_int: int > list_int > list_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 5.48/5.70 cons_nat: nat > list_nat > list_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 5.48/5.70 nil_int: list_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 5.48/5.70 nil_nat: list_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 5.48/5.70 hd_nat: list_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.48/5.70 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.48/5.70 set_o2: list_o > set_o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.48/5.70 set_complex2: list_complex > set_complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Oset_001t__Extended____Nat__Oenat,type,
% 5.48/5.70 set_Extended_enat2: list_Extended_enat > set_Extended_enat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.48/5.70 set_int2: list_int > set_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.48/5.70 set_nat2: list_nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Oset_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.48/5.70 set_option_nat2: list_option_nat > set_option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.48/5.70 set_real2: list_real > set_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Oset_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.48/5.70 set_set_nat_rat2: list_set_nat_rat > set_set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist__update_001_Eo,type,
% 5.48/5.70 list_update_o: list_o > nat > $o > list_o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 5.48/5.70 list_update_int: list_int > nat > int > list_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 5.48/5.70 list_update_nat: list_nat > nat > nat > list_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist__update_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.48/5.70 list_u3411377215356412978on_nat: list_option_nat > nat > option_nat > list_option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 5.48/5.70 list_update_real: list_real > nat > real > list_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist__update_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.48/5.70 list_u886106648575569423at_rat: list_set_nat_rat > nat > set_nat_rat > list_set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001_Eo,type,
% 5.48/5.70 nth_o: list_o > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.48/5.70 nth_int: list_int > nat > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.48/5.70 nth_nat: list_nat > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 5.48/5.70 nth_num: list_num > nat > num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.48/5.70 nth_option_nat: list_option_nat > nat > option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 5.48/5.70 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 5.48/5.70 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.48/5.70 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.48/5.70 nth_Pr4439495888332055232nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 5.48/5.70 nth_Pr8326237132889035090at_num: list_P1726324292696863441at_num > nat > product_prod_nat_num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.48/5.70 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.48/5.70 nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.48/5.70 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.48/5.70 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.48/5.70 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.48/5.70 nth_real: list_real > nat > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.48/5.70 nth_set_nat_rat: list_set_nat_rat > nat > set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.48/5.70 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 5.48/5.70 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
% 5.48/5.70 product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 5.48/5.70 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.48/5.70 product_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Num__Onum,type,
% 5.48/5.70 product_nat_num: list_nat > list_num > list_P1726324292696863441at_num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 5.48/5.70 product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.48/5.70 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.48/5.70 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.48/5.70 replicate_o: nat > $o > list_o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.48/5.70 replicate_int: nat > int > list_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.48/5.70 replicate_nat: nat > nat > list_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oreplicate_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.48/5.70 replicate_option_nat: nat > option_nat > list_option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.48/5.70 replicate_real: nat > real > list_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oreplicate_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.48/5.70 replic5516892415368941373at_rat: nat > set_nat_rat > list_set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 5.48/5.70 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.48/5.70 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 5.48/5.70 take_nat: nat > list_nat > list_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Otake_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oupt,type,
% 5.48/5.70 upt: nat > nat > list_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oupto,type,
% 5.48/5.70 upto: int > int > list_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_List_Oupto__aux,type,
% 5.48/5.70 upto_aux: int > int > list_int > list_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_OSuc,type,
% 5.48/5.70 suc: nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.48/5.70 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.48/5.70 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.48/5.70 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.48/5.70 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Onat_Opred,type,
% 5.48/5.70 pred: nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.48/5.70 semiri4939895301339042750nteger: nat > code_integer ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.48/5.70 semiri8010041392384452111omplex: nat > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.48/5.70 semiri1314217659103216013at_int: nat > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.48/5.70 semiri681578069525770553at_rat: nat > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.48/5.70 semiri5074537144036343181t_real: nat > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 5.48/5.70 semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Extended____Nat__Oenat,type,
% 5.48/5.70 semiri8563196900006977889d_enat: ( extended_enat > extended_enat ) > nat > extended_enat > extended_enat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 5.48/5.70 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 5.48/5.70 semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 5.48/5.70 semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.48/5.70 size_size_list_o: list_o > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.48/5.70 size_s3451745648224563538omplex: list_complex > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Extended____Nat__Oenat_J,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.48/5.70 size_size_list_int: list_int > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.48/5.70 size_size_list_nat: list_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 5.48/5.70 size_size_list_num: list_num > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Option__Ooption_It__Nat__Onat_J_J,type,
% 5.48/5.70 size_s6086282163384603972on_nat: list_option_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 5.48/5.70 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.48/5.70 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 5.48/5.70 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 5.48/5.70 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.48/5.70 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.48/5.70 size_size_list_real: list_real > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J_J,type,
% 5.48/5.70 size_s3959913991096427681at_rat: list_set_nat_rat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.48/5.70 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.48/5.70 size_size_num: num > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.48/5.70 size_size_option_nat: option_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.48/5.70 size_size_option_num: option_num > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.48/5.70 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
% 5.48/5.70 nat_list_decode_rel: nat > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.48/5.70 nat_list_encode: list_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 5.48/5.70 nat_list_encode_rel: list_nat > list_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 5.48/5.70 nat_prod_decode: nat > product_prod_nat_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 5.48/5.70 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.48/5.70 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.48/5.70 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.48/5.70 nat_set_decode: nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.48/5.70 nat_set_encode: set_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat__Bijection_Osum__decode,type,
% 5.48/5.70 nat_sum_decode: nat > sum_sum_nat_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat__Bijection_Osum__encode,type,
% 5.48/5.70 nat_sum_encode: sum_sum_nat_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.48/5.70 nat_triangle: nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_NthRoot_Oroot,type,
% 5.48/5.70 root: nat > real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_NthRoot_Osqrt,type,
% 5.48/5.70 sqrt: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_OBitM,type,
% 5.48/5.70 bitM: num > num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oinc,type,
% 5.48/5.70 inc: num > num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.48/5.70 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.48/5.70 neg_nu7009210354673126013omplex: complex > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.48/5.70 neg_numeral_dbl_int: int > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 5.48/5.70 neg_numeral_dbl_rat: rat > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.48/5.70 neg_numeral_dbl_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 5.48/5.70 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 5.48/5.70 neg_nu6511756317524482435omplex: complex > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 5.48/5.70 neg_nu3811975205180677377ec_int: int > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 5.48/5.70 neg_nu3179335615603231917ec_rat: rat > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 5.48/5.70 neg_nu6075765906172075777c_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.48/5.70 neg_nu8557863876264182079omplex: complex > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 5.48/5.70 neg_nu5219082963157363817nc_rat: rat > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 5.48/5.70 neg_numeral_sub_int: num > num > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Onum_OBit0,type,
% 5.48/5.70 bit0: num > num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Onum_OBit1,type,
% 5.48/5.70 bit1: num > num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Onum_OOne,type,
% 5.48/5.70 one: num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Onum_Osize__num,type,
% 5.48/5.70 size_num: num > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Num_Onum__of__nat,type,
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% 5.48/5.70 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
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% 5.48/5.70 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
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% 5.48/5.70 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
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% 5.48/5.70 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
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% 5.48/5.70 thf(sy_c_Num_Opow,type,
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% 5.48/5.70 thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
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% 5.48/5.70 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
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% 5.48/5.70 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
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% 5.48/5.70 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
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% 5.48/5.70 produc5703948589228662326_num_o: ( num > num > $o ) > product_prod_num_num > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Int__Oint_J,type,
% 5.48/5.70 produc6406642877701697732et_int: ( num > num > set_int ) > product_prod_num_num > set_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.48/5.70 produc1361121860356118632et_nat: ( num > num > set_nat ) > product_prod_num_num > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.48/5.70 produc8296048397933160132t_real: ( num > num > set_real ) > product_prod_num_num > set_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 5.48/5.70 produc6590410687421337004_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc859450856879609959at_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
% 5.48/5.70 produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 5.48/5.70 product_fst_int_int: product_prod_int_int > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.48/5.70 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 5.48/5.70 product_snd_int_int: product_prod_int_int > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.48/5.70 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Quotient_Oquot__type_Oabs_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 5.48/5.70 quot_a3129823074075660125t_real: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( set_nat_rat > real ) > ( nat > rat ) > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Quotient_Oquot__type_Orep_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 5.48/5.70 quot_r1730120044975580712at_rat: ( real > set_nat_rat ) > real > nat > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rat_OAbs__Rat,type,
% 5.48/5.70 abs_Rat: product_prod_int_int > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rat_OFract,type,
% 5.48/5.70 fract: int > int > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rat_OFrct,type,
% 5.48/5.70 frct: product_prod_int_int > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rat_ORep__Rat,type,
% 5.48/5.70 rep_Rat: rat > product_prod_int_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 5.48/5.70 field_5140801741446780682s_real: set_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rat_Ofield__char__0__class_Oof__rat_001t__Real__Oreal,type,
% 5.48/5.70 field_7254667332652039916t_real: rat > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rat_Onormalize,type,
% 5.48/5.70 normalize: product_prod_int_int > product_prod_int_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rat_Opcr__rat,type,
% 5.48/5.70 pcr_rat: product_prod_int_int > rat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rat_Opositive,type,
% 5.48/5.70 positive: rat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rat_Oquotient__of,type,
% 5.48/5.70 quotient_of: rat > product_prod_int_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rat_Oratrel,type,
% 5.48/5.70 ratrel: product_prod_int_int > product_prod_int_int > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real_OReal,type,
% 5.48/5.70 real2: ( nat > rat ) > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real_Ocauchy,type,
% 5.48/5.70 cauchy: ( nat > rat ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real_Ocr__real,type,
% 5.48/5.70 cr_real: ( nat > rat ) > real > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real_Opcr__real,type,
% 5.48/5.70 pcr_real: ( nat > rat ) > real > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real_Opositive,type,
% 5.48/5.70 positive2: real > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real_Oreal_OAbs__real,type,
% 5.48/5.70 abs_real: set_nat_rat > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real_Oreal_ORep__real,type,
% 5.48/5.70 rep_real: real > set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real_Orealrel,type,
% 5.48/5.70 realrel: ( nat > rat ) > ( nat > rat ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real_Orep__real,type,
% 5.48/5.70 rep_real2: real > nat > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real_Ovanishes,type,
% 5.48/5.70 vanishes: ( nat > rat ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 5.48/5.70 real_V2521375963428798218omplex: set_complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 5.48/5.70 real_V3694042436643373181omplex: complex > complex > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 5.48/5.70 real_V975177566351809787t_real: real > real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 5.48/5.70 real_V1022390504157884413omplex: complex > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 5.48/5.70 real_V7735802525324610683m_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 5.48/5.70 real_V4546457046886955230omplex: real > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal,type,
% 5.48/5.70 real_V1803761363581548252l_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Relation_ODomainp_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 5.48/5.70 domainp_nat_rat_real: ( ( nat > rat ) > real > $o ) > ( nat > rat ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Relation_ODomainp_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.48/5.70 domainp_nat_nat: ( nat > nat > $o ) > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Relation_ODomainp_001t__Rat__Orat_001t__Rat__Orat,type,
% 5.48/5.70 domainp_rat_rat: ( rat > rat > $o ) > rat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Relation_OField_001t__Nat__Onat,type,
% 5.48/5.70 field_nat: set_Pr1261947904930325089at_nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Relation_Orelcompp_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 5.48/5.70 relcom2856161143838007533t_real: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > real > $o ) > ( nat > rat ) > real > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Relation_Otransp_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 5.48/5.70 transp_nat_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Int__Oint,type,
% 5.48/5.70 algebr932160517623751201me_int: int > int > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Nat__Onat,type,
% 5.48/5.70 algebr934650988132801477me_nat: nat > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 5.48/5.70 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 5.48/5.70 divide1717551699836669952omplex: complex > complex > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 5.48/5.70 divide_divide_int: int > int > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 5.48/5.70 divide_divide_nat: nat > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 5.48/5.70 divide_divide_rat: rat > rat > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 5.48/5.70 divide_divide_real: real > real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 5.48/5.70 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 5.48/5.70 dvd_dvd_complex: complex > complex > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 5.48/5.70 dvd_dvd_int: int > int > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 5.48/5.70 dvd_dvd_nat: nat > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 5.48/5.70 dvd_dvd_rat: rat > rat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 5.48/5.70 dvd_dvd_real: real > real > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 5.48/5.70 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 5.48/5.70 modulo_modulo_int: int > int > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 5.48/5.70 modulo_modulo_nat: nat > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 5.48/5.70 zero_n356916108424825756nteger: $o > code_integer ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 5.48/5.70 zero_n1201886186963655149omplex: $o > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Extended____Nat__Oenat,type,
% 5.48/5.70 zero_n1046097342994218471d_enat: $o > extended_enat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 5.48/5.70 zero_n2684676970156552555ol_int: $o > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 5.48/5.70 zero_n2687167440665602831ol_nat: $o > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 5.48/5.70 zero_n2052037380579107095ol_rat: $o > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 5.48/5.70 zero_n3304061248610475627l_real: $o > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 5.48/5.70 suminf_complex: ( nat > complex ) > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
% 5.48/5.70 suminf_int: ( nat > int ) > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 5.48/5.70 suminf_nat: ( nat > nat ) > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 5.48/5.70 suminf_real: ( nat > real ) > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 5.48/5.70 summable_complex: ( nat > complex ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Series_Osummable_001t__Int__Oint,type,
% 5.48/5.70 summable_int: ( nat > int ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
% 5.48/5.70 summable_nat: ( nat > nat ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 5.48/5.70 summable_real: ( nat > real ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
% 5.48/5.70 sums_complex: ( nat > complex ) > complex > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Series_Osums_001t__Int__Oint,type,
% 5.48/5.70 sums_int: ( nat > int ) > int > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Series_Osums_001t__Nat__Onat,type,
% 5.48/5.70 sums_nat: ( nat > nat ) > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 5.48/5.70 sums_real: ( nat > real ) > real > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 5.48/5.70 collect_nat_rat: ( ( nat > rat ) > $o ) > set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
% 5.48/5.70 collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 5.48/5.70 collect_complex: ( complex > $o ) > set_complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Extended____Nat__Oenat,type,
% 5.48/5.70 collec4429806609662206161d_enat: ( extended_enat > $o ) > set_Extended_enat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__List__Olist_I_Eo_J,type,
% 5.48/5.70 collect_list_o: ( list_o > $o ) > set_list_o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.48/5.70 collect_list_complex: ( list_complex > $o ) > set_list_complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__List__Olist_It__Extended____Nat__Oenat_J,type,
% 5.48/5.70 collec8433460942617342167d_enat: ( list_Extended_enat > $o ) > set_li5464603477888414924d_enat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__List__Olist_It__Int__Oint_J,type,
% 5.48/5.70 collect_list_int: ( list_int > $o ) > set_list_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 5.48/5.70 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.48/5.70 collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 5.48/5.70 collect_nat: ( nat > $o ) > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Num__Onum,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Option__Ooption_It__Nat__Onat_J,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Rat__Orat,type,
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% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 5.48/5.70 collect_real: ( real > $o ) > set_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.48/5.70 collect_set_nat_rat: ( set_nat_rat > $o ) > set_set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.48/5.70 collect_set_nat: ( set_nat > $o ) > set_set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oimage_001t__Extended____Nat__Oenat_001t__Extended____Nat__Oenat,type,
% 5.48/5.70 image_80655429650038917d_enat: ( extended_enat > extended_enat ) > set_Extended_enat > set_Extended_enat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.48/5.70 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 5.48/5.70 image_nat_char: ( nat > char ) > set_nat > set_char ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 5.48/5.70 image_5971271580939081552omplex: ( real > filter6041513312241820739omplex ) > set_real > set_fi4554929511873752355omplex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 5.48/5.70 image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.48/5.70 image_real_real: ( real > real ) > set_real > set_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 5.48/5.70 image_char_nat: ( char > nat ) > set_char > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oimage_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.48/5.70 image_VEBT_VEBT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
% 5.48/5.70 insert_complex: complex > set_complex > set_complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oinsert_001t__Extended____Nat__Oenat,type,
% 5.48/5.70 insert_Extended_enat: extended_enat > set_Extended_enat > set_Extended_enat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 5.48/5.70 insert_int: int > set_int > set_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 5.48/5.70 insert_nat: nat > set_nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
% 5.48/5.70 insert_num: num > set_num > set_num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.48/5.70 insert_option_nat: option_nat > set_option_nat > set_option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
% 5.48/5.70 insert_rat: rat > set_rat > set_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 5.48/5.70 insert_real: real > set_real > set_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oinsert_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.48/5.70 insert_set_nat_rat: set_nat_rat > set_set_nat_rat > set_set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.48/5.70 vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
% 5.48/5.70 set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Extended____Nat__Oenat,type,
% 5.48/5.70 set_fo2538466533108834004d_enat: ( nat > extended_enat > extended_enat ) > nat > nat > extended_enat > extended_enat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
% 5.48/5.70 set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 5.48/5.70 set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 5.48/5.70 set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
% 5.48/5.70 set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Extended____Nat__Oenat,type,
% 5.48/5.70 set_or5403411693681687835d_enat: extended_enat > extended_enat > set_Extended_enat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 5.48/5.70 set_or1266510415728281911st_int: int > int > set_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 5.48/5.70 set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 5.48/5.70 set_or7049704709247886629st_num: num > num > set_num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 5.48/5.70 set_or633870826150836451st_rat: rat > rat > set_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 5.48/5.70 set_or1222579329274155063t_real: real > real > set_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.48/5.70 set_or5795412311047298440at_rat: set_nat_rat > set_nat_rat > set_set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.48/5.70 set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 5.48/5.70 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatMost_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 5.48/5.70 set_or5632376147039224640at_rat: ( nat > rat ) > set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 5.48/5.70 set_ord_atMost_int: int > set_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 5.48/5.70 set_ord_atMost_nat: nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
% 5.48/5.70 set_ord_atMost_num: num > set_num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Rat__Orat,type,
% 5.48/5.70 set_ord_atMost_rat: rat > set_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
% 5.48/5.70 set_ord_atMost_real: real > set_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.48/5.70 set_or3094126398206284534at_rat: set_nat_rat > set_set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.48/5.70 set_or4236626031148496127et_nat: set_nat > set_set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 5.48/5.70 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 5.48/5.70 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 5.48/5.70 set_or1633881224788618240n_real: real > real > set_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 5.48/5.70 set_or5849166863359141190n_real: real > set_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OlessThan_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 5.48/5.70 set_or6855495488841395556at_rat: ( nat > rat ) > set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 5.48/5.70 set_ord_lessThan_int: int > set_int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 5.48/5.70 set_ord_lessThan_nat: nat > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 5.48/5.70 set_ord_lessThan_num: num > set_num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 5.48/5.70 set_ord_lessThan_rat: rat > set_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 5.48/5.70 set_or5984915006950818249n_real: real > set_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.48/5.70 set_or6234697943151750426at_rat: set_nat_rat > set_set_nat_rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_String_OCode_Oabort_001t__Real__Oreal,type,
% 5.48/5.70 abort_real: literal > ( product_unit > real ) > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_String_OLiteral,type,
% 5.48/5.70 literal2: $o > $o > $o > $o > $o > $o > $o > literal > literal ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_String_Oascii__of,type,
% 5.48/5.70 ascii_of: char > char ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_String_Ochar_OChar,type,
% 5.48/5.70 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 5.48/5.70 comm_s629917340098488124ar_nat: char > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_String_Ointeger__of__char,type,
% 5.48/5.70 integer_of_char: char > code_integer ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 5.48/5.70 unique3096191561947761185of_nat: nat > char ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Sum__Type_OInl_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.48/5.70 sum_Inl_nat_nat: nat > sum_sum_nat_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Sum__Type_OInr_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.48/5.70 sum_Inr_nat_nat: nat > sum_sum_nat_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Sum__Type_Osum_Ocase__sum_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.48/5.70 sum_ca6763686470577984908at_nat: ( nat > nat ) > ( nat > nat ) > sum_sum_nat_nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.48/5.70 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.48/5.70 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 5.48/5.70 topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 5.48/5.70 topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 5.48/5.70 topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Omonoseq_001t__Rat__Orat,type,
% 5.48/5.70 topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 5.48/5.70 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.48/5.70 topolo7278393974255667507et_nat: ( nat > set_nat ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 5.48/5.70 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Otopological__space__class_Oconvergent_001t__Real__Oreal,type,
% 5.48/5.70 topolo7531315842566124627t_real: ( nat > real ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.48/5.70 topolo2815343760600316023s_real: real > filter_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.48/5.70 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 5.48/5.70 topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 5.48/5.70 topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Oarccos,type,
% 5.48/5.70 arccos: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.48/5.70 arcosh_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Oarcsin,type,
% 5.48/5.70 arcsin: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Oarctan,type,
% 5.48/5.70 arctan: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.48/5.70 arsinh_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.48/5.70 artanh_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 5.48/5.70 cos_complex: complex > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.48/5.70 cos_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.48/5.70 cos_coeff: nat > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.48/5.70 cosh_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.48/5.70 cot_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 5.48/5.70 diffs_complex: ( nat > complex ) > nat > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 5.48/5.70 diffs_int: ( nat > int ) > nat > int ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Odiffs_001t__Rat__Orat,type,
% 5.48/5.70 diffs_rat: ( nat > rat ) > nat > rat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 5.48/5.70 diffs_real: ( nat > real ) > nat > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.48/5.70 exp_complex: complex > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.48/5.70 exp_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.48/5.70 ln_ln_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Olog,type,
% 5.48/5.70 log: real > real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Opi,type,
% 5.48/5.70 pi: real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.48/5.70 powr_real: real > real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Opowr__real,type,
% 5.48/5.70 powr_real2: real > real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 5.48/5.70 sin_complex: complex > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.48/5.70 sin_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.48/5.70 sin_coeff: nat > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.48/5.70 sinh_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 5.48/5.70 tan_complex: complex > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.48/5.70 tan_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 5.48/5.70 tanh_complex: complex > complex ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.48/5.70 tanh_real: real > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transfer_Oleft__total_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 5.48/5.70 left_t2768085380646472630at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transfer_Oleft__unique_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.48/5.70 left_unique_nat_nat: ( nat > nat > $o ) > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 5.48/5.70 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.48/5.70 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Typedef_Otype__definition_001t__Extended____Nat__Oenat_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.48/5.70 type_d7649664348572268762on_nat: ( extended_enat > option_nat ) > ( option_nat > extended_enat ) > set_option_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Typedef_Otype__definition_001t__Real__Oreal_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.48/5.70 type_d8072115097938612567at_rat: ( real > set_nat_rat ) > ( set_nat_rat > real ) > set_set_nat_rat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t,type,
% 5.48/5.70 vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H,type,
% 5.48/5.70 vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H__rel,type,
% 5.48/5.70 vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t__rel,type,
% 5.48/5.70 vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t,type,
% 5.48/5.70 vEBT_T_m_a_x_t: vEBT_VEBT > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t__rel,type,
% 5.48/5.70 vEBT_T_m_a_x_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r,type,
% 5.48/5.70 vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H,type,
% 5.48/5.70 vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H__rel,type,
% 5.48/5.70 vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r__rel,type,
% 5.48/5.70 vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l,type,
% 5.48/5.70 vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l__rel,type,
% 5.48/5.70 vEBT_T5462971552011256508_l_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t,type,
% 5.48/5.70 vEBT_T_m_i_n_t: vEBT_VEBT > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t__rel,type,
% 5.48/5.70 vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c,type,
% 5.48/5.70 vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H,type,
% 5.48/5.70 vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H__rel,type,
% 5.48/5.70 vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c__rel,type,
% 5.48/5.70 vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.48/5.70 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.48/5.70 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.48/5.70 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.48/5.70 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead,type,
% 5.48/5.70 vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead__rel,type,
% 5.48/5.70 vEBT_V312737461966249ad_rel: produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.48/5.70 vEBT_VEBT_high: nat > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.48/5.70 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.48/5.70 vEBT_VEBT_low: nat > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.48/5.70 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.48/5.70 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.48/5.70 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.48/5.70 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.48/5.70 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.48/5.70 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.48/5.70 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.48/5.70 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.48/5.70 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.48/5.70 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight,type,
% 5.48/5.70 vEBT_VEBT_height: vEBT_VEBT > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight__rel,type,
% 5.48/5.70 vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.48/5.70 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.48/5.70 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.48/5.70 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.48/5.70 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.48/5.70 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.48/5.70 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.48/5.70 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.48/5.70 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.48/5.70 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.48/5.70 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.48/5.70 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.48/5.70 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.48/5.70 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 5.48/5.70 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 5.48/5.70 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 5.48/5.70 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 5.48/5.70 vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.48/5.70 vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 5.48/5.70 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 5.48/5.70 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 5.48/5.70 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 5.48/5.70 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 5.48/5.70 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 5.48/5.70 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 5.48/5.70 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 5.48/5.70 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 5.48/5.70 vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 5.48/5.70 vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 5.48/5.70 vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 5.48/5.70 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.48/5.70 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.48/5.70 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.48/5.70 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.48/5.70 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Extended____Nat__Oenat_J,type,
% 5.48/5.70 accp_P6183159247885693666d_enat: ( produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ) > produc7272778201969148633d_enat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.48/5.70 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Wellfounded_Oless__than,type,
% 5.48/5.70 less_than: set_Pr1261947904930325089at_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Wellfounded_Opred__nat,type,
% 5.48/5.70 pred_nat: set_Pr1261947904930325089at_nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 5.48/5.70 wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.48/5.70 fChoice_real: ( real > $o ) > real ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 5.48/5.70 member_nat_rat: ( nat > rat ) > set_nat_rat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001_Eo,type,
% 5.48/5.70 member_o: $o > set_o > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.48/5.70 member_complex: complex > set_complex > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__Extended____Nat__Oenat,type,
% 5.48/5.70 member_Extended_enat: extended_enat > set_Extended_enat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__Int__Oint,type,
% 5.48/5.70 member_int: int > set_int > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 5.48/5.70 member_list_o: list_o > set_list_o > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.48/5.70 member_list_nat: list_nat > set_list_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.48/5.70 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__Nat__Onat,type,
% 5.48/5.70 member_nat: nat > set_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__Num__Onum,type,
% 5.48/5.70 member_num: num > set_num > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.48/5.70 member_option_nat: option_nat > set_option_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.48/5.70 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.48/5.70 member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__Rat__Orat,type,
% 5.48/5.70 member_rat: rat > set_rat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__Real__Oreal,type,
% 5.48/5.70 member_real: real > set_real > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.48/5.70 member_set_nat_rat: set_nat_rat > set_set_nat_rat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.48/5.70 member_set_nat: set_nat > set_set_nat > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.48/5.70 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.48/5.70
% 5.48/5.70 thf(sy_v_deg____,type,
% 5.48/5.70 deg: nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_v_m____,type,
% 5.48/5.70 m: nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_v_ma____,type,
% 5.48/5.70 ma: nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_v_mi____,type,
% 5.48/5.70 mi: nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_v_na____,type,
% 5.48/5.70 na: nat ).
% 5.48/5.70
% 5.48/5.70 thf(sy_v_summary____,type,
% 5.48/5.70 summary: vEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_v_treeList____,type,
% 5.48/5.70 treeList: list_VEBT_VEBT ).
% 5.48/5.70
% 5.48/5.70 thf(sy_v_xa____,type,
% 5.48/5.70 xa: nat ).
% 5.48/5.70
% 5.48/5.70 % Relevant facts (10211)
% 5.48/5.70 thf(fact_0__C5_Ohyps_C_I7_J,axiom,
% 5.48/5.70 ord_less_eq_nat @ mi @ ma ).
% 5.48/5.70
% 5.48/5.70 % "5.hyps"(7)
% 5.48/5.70 thf(fact_1_max__in__set__def,axiom,
% 5.48/5.70 ( vEBT_VEBT_max_in_set
% 5.48/5.70 = ( ^ [Xs: set_nat,X: nat] :
% 5.48/5.70 ( ( member_nat @ X @ Xs )
% 5.48/5.70 & ! [Y: nat] :
% 5.48/5.70 ( ( member_nat @ Y @ Xs )
% 5.48/5.70 => ( ord_less_eq_nat @ Y @ X ) ) ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % max_in_set_def
% 5.48/5.70 thf(fact_2_min__in__set__def,axiom,
% 5.48/5.70 ( vEBT_VEBT_min_in_set
% 5.48/5.70 = ( ^ [Xs: set_nat,X: nat] :
% 5.48/5.70 ( ( member_nat @ X @ Xs )
% 5.48/5.70 & ! [Y: nat] :
% 5.48/5.70 ( ( member_nat @ Y @ Xs )
% 5.48/5.70 => ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % min_in_set_def
% 5.48/5.70 thf(fact_3_height__compose__summary,axiom,
% 5.48/5.70 ! [Summary: vEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ Summary ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % height_compose_summary
% 5.48/5.70 thf(fact_4__092_060open_0622_A_092_060le_062_Adeg_092_060close_062,axiom,
% 5.48/5.70 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 5.48/5.70
% 5.48/5.70 % \<open>2 \<le> deg\<close>
% 5.48/5.70 thf(fact_5__C5_OIH_C_I2_J,axiom,
% 5.48/5.70 ! [X2: nat] : ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c @ summary @ X2 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ summary ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % "5.IH"(2)
% 5.48/5.70 thf(fact_6__C2_C,axiom,
% 5.48/5.70 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.48/5.70 = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( vEBT_T_s_u_c_c @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.70 @ ( if_nat
% 5.48/5.70 @ ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.70 = none_nat )
% 5.48/5.70 @ one_one_nat
% 5.48/5.70 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % "2"
% 5.48/5.70 thf(fact_7_insert__simp__mima,axiom,
% 5.48/5.70 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.48/5.70 ( ( ( X2 = Mi )
% 5.48/5.70 | ( X2 = Ma ) )
% 5.48/5.70 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.48/5.70 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.48/5.70 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % insert_simp_mima
% 5.48/5.70 thf(fact_8_one__add__one,axiom,
% 5.48/5.70 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.48/5.70 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_add_one
% 5.48/5.70 thf(fact_9_one__add__one,axiom,
% 5.48/5.70 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.48/5.70 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_add_one
% 5.48/5.70 thf(fact_10_one__add__one,axiom,
% 5.48/5.70 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.48/5.70 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_add_one
% 5.48/5.70 thf(fact_11_one__add__one,axiom,
% 5.48/5.70 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.48/5.70 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_add_one
% 5.48/5.70 thf(fact_12_one__add__one,axiom,
% 5.48/5.70 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.48/5.70 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_add_one
% 5.48/5.70 thf(fact_13_numeral__plus__one,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 5.48/5.70 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_plus_one
% 5.48/5.70 thf(fact_14_numeral__plus__one,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.48/5.70 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_plus_one
% 5.48/5.70 thf(fact_15_numeral__plus__one,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.48/5.70 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_plus_one
% 5.48/5.70 thf(fact_16_numeral__plus__one,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.48/5.70 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_plus_one
% 5.48/5.70 thf(fact_17_numeral__plus__one,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.48/5.70 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_plus_one
% 5.48/5.70 thf(fact_18_one__plus__numeral,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 5.48/5.70 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_plus_numeral
% 5.48/5.70 thf(fact_19_one__plus__numeral,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.48/5.70 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_plus_numeral
% 5.48/5.70 thf(fact_20_one__plus__numeral,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.48/5.70 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_plus_numeral
% 5.48/5.70 thf(fact_21_one__plus__numeral,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.48/5.70 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_plus_numeral
% 5.48/5.70 thf(fact_22_one__plus__numeral,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.48/5.70 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_plus_numeral
% 5.48/5.70 thf(fact_23_numeral__le__one__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.48/5.70 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_le_one_iff
% 5.48/5.70 thf(fact_24_numeral__le__one__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.48/5.70 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_le_one_iff
% 5.48/5.70 thf(fact_25_numeral__le__one__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.48/5.70 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_le_one_iff
% 5.48/5.70 thf(fact_26_numeral__le__one__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.48/5.70 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_le_one_iff
% 5.48/5.70 thf(fact_27_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I3_J,axiom,
% 5.48/5.70 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.48/5.70 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.48/5.70 = one_one_nat ) ).
% 5.48/5.70
% 5.48/5.70 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(3)
% 5.48/5.70 thf(fact_28_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I3_J,axiom,
% 5.48/5.70 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.48/5.70 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.48/5.70 = one_one_nat ) ).
% 5.48/5.70
% 5.48/5.70 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(3)
% 5.48/5.70 thf(fact_29_maxt__bound,axiom,
% 5.48/5.70 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_a_x_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % maxt_bound
% 5.48/5.70 thf(fact_30_mint__bound,axiom,
% 5.48/5.70 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % mint_bound
% 5.48/5.70 thf(fact_31_numeral__eq__one__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( ( numera6690914467698888265omplex @ N )
% 5.48/5.70 = one_one_complex )
% 5.48/5.70 = ( N = one ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_eq_one_iff
% 5.48/5.70 thf(fact_32_numeral__eq__one__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( ( numeral_numeral_real @ N )
% 5.48/5.70 = one_one_real )
% 5.48/5.70 = ( N = one ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_eq_one_iff
% 5.48/5.70 thf(fact_33_numeral__eq__one__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( ( numeral_numeral_rat @ N )
% 5.48/5.70 = one_one_rat )
% 5.48/5.70 = ( N = one ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_eq_one_iff
% 5.48/5.70 thf(fact_34_numeral__eq__one__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( ( numeral_numeral_nat @ N )
% 5.48/5.70 = one_one_nat )
% 5.48/5.70 = ( N = one ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_eq_one_iff
% 5.48/5.70 thf(fact_35_numeral__eq__one__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( ( numeral_numeral_int @ N )
% 5.48/5.70 = one_one_int )
% 5.48/5.70 = ( N = one ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_eq_one_iff
% 5.48/5.70 thf(fact_36_one__eq__numeral__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( one_one_complex
% 5.48/5.70 = ( numera6690914467698888265omplex @ N ) )
% 5.48/5.70 = ( one = N ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_eq_numeral_iff
% 5.48/5.70 thf(fact_37_one__eq__numeral__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( one_one_real
% 5.48/5.70 = ( numeral_numeral_real @ N ) )
% 5.48/5.70 = ( one = N ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_eq_numeral_iff
% 5.48/5.70 thf(fact_38_one__eq__numeral__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( one_one_rat
% 5.48/5.70 = ( numeral_numeral_rat @ N ) )
% 5.48/5.70 = ( one = N ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_eq_numeral_iff
% 5.48/5.70 thf(fact_39_one__eq__numeral__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( one_one_nat
% 5.48/5.70 = ( numeral_numeral_nat @ N ) )
% 5.48/5.70 = ( one = N ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_eq_numeral_iff
% 5.48/5.70 thf(fact_40_one__eq__numeral__iff,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( one_one_int
% 5.48/5.70 = ( numeral_numeral_int @ N ) )
% 5.48/5.70 = ( one = N ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_eq_numeral_iff
% 5.48/5.70 thf(fact_41_numeral__eq__iff,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( ( numera6690914467698888265omplex @ M )
% 5.48/5.70 = ( numera6690914467698888265omplex @ N ) )
% 5.48/5.70 = ( M = N ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_eq_iff
% 5.48/5.70 thf(fact_42_numeral__eq__iff,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( ( numeral_numeral_real @ M )
% 5.48/5.70 = ( numeral_numeral_real @ N ) )
% 5.48/5.70 = ( M = N ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_eq_iff
% 5.48/5.70 thf(fact_43_numeral__eq__iff,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( ( numeral_numeral_rat @ M )
% 5.48/5.70 = ( numeral_numeral_rat @ N ) )
% 5.48/5.70 = ( M = N ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_eq_iff
% 5.48/5.70 thf(fact_44_numeral__eq__iff,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( ( numeral_numeral_nat @ M )
% 5.48/5.70 = ( numeral_numeral_nat @ N ) )
% 5.48/5.70 = ( M = N ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_eq_iff
% 5.48/5.70 thf(fact_45_numeral__eq__iff,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( ( numeral_numeral_int @ M )
% 5.48/5.70 = ( numeral_numeral_int @ N ) )
% 5.48/5.70 = ( M = N ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_eq_iff
% 5.48/5.70 thf(fact_46_mult__numeral__left__semiring__numeral,axiom,
% 5.48/5.70 ! [V: num,W: num,Z: complex] :
% 5.48/5.70 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.48/5.70 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.48/5.70
% 5.48/5.70 % mult_numeral_left_semiring_numeral
% 5.48/5.70 thf(fact_47_mult__numeral__left__semiring__numeral,axiom,
% 5.48/5.70 ! [V: num,W: num,Z: real] :
% 5.48/5.70 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.48/5.70 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.48/5.70
% 5.48/5.70 % mult_numeral_left_semiring_numeral
% 5.48/5.70 thf(fact_48_mult__numeral__left__semiring__numeral,axiom,
% 5.48/5.70 ! [V: num,W: num,Z: rat] :
% 5.48/5.70 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.48/5.70 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.48/5.70
% 5.48/5.70 % mult_numeral_left_semiring_numeral
% 5.48/5.70 thf(fact_49_mult__numeral__left__semiring__numeral,axiom,
% 5.48/5.70 ! [V: num,W: num,Z: nat] :
% 5.48/5.70 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.48/5.70 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.48/5.70
% 5.48/5.70 % mult_numeral_left_semiring_numeral
% 5.48/5.70 thf(fact_50_mult__numeral__left__semiring__numeral,axiom,
% 5.48/5.70 ! [V: num,W: num,Z: int] :
% 5.48/5.70 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.48/5.70 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.48/5.70
% 5.48/5.70 % mult_numeral_left_semiring_numeral
% 5.48/5.70 thf(fact_51_numeral__times__numeral,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.48/5.70 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_times_numeral
% 5.48/5.70 thf(fact_52_numeral__times__numeral,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.48/5.70 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_times_numeral
% 5.48/5.70 thf(fact_53_numeral__times__numeral,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.48/5.70 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_times_numeral
% 5.48/5.70 thf(fact_54_numeral__times__numeral,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.48/5.70 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_times_numeral
% 5.48/5.70 thf(fact_55_numeral__times__numeral,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.48/5.70 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_times_numeral
% 5.48/5.70 thf(fact_56_distrib__right__numeral,axiom,
% 5.48/5.70 ! [A: complex,B: complex,V: num] :
% 5.48/5.70 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.48/5.70 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % distrib_right_numeral
% 5.48/5.70 thf(fact_57_distrib__right__numeral,axiom,
% 5.48/5.70 ! [A: real,B: real,V: num] :
% 5.48/5.70 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.48/5.70 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % distrib_right_numeral
% 5.48/5.70 thf(fact_58_distrib__right__numeral,axiom,
% 5.48/5.70 ! [A: rat,B: rat,V: num] :
% 5.48/5.70 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.48/5.70 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % distrib_right_numeral
% 5.48/5.70 thf(fact_59_distrib__right__numeral,axiom,
% 5.48/5.70 ! [A: nat,B: nat,V: num] :
% 5.48/5.70 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.48/5.70 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % distrib_right_numeral
% 5.48/5.70 thf(fact_60_distrib__right__numeral,axiom,
% 5.48/5.70 ! [A: int,B: int,V: num] :
% 5.48/5.70 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.48/5.70 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % distrib_right_numeral
% 5.48/5.70 thf(fact_61_distrib__left__numeral,axiom,
% 5.48/5.70 ! [V: num,B: complex,C: complex] :
% 5.48/5.70 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.48/5.70 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % distrib_left_numeral
% 5.48/5.70 thf(fact_62_distrib__left__numeral,axiom,
% 5.48/5.70 ! [V: num,B: real,C: real] :
% 5.48/5.70 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.48/5.70 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % distrib_left_numeral
% 5.48/5.70 thf(fact_63_distrib__left__numeral,axiom,
% 5.48/5.70 ! [V: num,B: rat,C: rat] :
% 5.48/5.70 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.48/5.70 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % distrib_left_numeral
% 5.48/5.70 thf(fact_64_distrib__left__numeral,axiom,
% 5.48/5.70 ! [V: num,B: nat,C: nat] :
% 5.48/5.70 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.48/5.70 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % distrib_left_numeral
% 5.48/5.70 thf(fact_65_distrib__left__numeral,axiom,
% 5.48/5.70 ! [V: num,B: int,C: int] :
% 5.48/5.70 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.48/5.70 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % distrib_left_numeral
% 5.48/5.70 thf(fact_66_add__numeral__left,axiom,
% 5.48/5.70 ! [V: num,W: num,Z: complex] :
% 5.48/5.70 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.48/5.70 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.48/5.70
% 5.48/5.70 % add_numeral_left
% 5.48/5.70 thf(fact_67_add__numeral__left,axiom,
% 5.48/5.70 ! [V: num,W: num,Z: real] :
% 5.48/5.70 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.48/5.70 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.48/5.70
% 5.48/5.70 % add_numeral_left
% 5.48/5.70 thf(fact_68_add__numeral__left,axiom,
% 5.48/5.70 ! [V: num,W: num,Z: rat] :
% 5.48/5.70 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.48/5.70 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.48/5.70
% 5.48/5.70 % add_numeral_left
% 5.48/5.70 thf(fact_69_add__numeral__left,axiom,
% 5.48/5.70 ! [V: num,W: num,Z: nat] :
% 5.48/5.70 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.48/5.70 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.48/5.70
% 5.48/5.70 % add_numeral_left
% 5.48/5.70 thf(fact_70_add__numeral__left,axiom,
% 5.48/5.70 ! [V: num,W: num,Z: int] :
% 5.48/5.70 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.48/5.70 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.48/5.70
% 5.48/5.70 % add_numeral_left
% 5.48/5.70 thf(fact_71_numeral__plus__numeral,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.48/5.70 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_plus_numeral
% 5.48/5.70 thf(fact_72_numeral__plus__numeral,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.48/5.70 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_plus_numeral
% 5.48/5.70 thf(fact_73_numeral__plus__numeral,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.48/5.70 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_plus_numeral
% 5.48/5.70 thf(fact_74_numeral__plus__numeral,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.48/5.70 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_plus_numeral
% 5.48/5.70 thf(fact_75_numeral__plus__numeral,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.48/5.70 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_plus_numeral
% 5.48/5.70 thf(fact_76_numeral__le__iff,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.48/5.70 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_le_iff
% 5.48/5.70 thf(fact_77_numeral__le__iff,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.48/5.70 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_le_iff
% 5.48/5.70 thf(fact_78_numeral__le__iff,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.48/5.70 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_le_iff
% 5.48/5.70 thf(fact_79_numeral__le__iff,axiom,
% 5.48/5.70 ! [M: num,N: num] :
% 5.48/5.70 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.48/5.70 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.48/5.70
% 5.48/5.70 % numeral_le_iff
% 5.48/5.70 thf(fact_80_le__divide__eq__numeral1_I1_J,axiom,
% 5.48/5.70 ! [A: real,B: real,W: num] :
% 5.48/5.70 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.48/5.70 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.48/5.70
% 5.48/5.70 % le_divide_eq_numeral1(1)
% 5.48/5.70 thf(fact_81_le__divide__eq__numeral1_I1_J,axiom,
% 5.48/5.70 ! [A: rat,B: rat,W: num] :
% 5.48/5.70 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.48/5.70 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.48/5.70
% 5.48/5.70 % le_divide_eq_numeral1(1)
% 5.48/5.70 thf(fact_82_divide__le__eq__numeral1_I1_J,axiom,
% 5.48/5.70 ! [B: real,W: num,A: real] :
% 5.48/5.70 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.48/5.70 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % divide_le_eq_numeral1(1)
% 5.48/5.70 thf(fact_83_divide__le__eq__numeral1_I1_J,axiom,
% 5.48/5.70 ! [B: rat,W: num,A: rat] :
% 5.48/5.70 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.48/5.70 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % divide_le_eq_numeral1(1)
% 5.48/5.70 thf(fact_84_add__One__commute,axiom,
% 5.48/5.70 ! [N: num] :
% 5.48/5.70 ( ( plus_plus_num @ one @ N )
% 5.48/5.70 = ( plus_plus_num @ N @ one ) ) ).
% 5.48/5.70
% 5.48/5.70 % add_One_commute
% 5.48/5.70 thf(fact_85_le__num__One__iff,axiom,
% 5.48/5.70 ! [X2: num] :
% 5.48/5.70 ( ( ord_less_eq_num @ X2 @ one )
% 5.48/5.70 = ( X2 = one ) ) ).
% 5.48/5.70
% 5.48/5.70 % le_num_One_iff
% 5.48/5.70 thf(fact_86_is__num__normalize_I1_J,axiom,
% 5.48/5.70 ! [A: real,B: real,C: real] :
% 5.48/5.70 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.48/5.70 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % is_num_normalize(1)
% 5.48/5.70 thf(fact_87_is__num__normalize_I1_J,axiom,
% 5.48/5.70 ! [A: rat,B: rat,C: rat] :
% 5.48/5.70 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.48/5.70 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % is_num_normalize(1)
% 5.48/5.70 thf(fact_88_is__num__normalize_I1_J,axiom,
% 5.48/5.70 ! [A: int,B: int,C: int] :
% 5.48/5.70 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.48/5.70 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % is_num_normalize(1)
% 5.48/5.70 thf(fact_89_is__num__normalize_I1_J,axiom,
% 5.48/5.70 ! [A: complex,B: complex,C: complex] :
% 5.48/5.70 ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.48/5.70 = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.48/5.70
% 5.48/5.70 % is_num_normalize(1)
% 5.48/5.70 thf(fact_90_divide__numeral__1,axiom,
% 5.48/5.70 ! [A: complex] :
% 5.48/5.70 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.48/5.70 = A ) ).
% 5.48/5.70
% 5.48/5.70 % divide_numeral_1
% 5.48/5.70 thf(fact_91_divide__numeral__1,axiom,
% 5.48/5.70 ! [A: real] :
% 5.48/5.70 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.48/5.70 = A ) ).
% 5.48/5.70
% 5.48/5.70 % divide_numeral_1
% 5.48/5.70 thf(fact_92_divide__numeral__1,axiom,
% 5.48/5.70 ! [A: rat] :
% 5.48/5.70 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.48/5.70 = A ) ).
% 5.48/5.70
% 5.48/5.70 % divide_numeral_1
% 5.48/5.70 thf(fact_93_le__numeral__extra_I4_J,axiom,
% 5.48/5.70 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.48/5.70
% 5.48/5.70 % le_numeral_extra(4)
% 5.48/5.70 thf(fact_94_le__numeral__extra_I4_J,axiom,
% 5.48/5.70 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.48/5.70
% 5.48/5.70 % le_numeral_extra(4)
% 5.48/5.70 thf(fact_95_le__numeral__extra_I4_J,axiom,
% 5.48/5.70 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.48/5.70
% 5.48/5.70 % le_numeral_extra(4)
% 5.48/5.70 thf(fact_96_le__numeral__extra_I4_J,axiom,
% 5.48/5.70 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.48/5.70
% 5.48/5.70 % le_numeral_extra(4)
% 5.48/5.70 thf(fact_97_one__le__numeral,axiom,
% 5.48/5.70 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_le_numeral
% 5.48/5.70 thf(fact_98_one__le__numeral,axiom,
% 5.48/5.70 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_le_numeral
% 5.48/5.70 thf(fact_99_one__le__numeral,axiom,
% 5.48/5.70 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_le_numeral
% 5.48/5.70 thf(fact_100_one__le__numeral,axiom,
% 5.48/5.70 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.48/5.70
% 5.48/5.70 % one_le_numeral
% 5.48/5.70 thf(fact_101_mult__numeral__1__right,axiom,
% 5.48/5.70 ! [A: complex] :
% 5.48/5.70 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.48/5.70 = A ) ).
% 5.48/5.70
% 5.48/5.70 % mult_numeral_1_right
% 5.48/5.70 thf(fact_102_mult__numeral__1__right,axiom,
% 5.48/5.70 ! [A: real] :
% 5.48/5.70 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.48/5.70 = A ) ).
% 5.48/5.70
% 5.48/5.70 % mult_numeral_1_right
% 5.48/5.70 thf(fact_103_mult__numeral__1__right,axiom,
% 5.48/5.70 ! [A: rat] :
% 5.48/5.70 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.48/5.70 = A ) ).
% 5.48/5.70
% 5.48/5.70 % mult_numeral_1_right
% 5.48/5.70 thf(fact_104_mult__numeral__1__right,axiom,
% 5.48/5.70 ! [A: nat] :
% 5.48/5.70 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.48/5.70 = A ) ).
% 5.48/5.70
% 5.48/5.70 % mult_numeral_1_right
% 5.48/5.71 thf(fact_105_mult__numeral__1__right,axiom,
% 5.48/5.71 ! [A: int] :
% 5.48/5.71 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult_numeral_1_right
% 5.48/5.71 thf(fact_106_mult__numeral__1,axiom,
% 5.48/5.71 ! [A: complex] :
% 5.48/5.71 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult_numeral_1
% 5.48/5.71 thf(fact_107_mult__numeral__1,axiom,
% 5.48/5.71 ! [A: real] :
% 5.48/5.71 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult_numeral_1
% 5.48/5.71 thf(fact_108_mult__numeral__1,axiom,
% 5.48/5.71 ! [A: rat] :
% 5.48/5.71 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult_numeral_1
% 5.48/5.71 thf(fact_109_mult__numeral__1,axiom,
% 5.48/5.71 ! [A: nat] :
% 5.48/5.71 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult_numeral_1
% 5.48/5.71 thf(fact_110_mult__numeral__1,axiom,
% 5.48/5.71 ! [A: int] :
% 5.48/5.71 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult_numeral_1
% 5.48/5.71 thf(fact_111_one__plus__numeral__commute,axiom,
% 5.48/5.71 ! [X2: num] :
% 5.48/5.71 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X2 ) )
% 5.48/5.71 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X2 ) @ one_one_complex ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_plus_numeral_commute
% 5.48/5.71 thf(fact_112_one__plus__numeral__commute,axiom,
% 5.48/5.71 ! [X2: num] :
% 5.48/5.71 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 5.48/5.71 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_plus_numeral_commute
% 5.48/5.71 thf(fact_113_one__plus__numeral__commute,axiom,
% 5.48/5.71 ! [X2: num] :
% 5.48/5.71 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.48/5.71 = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_plus_numeral_commute
% 5.48/5.71 thf(fact_114_one__plus__numeral__commute,axiom,
% 5.48/5.71 ! [X2: num] :
% 5.48/5.71 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.48/5.71 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_plus_numeral_commute
% 5.48/5.71 thf(fact_115_one__plus__numeral__commute,axiom,
% 5.48/5.71 ! [X2: num] :
% 5.48/5.71 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 5.48/5.71 = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_plus_numeral_commute
% 5.48/5.71 thf(fact_116_numeral__Bit0,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.48/5.71 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit0
% 5.48/5.71 thf(fact_117_numeral__Bit0,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.48/5.71 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit0
% 5.48/5.71 thf(fact_118_numeral__Bit0,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.48/5.71 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit0
% 5.48/5.71 thf(fact_119_numeral__Bit0,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.48/5.71 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit0
% 5.48/5.71 thf(fact_120_numeral__Bit0,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.48/5.71 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit0
% 5.48/5.71 thf(fact_121_numeral__One,axiom,
% 5.48/5.71 ( ( numera6690914467698888265omplex @ one )
% 5.48/5.71 = one_one_complex ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_One
% 5.48/5.71 thf(fact_122_numeral__One,axiom,
% 5.48/5.71 ( ( numeral_numeral_real @ one )
% 5.48/5.71 = one_one_real ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_One
% 5.48/5.71 thf(fact_123_numeral__One,axiom,
% 5.48/5.71 ( ( numeral_numeral_rat @ one )
% 5.48/5.71 = one_one_rat ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_One
% 5.48/5.71 thf(fact_124_numeral__One,axiom,
% 5.48/5.71 ( ( numeral_numeral_nat @ one )
% 5.48/5.71 = one_one_nat ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_One
% 5.48/5.71 thf(fact_125_numeral__One,axiom,
% 5.48/5.71 ( ( numeral_numeral_int @ one )
% 5.48/5.71 = one_one_int ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_One
% 5.48/5.71 thf(fact_126_num_Oexhaust,axiom,
% 5.48/5.71 ! [Y2: num] :
% 5.48/5.71 ( ( Y2 != one )
% 5.48/5.71 => ( ! [X22: num] :
% 5.48/5.71 ( Y2
% 5.48/5.71 != ( bit0 @ X22 ) )
% 5.48/5.71 => ~ ! [X3: num] :
% 5.48/5.71 ( Y2
% 5.48/5.71 != ( bit1 @ X3 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % num.exhaust
% 5.48/5.71 thf(fact_127_numerals_I1_J,axiom,
% 5.48/5.71 ( ( numeral_numeral_nat @ one )
% 5.48/5.71 = one_one_nat ) ).
% 5.48/5.71
% 5.48/5.71 % numerals(1)
% 5.48/5.71 thf(fact_128_numeral__Bit1,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.48/5.71 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit1
% 5.48/5.71 thf(fact_129_numeral__Bit1,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.48/5.71 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit1
% 5.48/5.71 thf(fact_130_numeral__Bit1,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.48/5.71 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit1
% 5.48/5.71 thf(fact_131_numeral__Bit1,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.48/5.71 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit1
% 5.48/5.71 thf(fact_132_numeral__Bit1,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.48/5.71 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit1
% 5.48/5.71 thf(fact_133_left__add__twice,axiom,
% 5.48/5.71 ! [A: complex,B: complex] :
% 5.48/5.71 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.48/5.71 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % left_add_twice
% 5.48/5.71 thf(fact_134_left__add__twice,axiom,
% 5.48/5.71 ! [A: real,B: real] :
% 5.48/5.71 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.48/5.71 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % left_add_twice
% 5.48/5.71 thf(fact_135_left__add__twice,axiom,
% 5.48/5.71 ! [A: rat,B: rat] :
% 5.48/5.71 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.48/5.71 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % left_add_twice
% 5.48/5.71 thf(fact_136_left__add__twice,axiom,
% 5.48/5.71 ! [A: nat,B: nat] :
% 5.48/5.71 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.48/5.71 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % left_add_twice
% 5.48/5.71 thf(fact_137_left__add__twice,axiom,
% 5.48/5.71 ! [A: int,B: int] :
% 5.48/5.71 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.48/5.71 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % left_add_twice
% 5.48/5.71 thf(fact_138_mem__Collect__eq,axiom,
% 5.48/5.71 ! [A: option_nat,P: option_nat > $o] :
% 5.48/5.71 ( ( member_option_nat @ A @ ( collect_option_nat @ P ) )
% 5.48/5.71 = ( P @ A ) ) ).
% 5.48/5.71
% 5.48/5.71 % mem_Collect_eq
% 5.48/5.71 thf(fact_139_mem__Collect__eq,axiom,
% 5.48/5.71 ! [A: real,P: real > $o] :
% 5.48/5.71 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.48/5.71 = ( P @ A ) ) ).
% 5.48/5.71
% 5.48/5.71 % mem_Collect_eq
% 5.48/5.71 thf(fact_140_mem__Collect__eq,axiom,
% 5.48/5.71 ! [A: list_nat,P: list_nat > $o] :
% 5.48/5.71 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 5.48/5.71 = ( P @ A ) ) ).
% 5.48/5.71
% 5.48/5.71 % mem_Collect_eq
% 5.48/5.71 thf(fact_141_mem__Collect__eq,axiom,
% 5.48/5.71 ! [A: set_nat_rat,P: set_nat_rat > $o] :
% 5.48/5.71 ( ( member_set_nat_rat @ A @ ( collect_set_nat_rat @ P ) )
% 5.48/5.71 = ( P @ A ) ) ).
% 5.48/5.71
% 5.48/5.71 % mem_Collect_eq
% 5.48/5.71 thf(fact_142_mem__Collect__eq,axiom,
% 5.48/5.71 ! [A: nat,P: nat > $o] :
% 5.48/5.71 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.48/5.71 = ( P @ A ) ) ).
% 5.48/5.71
% 5.48/5.71 % mem_Collect_eq
% 5.48/5.71 thf(fact_143_mem__Collect__eq,axiom,
% 5.48/5.71 ! [A: int,P: int > $o] :
% 5.48/5.71 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.48/5.71 = ( P @ A ) ) ).
% 5.48/5.71
% 5.48/5.71 % mem_Collect_eq
% 5.48/5.71 thf(fact_144_mem__Collect__eq,axiom,
% 5.48/5.71 ! [A: nat > rat,P: ( nat > rat ) > $o] :
% 5.48/5.71 ( ( member_nat_rat @ A @ ( collect_nat_rat @ P ) )
% 5.48/5.71 = ( P @ A ) ) ).
% 5.48/5.71
% 5.48/5.71 % mem_Collect_eq
% 5.48/5.71 thf(fact_145_Collect__mem__eq,axiom,
% 5.48/5.71 ! [A2: set_option_nat] :
% 5.48/5.71 ( ( collect_option_nat
% 5.48/5.71 @ ^ [X: option_nat] : ( member_option_nat @ X @ A2 ) )
% 5.48/5.71 = A2 ) ).
% 5.48/5.71
% 5.48/5.71 % Collect_mem_eq
% 5.48/5.71 thf(fact_146_Collect__mem__eq,axiom,
% 5.48/5.71 ! [A2: set_real] :
% 5.48/5.71 ( ( collect_real
% 5.48/5.71 @ ^ [X: real] : ( member_real @ X @ A2 ) )
% 5.48/5.71 = A2 ) ).
% 5.48/5.71
% 5.48/5.71 % Collect_mem_eq
% 5.48/5.71 thf(fact_147_Collect__mem__eq,axiom,
% 5.48/5.71 ! [A2: set_list_nat] :
% 5.48/5.71 ( ( collect_list_nat
% 5.48/5.71 @ ^ [X: list_nat] : ( member_list_nat @ X @ A2 ) )
% 5.48/5.71 = A2 ) ).
% 5.48/5.71
% 5.48/5.71 % Collect_mem_eq
% 5.48/5.71 thf(fact_148_Collect__mem__eq,axiom,
% 5.48/5.71 ! [A2: set_set_nat_rat] :
% 5.48/5.71 ( ( collect_set_nat_rat
% 5.48/5.71 @ ^ [X: set_nat_rat] : ( member_set_nat_rat @ X @ A2 ) )
% 5.48/5.71 = A2 ) ).
% 5.48/5.71
% 5.48/5.71 % Collect_mem_eq
% 5.48/5.71 thf(fact_149_Collect__mem__eq,axiom,
% 5.48/5.71 ! [A2: set_nat] :
% 5.48/5.71 ( ( collect_nat
% 5.48/5.71 @ ^ [X: nat] : ( member_nat @ X @ A2 ) )
% 5.48/5.71 = A2 ) ).
% 5.48/5.71
% 5.48/5.71 % Collect_mem_eq
% 5.48/5.71 thf(fact_150_Collect__mem__eq,axiom,
% 5.48/5.71 ! [A2: set_int] :
% 5.48/5.71 ( ( collect_int
% 5.48/5.71 @ ^ [X: int] : ( member_int @ X @ A2 ) )
% 5.48/5.71 = A2 ) ).
% 5.48/5.71
% 5.48/5.71 % Collect_mem_eq
% 5.48/5.71 thf(fact_151_Collect__mem__eq,axiom,
% 5.48/5.71 ! [A2: set_nat_rat] :
% 5.48/5.71 ( ( collect_nat_rat
% 5.48/5.71 @ ^ [X: nat > rat] : ( member_nat_rat @ X @ A2 ) )
% 5.48/5.71 = A2 ) ).
% 5.48/5.71
% 5.48/5.71 % Collect_mem_eq
% 5.48/5.71 thf(fact_152_Collect__cong,axiom,
% 5.48/5.71 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.48/5.71 ( ! [X4: list_nat] :
% 5.48/5.71 ( ( P @ X4 )
% 5.48/5.71 = ( Q @ X4 ) )
% 5.48/5.71 => ( ( collect_list_nat @ P )
% 5.48/5.71 = ( collect_list_nat @ Q ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % Collect_cong
% 5.48/5.71 thf(fact_153_Collect__cong,axiom,
% 5.48/5.71 ! [P: set_nat_rat > $o,Q: set_nat_rat > $o] :
% 5.48/5.71 ( ! [X4: set_nat_rat] :
% 5.48/5.71 ( ( P @ X4 )
% 5.48/5.71 = ( Q @ X4 ) )
% 5.48/5.71 => ( ( collect_set_nat_rat @ P )
% 5.48/5.71 = ( collect_set_nat_rat @ Q ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % Collect_cong
% 5.48/5.71 thf(fact_154_Collect__cong,axiom,
% 5.48/5.71 ! [P: nat > $o,Q: nat > $o] :
% 5.48/5.71 ( ! [X4: nat] :
% 5.48/5.71 ( ( P @ X4 )
% 5.48/5.71 = ( Q @ X4 ) )
% 5.48/5.71 => ( ( collect_nat @ P )
% 5.48/5.71 = ( collect_nat @ Q ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % Collect_cong
% 5.48/5.71 thf(fact_155_Collect__cong,axiom,
% 5.48/5.71 ! [P: int > $o,Q: int > $o] :
% 5.48/5.71 ( ! [X4: int] :
% 5.48/5.71 ( ( P @ X4 )
% 5.48/5.71 = ( Q @ X4 ) )
% 5.48/5.71 => ( ( collect_int @ P )
% 5.48/5.71 = ( collect_int @ Q ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % Collect_cong
% 5.48/5.71 thf(fact_156_Collect__cong,axiom,
% 5.48/5.71 ! [P: ( nat > rat ) > $o,Q: ( nat > rat ) > $o] :
% 5.48/5.71 ( ! [X4: nat > rat] :
% 5.48/5.71 ( ( P @ X4 )
% 5.48/5.71 = ( Q @ X4 ) )
% 5.48/5.71 => ( ( collect_nat_rat @ P )
% 5.48/5.71 = ( collect_nat_rat @ Q ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % Collect_cong
% 5.48/5.71 thf(fact_157_mult__2__right,axiom,
% 5.48/5.71 ! [Z: complex] :
% 5.48/5.71 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.48/5.71 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_2_right
% 5.48/5.71 thf(fact_158_mult__2__right,axiom,
% 5.48/5.71 ! [Z: real] :
% 5.48/5.71 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.48/5.71 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_2_right
% 5.48/5.71 thf(fact_159_mult__2__right,axiom,
% 5.48/5.71 ! [Z: rat] :
% 5.48/5.71 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.48/5.71 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_2_right
% 5.48/5.71 thf(fact_160_mult__2__right,axiom,
% 5.48/5.71 ! [Z: nat] :
% 5.48/5.71 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.71 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_2_right
% 5.48/5.71 thf(fact_161_mult__2__right,axiom,
% 5.48/5.71 ! [Z: int] :
% 5.48/5.71 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.48/5.71 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_2_right
% 5.48/5.71 thf(fact_162_mult__2,axiom,
% 5.48/5.71 ! [Z: complex] :
% 5.48/5.71 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.48/5.71 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_2
% 5.48/5.71 thf(fact_163_mult__2,axiom,
% 5.48/5.71 ! [Z: real] :
% 5.48/5.71 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.48/5.71 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_2
% 5.48/5.71 thf(fact_164_mult__2,axiom,
% 5.48/5.71 ! [Z: rat] :
% 5.48/5.71 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.48/5.71 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_2
% 5.48/5.71 thf(fact_165_mult__2,axiom,
% 5.48/5.71 ! [Z: nat] :
% 5.48/5.71 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.48/5.71 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_2
% 5.48/5.71 thf(fact_166_mult__2,axiom,
% 5.48/5.71 ! [Z: int] :
% 5.48/5.71 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.48/5.71 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_2
% 5.48/5.71 thf(fact_167_nat__1__add__1,axiom,
% 5.48/5.71 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.48/5.71 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % nat_1_add_1
% 5.48/5.71 thf(fact_168_add__self__div__2,axiom,
% 5.48/5.71 ! [M: nat] :
% 5.48/5.71 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.71 = M ) ).
% 5.48/5.71
% 5.48/5.71 % add_self_div_2
% 5.48/5.71 thf(fact_169_semiring__norm_I3_J,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 5.48/5.71 = ( bit1 @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(3)
% 5.48/5.71 thf(fact_170_semiring__norm_I4_J,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 5.48/5.71 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(4)
% 5.48/5.71 thf(fact_171_semiring__norm_I5_J,axiom,
% 5.48/5.71 ! [M: num] :
% 5.48/5.71 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.48/5.71 = ( bit1 @ M ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(5)
% 5.48/5.71 thf(fact_172_semiring__norm_I8_J,axiom,
% 5.48/5.71 ! [M: num] :
% 5.48/5.71 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.48/5.71 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(8)
% 5.48/5.71 thf(fact_173_semiring__norm_I10_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.48/5.71 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(10)
% 5.48/5.71 thf(fact_174_succ__list__to__short,axiom,
% 5.48/5.71 ! [Deg: nat,Mi: nat,X2: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.48/5.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.48/5.71 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.48/5.71 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.71 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.48/5.71 = none_nat ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % succ_list_to_short
% 5.48/5.71 thf(fact_175_semiring__norm_I70_J,axiom,
% 5.48/5.71 ! [M: num] :
% 5.48/5.71 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(70)
% 5.48/5.71 thf(fact_176_semiring__norm_I72_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.48/5.71 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(72)
% 5.48/5.71 thf(fact_177_semiring__norm_I69_J,axiom,
% 5.48/5.71 ! [M: num] :
% 5.48/5.71 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(69)
% 5.48/5.71 thf(fact_178_option_Ocollapse,axiom,
% 5.48/5.71 ! [Option: option4927543243414619207at_nat] :
% 5.48/5.71 ( ( Option != none_P5556105721700978146at_nat )
% 5.48/5.71 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 5.48/5.71 = Option ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.collapse
% 5.48/5.71 thf(fact_179_option_Ocollapse,axiom,
% 5.48/5.71 ! [Option: option_nat] :
% 5.48/5.71 ( ( Option != none_nat )
% 5.48/5.71 => ( ( some_nat @ ( the_nat @ Option ) )
% 5.48/5.71 = Option ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.collapse
% 5.48/5.71 thf(fact_180_option_Ocollapse,axiom,
% 5.48/5.71 ! [Option: option_num] :
% 5.48/5.71 ( ( Option != none_num )
% 5.48/5.71 => ( ( some_num @ ( the_num @ Option ) )
% 5.48/5.71 = Option ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.collapse
% 5.48/5.71 thf(fact_181_semiring__norm_I7_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.48/5.71 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(7)
% 5.48/5.71 thf(fact_182_semiring__norm_I87_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ( bit0 @ M )
% 5.48/5.71 = ( bit0 @ N ) )
% 5.48/5.71 = ( M = N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(87)
% 5.48/5.71 thf(fact_183_semiring__norm_I90_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ( bit1 @ M )
% 5.48/5.71 = ( bit1 @ N ) )
% 5.48/5.71 = ( M = N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(90)
% 5.48/5.71 thf(fact_184_option_Oinject,axiom,
% 5.48/5.71 ! [X23: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 5.48/5.71 ( ( ( some_P7363390416028606310at_nat @ X23 )
% 5.48/5.71 = ( some_P7363390416028606310at_nat @ Y22 ) )
% 5.48/5.71 = ( X23 = Y22 ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.inject
% 5.48/5.71 thf(fact_185_option_Oinject,axiom,
% 5.48/5.71 ! [X23: nat,Y22: nat] :
% 5.48/5.71 ( ( ( some_nat @ X23 )
% 5.48/5.71 = ( some_nat @ Y22 ) )
% 5.48/5.71 = ( X23 = Y22 ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.inject
% 5.48/5.71 thf(fact_186_option_Oinject,axiom,
% 5.48/5.71 ! [X23: num,Y22: num] :
% 5.48/5.71 ( ( ( some_num @ X23 )
% 5.48/5.71 = ( some_num @ Y22 ) )
% 5.48/5.71 = ( X23 = Y22 ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.inject
% 5.48/5.71 thf(fact_187_semiring__norm_I85_J,axiom,
% 5.48/5.71 ! [M: num] :
% 5.48/5.71 ( ( bit0 @ M )
% 5.48/5.71 != one ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(85)
% 5.48/5.71 thf(fact_188_semiring__norm_I83_J,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( one
% 5.48/5.71 != ( bit0 @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(83)
% 5.48/5.71 thf(fact_189_semiring__norm_I89_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( bit1 @ M )
% 5.48/5.71 != ( bit0 @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(89)
% 5.48/5.71 thf(fact_190_semiring__norm_I88_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( bit0 @ M )
% 5.48/5.71 != ( bit1 @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(88)
% 5.48/5.71 thf(fact_191_semiring__norm_I86_J,axiom,
% 5.48/5.71 ! [M: num] :
% 5.48/5.71 ( ( bit1 @ M )
% 5.48/5.71 != one ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(86)
% 5.48/5.71 thf(fact_192_semiring__norm_I84_J,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( one
% 5.48/5.71 != ( bit1 @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(84)
% 5.48/5.71 thf(fact_193_not__None__eq,axiom,
% 5.48/5.71 ! [X2: option4927543243414619207at_nat] :
% 5.48/5.71 ( ( X2 != none_P5556105721700978146at_nat )
% 5.48/5.71 = ( ? [Y: product_prod_nat_nat] :
% 5.48/5.71 ( X2
% 5.48/5.71 = ( some_P7363390416028606310at_nat @ Y ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % not_None_eq
% 5.48/5.71 thf(fact_194_not__None__eq,axiom,
% 5.48/5.71 ! [X2: option_nat] :
% 5.48/5.71 ( ( X2 != none_nat )
% 5.48/5.71 = ( ? [Y: nat] :
% 5.48/5.71 ( X2
% 5.48/5.71 = ( some_nat @ Y ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % not_None_eq
% 5.48/5.71 thf(fact_195_not__None__eq,axiom,
% 5.48/5.71 ! [X2: option_num] :
% 5.48/5.71 ( ( X2 != none_num )
% 5.48/5.71 = ( ? [Y: num] :
% 5.48/5.71 ( X2
% 5.48/5.71 = ( some_num @ Y ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % not_None_eq
% 5.48/5.71 thf(fact_196_not__Some__eq,axiom,
% 5.48/5.71 ! [X2: option4927543243414619207at_nat] :
% 5.48/5.71 ( ( ! [Y: product_prod_nat_nat] :
% 5.48/5.71 ( X2
% 5.48/5.71 != ( some_P7363390416028606310at_nat @ Y ) ) )
% 5.48/5.71 = ( X2 = none_P5556105721700978146at_nat ) ) ).
% 5.48/5.71
% 5.48/5.71 % not_Some_eq
% 5.48/5.71 thf(fact_197_not__Some__eq,axiom,
% 5.48/5.71 ! [X2: option_nat] :
% 5.48/5.71 ( ( ! [Y: nat] :
% 5.48/5.71 ( X2
% 5.48/5.71 != ( some_nat @ Y ) ) )
% 5.48/5.71 = ( X2 = none_nat ) ) ).
% 5.48/5.71
% 5.48/5.71 % not_Some_eq
% 5.48/5.71 thf(fact_198_not__Some__eq,axiom,
% 5.48/5.71 ! [X2: option_num] :
% 5.48/5.71 ( ( ! [Y: num] :
% 5.48/5.71 ( X2
% 5.48/5.71 != ( some_num @ Y ) ) )
% 5.48/5.71 = ( X2 = none_num ) ) ).
% 5.48/5.71
% 5.48/5.71 % not_Some_eq
% 5.48/5.71 thf(fact_199_semiring__norm_I6_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.48/5.71 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(6)
% 5.48/5.71 thf(fact_200_semiring__norm_I13_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.48/5.71 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(13)
% 5.48/5.71 thf(fact_201_semiring__norm_I12_J,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( times_times_num @ one @ N )
% 5.48/5.71 = N ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(12)
% 5.48/5.71 thf(fact_202_semiring__norm_I11_J,axiom,
% 5.48/5.71 ! [M: num] :
% 5.48/5.71 ( ( times_times_num @ M @ one )
% 5.48/5.71 = M ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(11)
% 5.48/5.71 thf(fact_203_semiring__norm_I71_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.48/5.71 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(71)
% 5.48/5.71 thf(fact_204_semiring__norm_I68_J,axiom,
% 5.48/5.71 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(68)
% 5.48/5.71 thf(fact_205_semiring__norm_I73_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.48/5.71 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(73)
% 5.48/5.71 thf(fact_206_lesseq__shift,axiom,
% 5.48/5.71 ( ord_less_eq_nat
% 5.48/5.71 = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % lesseq_shift
% 5.48/5.71 thf(fact_207_semiring__norm_I2_J,axiom,
% 5.48/5.71 ( ( plus_plus_num @ one @ one )
% 5.48/5.71 = ( bit0 @ one ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(2)
% 5.48/5.71 thf(fact_208_semiring__norm_I9_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.48/5.71 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(9)
% 5.48/5.71 thf(fact_209_num__double,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 5.48/5.71 = ( bit0 @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % num_double
% 5.48/5.71 thf(fact_210_semiring__norm_I15_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.48/5.71 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(15)
% 5.48/5.71 thf(fact_211_semiring__norm_I14_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.48/5.71 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(14)
% 5.48/5.71 thf(fact_212_semiring__norm_I16_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.48/5.71 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(16)
% 5.48/5.71 thf(fact_213_True,axiom,
% 5.48/5.71 ord_less_nat @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ).
% 5.48/5.71
% 5.48/5.71 % True
% 5.48/5.71 thf(fact_214_div__mult2__numeral__eq,axiom,
% 5.48/5.71 ! [A: nat,K: num,L: num] :
% 5.48/5.71 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 5.48/5.71 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % div_mult2_numeral_eq
% 5.48/5.71 thf(fact_215_div__mult2__numeral__eq,axiom,
% 5.48/5.71 ! [A: int,K: num,L: num] :
% 5.48/5.71 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 5.48/5.71 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % div_mult2_numeral_eq
% 5.48/5.71 thf(fact_216_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I3_J,axiom,
% 5.48/5.71 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.48/5.71 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.48/5.71 = one_one_nat ) ).
% 5.48/5.71
% 5.48/5.71 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(3)
% 5.48/5.71 thf(fact_217_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I2_J,axiom,
% 5.48/5.71 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.48/5.71 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.48/5.71 = one_one_nat ) ).
% 5.48/5.71
% 5.48/5.71 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(2)
% 5.48/5.71 thf(fact_218_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I2_J,axiom,
% 5.48/5.71 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.48/5.71 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.48/5.71 = one_one_nat ) ).
% 5.48/5.71
% 5.48/5.71 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(2)
% 5.48/5.71 thf(fact_219_option_Odistinct_I1_J,axiom,
% 5.48/5.71 ! [X23: product_prod_nat_nat] :
% 5.48/5.71 ( none_P5556105721700978146at_nat
% 5.48/5.71 != ( some_P7363390416028606310at_nat @ X23 ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.distinct(1)
% 5.48/5.71 thf(fact_220_option_Odistinct_I1_J,axiom,
% 5.48/5.71 ! [X23: nat] :
% 5.48/5.71 ( none_nat
% 5.48/5.71 != ( some_nat @ X23 ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.distinct(1)
% 5.48/5.71 thf(fact_221_option_Odistinct_I1_J,axiom,
% 5.48/5.71 ! [X23: num] :
% 5.48/5.71 ( none_num
% 5.48/5.71 != ( some_num @ X23 ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.distinct(1)
% 5.48/5.71 thf(fact_222_option_OdiscI,axiom,
% 5.48/5.71 ! [Option: option4927543243414619207at_nat,X23: product_prod_nat_nat] :
% 5.48/5.71 ( ( Option
% 5.48/5.71 = ( some_P7363390416028606310at_nat @ X23 ) )
% 5.48/5.71 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.discI
% 5.48/5.71 thf(fact_223_option_OdiscI,axiom,
% 5.48/5.71 ! [Option: option_nat,X23: nat] :
% 5.48/5.71 ( ( Option
% 5.48/5.71 = ( some_nat @ X23 ) )
% 5.48/5.71 => ( Option != none_nat ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.discI
% 5.48/5.71 thf(fact_224_option_OdiscI,axiom,
% 5.48/5.71 ! [Option: option_num,X23: num] :
% 5.48/5.71 ( ( Option
% 5.48/5.71 = ( some_num @ X23 ) )
% 5.48/5.71 => ( Option != none_num ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.discI
% 5.48/5.71 thf(fact_225_option_Oexhaust,axiom,
% 5.48/5.71 ! [Y2: option4927543243414619207at_nat] :
% 5.48/5.71 ( ( Y2 != none_P5556105721700978146at_nat )
% 5.48/5.71 => ~ ! [X22: product_prod_nat_nat] :
% 5.48/5.71 ( Y2
% 5.48/5.71 != ( some_P7363390416028606310at_nat @ X22 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.exhaust
% 5.48/5.71 thf(fact_226_option_Oexhaust,axiom,
% 5.48/5.71 ! [Y2: option_nat] :
% 5.48/5.71 ( ( Y2 != none_nat )
% 5.48/5.71 => ~ ! [X22: nat] :
% 5.48/5.71 ( Y2
% 5.48/5.71 != ( some_nat @ X22 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.exhaust
% 5.48/5.71 thf(fact_227_option_Oexhaust,axiom,
% 5.48/5.71 ! [Y2: option_num] :
% 5.48/5.71 ( ( Y2 != none_num )
% 5.48/5.71 => ~ ! [X22: num] :
% 5.48/5.71 ( Y2
% 5.48/5.71 != ( some_num @ X22 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.exhaust
% 5.48/5.71 thf(fact_228_split__option__ex,axiom,
% 5.48/5.71 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.48/5.71 ? [X5: option4927543243414619207at_nat] : ( P2 @ X5 ) )
% 5.48/5.71 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.48/5.71 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.48/5.71 | ? [X: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % split_option_ex
% 5.48/5.71 thf(fact_229_split__option__ex,axiom,
% 5.48/5.71 ( ( ^ [P2: option_nat > $o] :
% 5.48/5.71 ? [X5: option_nat] : ( P2 @ X5 ) )
% 5.48/5.71 = ( ^ [P3: option_nat > $o] :
% 5.48/5.71 ( ( P3 @ none_nat )
% 5.48/5.71 | ? [X: nat] : ( P3 @ ( some_nat @ X ) ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % split_option_ex
% 5.48/5.71 thf(fact_230_split__option__ex,axiom,
% 5.48/5.71 ( ( ^ [P2: option_num > $o] :
% 5.48/5.71 ? [X5: option_num] : ( P2 @ X5 ) )
% 5.48/5.71 = ( ^ [P3: option_num > $o] :
% 5.48/5.71 ( ( P3 @ none_num )
% 5.48/5.71 | ? [X: num] : ( P3 @ ( some_num @ X ) ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % split_option_ex
% 5.48/5.71 thf(fact_231_split__option__all,axiom,
% 5.48/5.71 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.48/5.71 ! [X5: option4927543243414619207at_nat] : ( P2 @ X5 ) )
% 5.48/5.71 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.48/5.71 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.48/5.71 & ! [X: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % split_option_all
% 5.48/5.71 thf(fact_232_split__option__all,axiom,
% 5.48/5.71 ( ( ^ [P2: option_nat > $o] :
% 5.48/5.71 ! [X5: option_nat] : ( P2 @ X5 ) )
% 5.48/5.71 = ( ^ [P3: option_nat > $o] :
% 5.48/5.71 ( ( P3 @ none_nat )
% 5.48/5.71 & ! [X: nat] : ( P3 @ ( some_nat @ X ) ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % split_option_all
% 5.48/5.71 thf(fact_233_split__option__all,axiom,
% 5.48/5.71 ( ( ^ [P2: option_num > $o] :
% 5.48/5.71 ! [X5: option_num] : ( P2 @ X5 ) )
% 5.48/5.71 = ( ^ [P3: option_num > $o] :
% 5.48/5.71 ( ( P3 @ none_num )
% 5.48/5.71 & ! [X: num] : ( P3 @ ( some_num @ X ) ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % split_option_all
% 5.48/5.71 thf(fact_234_combine__options__cases,axiom,
% 5.48/5.71 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 5.48/5.71 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ! [A3: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.48/5.71 ( ( X2
% 5.48/5.71 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.48/5.71 => ( ( Y2
% 5.48/5.71 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_options_cases
% 5.48/5.71 thf(fact_235_combine__options__cases,axiom,
% 5.48/5.71 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y2: option_nat] :
% 5.48/5.71 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ( ( Y2 = none_nat )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ! [A3: product_prod_nat_nat,B2: nat] :
% 5.48/5.71 ( ( X2
% 5.48/5.71 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.48/5.71 => ( ( Y2
% 5.48/5.71 = ( some_nat @ B2 ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_options_cases
% 5.48/5.71 thf(fact_236_combine__options__cases,axiom,
% 5.48/5.71 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y2: option_num] :
% 5.48/5.71 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ( ( Y2 = none_num )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ! [A3: product_prod_nat_nat,B2: num] :
% 5.48/5.71 ( ( X2
% 5.48/5.71 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.48/5.71 => ( ( Y2
% 5.48/5.71 = ( some_num @ B2 ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_options_cases
% 5.48/5.71 thf(fact_237_combine__options__cases,axiom,
% 5.48/5.71 ! [X2: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 5.48/5.71 ( ( ( X2 = none_nat )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ! [A3: nat,B2: product_prod_nat_nat] :
% 5.48/5.71 ( ( X2
% 5.48/5.71 = ( some_nat @ A3 ) )
% 5.48/5.71 => ( ( Y2
% 5.48/5.71 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_options_cases
% 5.48/5.71 thf(fact_238_combine__options__cases,axiom,
% 5.48/5.71 ! [X2: option_nat,P: option_nat > option_nat > $o,Y2: option_nat] :
% 5.48/5.71 ( ( ( X2 = none_nat )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ( ( Y2 = none_nat )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ! [A3: nat,B2: nat] :
% 5.48/5.71 ( ( X2
% 5.48/5.71 = ( some_nat @ A3 ) )
% 5.48/5.71 => ( ( Y2
% 5.48/5.71 = ( some_nat @ B2 ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_options_cases
% 5.48/5.71 thf(fact_239_combine__options__cases,axiom,
% 5.48/5.71 ! [X2: option_nat,P: option_nat > option_num > $o,Y2: option_num] :
% 5.48/5.71 ( ( ( X2 = none_nat )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ( ( Y2 = none_num )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ! [A3: nat,B2: num] :
% 5.48/5.71 ( ( X2
% 5.48/5.71 = ( some_nat @ A3 ) )
% 5.48/5.71 => ( ( Y2
% 5.48/5.71 = ( some_num @ B2 ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_options_cases
% 5.48/5.71 thf(fact_240_combine__options__cases,axiom,
% 5.48/5.71 ! [X2: option_num,P: option_num > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 5.48/5.71 ( ( ( X2 = none_num )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ! [A3: num,B2: product_prod_nat_nat] :
% 5.48/5.71 ( ( X2
% 5.48/5.71 = ( some_num @ A3 ) )
% 5.48/5.71 => ( ( Y2
% 5.48/5.71 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_options_cases
% 5.48/5.71 thf(fact_241_combine__options__cases,axiom,
% 5.48/5.71 ! [X2: option_num,P: option_num > option_nat > $o,Y2: option_nat] :
% 5.48/5.71 ( ( ( X2 = none_num )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ( ( Y2 = none_nat )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ! [A3: num,B2: nat] :
% 5.48/5.71 ( ( X2
% 5.48/5.71 = ( some_num @ A3 ) )
% 5.48/5.71 => ( ( Y2
% 5.48/5.71 = ( some_nat @ B2 ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_options_cases
% 5.48/5.71 thf(fact_242_combine__options__cases,axiom,
% 5.48/5.71 ! [X2: option_num,P: option_num > option_num > $o,Y2: option_num] :
% 5.48/5.71 ( ( ( X2 = none_num )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ( ( Y2 = none_num )
% 5.48/5.71 => ( P @ X2 @ Y2 ) )
% 5.48/5.71 => ( ! [A3: num,B2: num] :
% 5.48/5.71 ( ( X2
% 5.48/5.71 = ( some_num @ A3 ) )
% 5.48/5.71 => ( ( Y2
% 5.48/5.71 = ( some_num @ B2 ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) )
% 5.48/5.71 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_options_cases
% 5.48/5.71 thf(fact_243_div__le__mono,axiom,
% 5.48/5.71 ! [M: nat,N: nat,K: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.71 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % div_le_mono
% 5.48/5.71 thf(fact_244_div__le__dividend,axiom,
% 5.48/5.71 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 5.48/5.71
% 5.48/5.71 % div_le_dividend
% 5.48/5.71 thf(fact_245_left__add__mult__distrib,axiom,
% 5.48/5.71 ! [I: nat,U: nat,J: nat,K: nat] :
% 5.48/5.71 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 5.48/5.71 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 5.48/5.71
% 5.48/5.71 % left_add_mult_distrib
% 5.48/5.71 thf(fact_246_div__mult2__eq,axiom,
% 5.48/5.71 ! [M: nat,N: nat,Q2: nat] :
% 5.48/5.71 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.48/5.71 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 5.48/5.71
% 5.48/5.71 % div_mult2_eq
% 5.48/5.71 thf(fact_247_option_Osel,axiom,
% 5.48/5.71 ! [X23: product_prod_nat_nat] :
% 5.48/5.71 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X23 ) )
% 5.48/5.71 = X23 ) ).
% 5.48/5.71
% 5.48/5.71 % option.sel
% 5.48/5.71 thf(fact_248_option_Osel,axiom,
% 5.48/5.71 ! [X23: nat] :
% 5.48/5.71 ( ( the_nat @ ( some_nat @ X23 ) )
% 5.48/5.71 = X23 ) ).
% 5.48/5.71
% 5.48/5.71 % option.sel
% 5.48/5.71 thf(fact_249_option_Osel,axiom,
% 5.48/5.71 ! [X23: num] :
% 5.48/5.71 ( ( the_num @ ( some_num @ X23 ) )
% 5.48/5.71 = X23 ) ).
% 5.48/5.71
% 5.48/5.71 % option.sel
% 5.48/5.71 thf(fact_250_option_Oexpand,axiom,
% 5.48/5.71 ! [Option: option_nat,Option2: option_nat] :
% 5.48/5.71 ( ( ( Option = none_nat )
% 5.48/5.71 = ( Option2 = none_nat ) )
% 5.48/5.71 => ( ( ( Option != none_nat )
% 5.48/5.71 => ( ( Option2 != none_nat )
% 5.48/5.71 => ( ( the_nat @ Option )
% 5.48/5.71 = ( the_nat @ Option2 ) ) ) )
% 5.48/5.71 => ( Option = Option2 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.expand
% 5.48/5.71 thf(fact_251_option_Oexpand,axiom,
% 5.48/5.71 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 5.48/5.71 ( ( ( Option = none_P5556105721700978146at_nat )
% 5.48/5.71 = ( Option2 = none_P5556105721700978146at_nat ) )
% 5.48/5.71 => ( ( ( Option != none_P5556105721700978146at_nat )
% 5.48/5.71 => ( ( Option2 != none_P5556105721700978146at_nat )
% 5.48/5.71 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 5.48/5.71 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 5.48/5.71 => ( Option = Option2 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.expand
% 5.48/5.71 thf(fact_252_option_Oexpand,axiom,
% 5.48/5.71 ! [Option: option_num,Option2: option_num] :
% 5.48/5.71 ( ( ( Option = none_num )
% 5.48/5.71 = ( Option2 = none_num ) )
% 5.48/5.71 => ( ( ( Option != none_num )
% 5.48/5.71 => ( ( Option2 != none_num )
% 5.48/5.71 => ( ( the_num @ Option )
% 5.48/5.71 = ( the_num @ Option2 ) ) ) )
% 5.48/5.71 => ( Option = Option2 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.expand
% 5.48/5.71 thf(fact_253_div__times__less__eq__dividend,axiom,
% 5.48/5.71 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 5.48/5.71
% 5.48/5.71 % div_times_less_eq_dividend
% 5.48/5.71 thf(fact_254_times__div__less__eq__dividend,axiom,
% 5.48/5.71 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 5.48/5.71
% 5.48/5.71 % times_div_less_eq_dividend
% 5.48/5.71 thf(fact_255_option_Oexhaust__sel,axiom,
% 5.48/5.71 ! [Option: option4927543243414619207at_nat] :
% 5.48/5.71 ( ( Option != none_P5556105721700978146at_nat )
% 5.48/5.71 => ( Option
% 5.48/5.71 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.exhaust_sel
% 5.48/5.71 thf(fact_256_option_Oexhaust__sel,axiom,
% 5.48/5.71 ! [Option: option_nat] :
% 5.48/5.71 ( ( Option != none_nat )
% 5.48/5.71 => ( Option
% 5.48/5.71 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.exhaust_sel
% 5.48/5.71 thf(fact_257_option_Oexhaust__sel,axiom,
% 5.48/5.71 ! [Option: option_num] :
% 5.48/5.71 ( ( Option != none_num )
% 5.48/5.71 => ( Option
% 5.48/5.71 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % option.exhaust_sel
% 5.48/5.71 thf(fact_258_numeral__Bit0__div__2,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.71 = ( numeral_numeral_nat @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit0_div_2
% 5.48/5.71 thf(fact_259_numeral__Bit0__div__2,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.48/5.71 = ( numeral_numeral_int @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit0_div_2
% 5.48/5.71 thf(fact_260_numeral__Bit1__div__2,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.71 = ( numeral_numeral_nat @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit1_div_2
% 5.48/5.71 thf(fact_261_numeral__Bit1__div__2,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.48/5.71 = ( numeral_numeral_int @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_Bit1_div_2
% 5.48/5.71 thf(fact_262_pred__list__to__short,axiom,
% 5.48/5.71 ! [Deg: nat,X2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.48/5.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.48/5.71 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.48/5.71 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.71 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.48/5.71 = none_nat ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % pred_list_to_short
% 5.48/5.71 thf(fact_263_succ__min,axiom,
% 5.48/5.71 ! [Deg: nat,X2: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.48/5.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.48/5.71 => ( ( ord_less_nat @ X2 @ Mi )
% 5.48/5.71 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.48/5.71 = ( some_nat @ Mi ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % succ_min
% 5.48/5.71 thf(fact_264_nat__1__eq__mult__iff,axiom,
% 5.48/5.71 ! [M: nat,N: nat] :
% 5.48/5.71 ( ( one_one_nat
% 5.48/5.71 = ( times_times_nat @ M @ N ) )
% 5.48/5.71 = ( ( M = one_one_nat )
% 5.48/5.71 & ( N = one_one_nat ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % nat_1_eq_mult_iff
% 5.48/5.71 thf(fact_265_nat__mult__eq__1__iff,axiom,
% 5.48/5.71 ! [M: nat,N: nat] :
% 5.48/5.71 ( ( ( times_times_nat @ M @ N )
% 5.48/5.71 = one_one_nat )
% 5.48/5.71 = ( ( M = one_one_nat )
% 5.48/5.71 & ( N = one_one_nat ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % nat_mult_eq_1_iff
% 5.48/5.71 thf(fact_266_nat__add__left__cancel__le,axiom,
% 5.48/5.71 ! [K: nat,M: nat,N: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.48/5.71 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % nat_add_left_cancel_le
% 5.48/5.71 thf(fact_267_enat__ord__number_I1_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.48/5.71 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % enat_ord_number(1)
% 5.48/5.71 thf(fact_268_zdiv__numeral__Bit1,axiom,
% 5.48/5.71 ! [V: num,W: num] :
% 5.48/5.71 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.48/5.71 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % zdiv_numeral_Bit1
% 5.48/5.71 thf(fact_269_div__by__1,axiom,
% 5.48/5.71 ! [A: complex] :
% 5.48/5.71 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % div_by_1
% 5.48/5.71 thf(fact_270_div__by__1,axiom,
% 5.48/5.71 ! [A: real] :
% 5.48/5.71 ( ( divide_divide_real @ A @ one_one_real )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % div_by_1
% 5.48/5.71 thf(fact_271_div__by__1,axiom,
% 5.48/5.71 ! [A: rat] :
% 5.48/5.71 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % div_by_1
% 5.48/5.71 thf(fact_272_div__by__1,axiom,
% 5.48/5.71 ! [A: nat] :
% 5.48/5.71 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % div_by_1
% 5.48/5.71 thf(fact_273_div__by__1,axiom,
% 5.48/5.71 ! [A: int] :
% 5.48/5.71 ( ( divide_divide_int @ A @ one_one_int )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % div_by_1
% 5.48/5.71 thf(fact_274_bits__div__by__1,axiom,
% 5.48/5.71 ! [A: nat] :
% 5.48/5.71 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % bits_div_by_1
% 5.48/5.71 thf(fact_275_bits__div__by__1,axiom,
% 5.48/5.71 ! [A: int] :
% 5.48/5.71 ( ( divide_divide_int @ A @ one_one_int )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % bits_div_by_1
% 5.48/5.71 thf(fact_276_times__divide__eq__left,axiom,
% 5.48/5.71 ! [B: complex,C: complex,A: complex] :
% 5.48/5.71 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.48/5.71 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.48/5.71
% 5.48/5.71 % times_divide_eq_left
% 5.48/5.71 thf(fact_277_times__divide__eq__left,axiom,
% 5.48/5.71 ! [B: real,C: real,A: real] :
% 5.48/5.71 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.48/5.71 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.48/5.71
% 5.48/5.71 % times_divide_eq_left
% 5.48/5.71 thf(fact_278_times__divide__eq__left,axiom,
% 5.48/5.71 ! [B: rat,C: rat,A: rat] :
% 5.48/5.71 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.48/5.71 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 5.48/5.71
% 5.48/5.71 % times_divide_eq_left
% 5.48/5.71 thf(fact_279_divide__divide__eq__left,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.48/5.71 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_divide_eq_left
% 5.48/5.71 thf(fact_280_divide__divide__eq__left,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.48/5.71 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_divide_eq_left
% 5.48/5.71 thf(fact_281_divide__divide__eq__left,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.48/5.71 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_divide_eq_left
% 5.48/5.71 thf(fact_282_divide__divide__eq__right,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.48/5.71 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_divide_eq_right
% 5.48/5.71 thf(fact_283_divide__divide__eq__right,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.48/5.71 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_divide_eq_right
% 5.48/5.71 thf(fact_284_divide__divide__eq__right,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.48/5.71 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_divide_eq_right
% 5.48/5.71 thf(fact_285_numeral__less__iff,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.48/5.71 = ( ord_less_num @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_less_iff
% 5.48/5.71 thf(fact_286_numeral__less__iff,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.48/5.71 = ( ord_less_num @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_less_iff
% 5.48/5.71 thf(fact_287_numeral__less__iff,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.48/5.71 = ( ord_less_num @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_less_iff
% 5.48/5.71 thf(fact_288_numeral__less__iff,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.48/5.71 = ( ord_less_num @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % numeral_less_iff
% 5.48/5.71 thf(fact_289_times__divide__eq__right,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.48/5.71 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.48/5.71
% 5.48/5.71 % times_divide_eq_right
% 5.48/5.71 thf(fact_290_times__divide__eq__right,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.48/5.71 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.48/5.71
% 5.48/5.71 % times_divide_eq_right
% 5.48/5.71 thf(fact_291_times__divide__eq__right,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.48/5.71 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 5.48/5.71
% 5.48/5.71 % times_divide_eq_right
% 5.48/5.71 thf(fact_292_nat__add__left__cancel__less,axiom,
% 5.48/5.71 ! [K: nat,M: nat,N: nat] :
% 5.48/5.71 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.48/5.71 = ( ord_less_nat @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % nat_add_left_cancel_less
% 5.48/5.71 thf(fact_293_pred__max,axiom,
% 5.48/5.71 ! [Deg: nat,Ma: nat,X2: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.48/5.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.48/5.71 => ( ( ord_less_nat @ Ma @ X2 )
% 5.48/5.71 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.48/5.71 = ( some_nat @ Ma ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % pred_max
% 5.48/5.71 thf(fact_294_zdiv__numeral__Bit0,axiom,
% 5.48/5.71 ! [V: num,W: num] :
% 5.48/5.71 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.48/5.71 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % zdiv_numeral_Bit0
% 5.48/5.71 thf(fact_295_one__less__numeral__iff,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.48/5.71 = ( ord_less_num @ one @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_less_numeral_iff
% 5.48/5.71 thf(fact_296_one__less__numeral__iff,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.48/5.71 = ( ord_less_num @ one @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_less_numeral_iff
% 5.48/5.71 thf(fact_297_one__less__numeral__iff,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.48/5.71 = ( ord_less_num @ one @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_less_numeral_iff
% 5.48/5.71 thf(fact_298_one__less__numeral__iff,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.48/5.71 = ( ord_less_num @ one @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_less_numeral_iff
% 5.48/5.71 thf(fact_299_less__divide__eq__numeral1_I1_J,axiom,
% 5.48/5.71 ! [A: real,B: real,W: num] :
% 5.48/5.71 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.48/5.71 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_divide_eq_numeral1(1)
% 5.48/5.71 thf(fact_300_less__divide__eq__numeral1_I1_J,axiom,
% 5.48/5.71 ! [A: rat,B: rat,W: num] :
% 5.48/5.71 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.48/5.71 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_divide_eq_numeral1(1)
% 5.48/5.71 thf(fact_301_divide__less__eq__numeral1_I1_J,axiom,
% 5.48/5.71 ! [B: real,W: num,A: real] :
% 5.48/5.71 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.48/5.71 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_less_eq_numeral1(1)
% 5.48/5.71 thf(fact_302_divide__less__eq__numeral1_I1_J,axiom,
% 5.48/5.71 ! [B: rat,W: num,A: rat] :
% 5.48/5.71 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.48/5.71 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_less_eq_numeral1(1)
% 5.48/5.71 thf(fact_303__C5_Ohyps_C_I8_J,axiom,
% 5.48/5.71 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.48/5.71
% 5.48/5.71 % "5.hyps"(8)
% 5.48/5.71 thf(fact_304_linordered__field__no__lb,axiom,
% 5.48/5.71 ! [X6: real] :
% 5.48/5.71 ? [Y3: real] : ( ord_less_real @ Y3 @ X6 ) ).
% 5.48/5.71
% 5.48/5.71 % linordered_field_no_lb
% 5.48/5.71 thf(fact_305_linordered__field__no__lb,axiom,
% 5.48/5.71 ! [X6: rat] :
% 5.48/5.71 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X6 ) ).
% 5.48/5.71
% 5.48/5.71 % linordered_field_no_lb
% 5.48/5.71 thf(fact_306_linordered__field__no__ub,axiom,
% 5.48/5.71 ! [X6: real] :
% 5.48/5.71 ? [X_1: real] : ( ord_less_real @ X6 @ X_1 ) ).
% 5.48/5.71
% 5.48/5.71 % linordered_field_no_ub
% 5.48/5.71 thf(fact_307_linordered__field__no__ub,axiom,
% 5.48/5.71 ! [X6: rat] :
% 5.48/5.71 ? [X_1: rat] : ( ord_less_rat @ X6 @ X_1 ) ).
% 5.48/5.71
% 5.48/5.71 % linordered_field_no_ub
% 5.48/5.71 thf(fact_308_linorder__neqE__linordered__idom,axiom,
% 5.48/5.71 ! [X2: real,Y2: real] :
% 5.48/5.71 ( ( X2 != Y2 )
% 5.48/5.71 => ( ~ ( ord_less_real @ X2 @ Y2 )
% 5.48/5.71 => ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % linorder_neqE_linordered_idom
% 5.48/5.71 thf(fact_309_linorder__neqE__linordered__idom,axiom,
% 5.48/5.71 ! [X2: rat,Y2: rat] :
% 5.48/5.71 ( ( X2 != Y2 )
% 5.48/5.71 => ( ~ ( ord_less_rat @ X2 @ Y2 )
% 5.48/5.71 => ( ord_less_rat @ Y2 @ X2 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % linorder_neqE_linordered_idom
% 5.48/5.71 thf(fact_310_linorder__neqE__linordered__idom,axiom,
% 5.48/5.71 ! [X2: int,Y2: int] :
% 5.48/5.71 ( ( X2 != Y2 )
% 5.48/5.71 => ( ~ ( ord_less_int @ X2 @ Y2 )
% 5.48/5.71 => ( ord_less_int @ Y2 @ X2 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % linorder_neqE_linordered_idom
% 5.48/5.71 thf(fact_311_nat__neq__iff,axiom,
% 5.48/5.71 ! [M: nat,N: nat] :
% 5.48/5.71 ( ( M != N )
% 5.48/5.71 = ( ( ord_less_nat @ M @ N )
% 5.48/5.71 | ( ord_less_nat @ N @ M ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % nat_neq_iff
% 5.48/5.71 thf(fact_312_less__not__refl,axiom,
% 5.48/5.71 ! [N: nat] :
% 5.48/5.71 ~ ( ord_less_nat @ N @ N ) ).
% 5.48/5.71
% 5.48/5.71 % less_not_refl
% 5.48/5.71 thf(fact_313_less__not__refl2,axiom,
% 5.48/5.71 ! [N: nat,M: nat] :
% 5.48/5.71 ( ( ord_less_nat @ N @ M )
% 5.48/5.71 => ( M != N ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_not_refl2
% 5.48/5.71 thf(fact_314_less__not__refl3,axiom,
% 5.48/5.71 ! [S: nat,T: nat] :
% 5.48/5.71 ( ( ord_less_nat @ S @ T )
% 5.48/5.71 => ( S != T ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_not_refl3
% 5.48/5.71 thf(fact_315_less__irrefl__nat,axiom,
% 5.48/5.71 ! [N: nat] :
% 5.48/5.71 ~ ( ord_less_nat @ N @ N ) ).
% 5.48/5.71
% 5.48/5.71 % less_irrefl_nat
% 5.48/5.71 thf(fact_316_nat__less__induct,axiom,
% 5.48/5.71 ! [P: nat > $o,N: nat] :
% 5.48/5.71 ( ! [N2: nat] :
% 5.48/5.71 ( ! [M2: nat] :
% 5.48/5.71 ( ( ord_less_nat @ M2 @ N2 )
% 5.48/5.71 => ( P @ M2 ) )
% 5.48/5.71 => ( P @ N2 ) )
% 5.48/5.71 => ( P @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % nat_less_induct
% 5.48/5.71 thf(fact_317_infinite__descent,axiom,
% 5.48/5.71 ! [P: nat > $o,N: nat] :
% 5.48/5.71 ( ! [N2: nat] :
% 5.48/5.71 ( ~ ( P @ N2 )
% 5.48/5.71 => ? [M2: nat] :
% 5.48/5.71 ( ( ord_less_nat @ M2 @ N2 )
% 5.48/5.71 & ~ ( P @ M2 ) ) )
% 5.48/5.71 => ( P @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % infinite_descent
% 5.48/5.71 thf(fact_318_linorder__neqE__nat,axiom,
% 5.48/5.71 ! [X2: nat,Y2: nat] :
% 5.48/5.71 ( ( X2 != Y2 )
% 5.48/5.71 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 5.48/5.71 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % linorder_neqE_nat
% 5.48/5.71 thf(fact_319_less__mono__imp__le__mono,axiom,
% 5.48/5.71 ! [F: nat > nat,I: nat,J: nat] :
% 5.48/5.71 ( ! [I2: nat,J2: nat] :
% 5.48/5.71 ( ( ord_less_nat @ I2 @ J2 )
% 5.48/5.71 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 5.48/5.71 => ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.71 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_mono_imp_le_mono
% 5.48/5.71 thf(fact_320_le__neq__implies__less,axiom,
% 5.48/5.71 ! [M: nat,N: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.71 => ( ( M != N )
% 5.48/5.71 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % le_neq_implies_less
% 5.48/5.71 thf(fact_321_less__or__eq__imp__le,axiom,
% 5.48/5.71 ! [M: nat,N: nat] :
% 5.48/5.71 ( ( ( ord_less_nat @ M @ N )
% 5.48/5.71 | ( M = N ) )
% 5.48/5.71 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_or_eq_imp_le
% 5.48/5.71 thf(fact_322_le__eq__less__or__eq,axiom,
% 5.48/5.71 ( ord_less_eq_nat
% 5.48/5.71 = ( ^ [M3: nat,N3: nat] :
% 5.48/5.71 ( ( ord_less_nat @ M3 @ N3 )
% 5.48/5.71 | ( M3 = N3 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % le_eq_less_or_eq
% 5.48/5.71 thf(fact_323_less__imp__le__nat,axiom,
% 5.48/5.71 ! [M: nat,N: nat] :
% 5.48/5.71 ( ( ord_less_nat @ M @ N )
% 5.48/5.71 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_imp_le_nat
% 5.48/5.71 thf(fact_324_nat__less__le,axiom,
% 5.48/5.71 ( ord_less_nat
% 5.48/5.71 = ( ^ [M3: nat,N3: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.48/5.71 & ( M3 != N3 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % nat_less_le
% 5.48/5.71 thf(fact_325_less__add__eq__less,axiom,
% 5.48/5.71 ! [K: nat,L: nat,M: nat,N: nat] :
% 5.48/5.71 ( ( ord_less_nat @ K @ L )
% 5.48/5.71 => ( ( ( plus_plus_nat @ M @ L )
% 5.48/5.71 = ( plus_plus_nat @ K @ N ) )
% 5.48/5.71 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_add_eq_less
% 5.48/5.71 thf(fact_326_trans__less__add2,axiom,
% 5.48/5.71 ! [I: nat,J: nat,M: nat] :
% 5.48/5.71 ( ( ord_less_nat @ I @ J )
% 5.48/5.71 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % trans_less_add2
% 5.48/5.71 thf(fact_327_trans__less__add1,axiom,
% 5.48/5.71 ! [I: nat,J: nat,M: nat] :
% 5.48/5.71 ( ( ord_less_nat @ I @ J )
% 5.48/5.71 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % trans_less_add1
% 5.48/5.71 thf(fact_328_add__less__mono1,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat] :
% 5.48/5.71 ( ( ord_less_nat @ I @ J )
% 5.48/5.71 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_less_mono1
% 5.48/5.71 thf(fact_329_not__add__less2,axiom,
% 5.48/5.71 ! [J: nat,I: nat] :
% 5.48/5.71 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 5.48/5.71
% 5.48/5.71 % not_add_less2
% 5.48/5.71 thf(fact_330_not__add__less1,axiom,
% 5.48/5.71 ! [I: nat,J: nat] :
% 5.48/5.71 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 5.48/5.71
% 5.48/5.71 % not_add_less1
% 5.48/5.71 thf(fact_331_add__less__mono,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.48/5.71 ( ( ord_less_nat @ I @ J )
% 5.48/5.71 => ( ( ord_less_nat @ K @ L )
% 5.48/5.71 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_less_mono
% 5.48/5.71 thf(fact_332_add__lessD1,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat] :
% 5.48/5.71 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.48/5.71 => ( ord_less_nat @ I @ K ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_lessD1
% 5.48/5.71 thf(fact_333_less__numeral__extra_I4_J,axiom,
% 5.48/5.71 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.48/5.71
% 5.48/5.71 % less_numeral_extra(4)
% 5.48/5.71 thf(fact_334_less__numeral__extra_I4_J,axiom,
% 5.48/5.71 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.48/5.71
% 5.48/5.71 % less_numeral_extra(4)
% 5.48/5.71 thf(fact_335_less__numeral__extra_I4_J,axiom,
% 5.48/5.71 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.48/5.71
% 5.48/5.71 % less_numeral_extra(4)
% 5.48/5.71 thf(fact_336_less__numeral__extra_I4_J,axiom,
% 5.48/5.71 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.48/5.71
% 5.48/5.71 % less_numeral_extra(4)
% 5.48/5.71 thf(fact_337_less__1__mult,axiom,
% 5.48/5.71 ! [M: real,N: real] :
% 5.48/5.71 ( ( ord_less_real @ one_one_real @ M )
% 5.48/5.71 => ( ( ord_less_real @ one_one_real @ N )
% 5.48/5.71 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_1_mult
% 5.48/5.71 thf(fact_338_less__1__mult,axiom,
% 5.48/5.71 ! [M: rat,N: rat] :
% 5.48/5.71 ( ( ord_less_rat @ one_one_rat @ M )
% 5.48/5.71 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.48/5.71 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_1_mult
% 5.48/5.71 thf(fact_339_less__1__mult,axiom,
% 5.48/5.71 ! [M: nat,N: nat] :
% 5.48/5.71 ( ( ord_less_nat @ one_one_nat @ M )
% 5.48/5.71 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.48/5.71 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_1_mult
% 5.48/5.71 thf(fact_340_less__1__mult,axiom,
% 5.48/5.71 ! [M: int,N: int] :
% 5.48/5.71 ( ( ord_less_int @ one_one_int @ M )
% 5.48/5.71 => ( ( ord_less_int @ one_one_int @ N )
% 5.48/5.71 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_1_mult
% 5.48/5.71 thf(fact_341_add__mono1,axiom,
% 5.48/5.71 ! [A: real,B: real] :
% 5.48/5.71 ( ( ord_less_real @ A @ B )
% 5.48/5.71 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono1
% 5.48/5.71 thf(fact_342_add__mono1,axiom,
% 5.48/5.71 ! [A: rat,B: rat] :
% 5.48/5.71 ( ( ord_less_rat @ A @ B )
% 5.48/5.71 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono1
% 5.48/5.71 thf(fact_343_add__mono1,axiom,
% 5.48/5.71 ! [A: nat,B: nat] :
% 5.48/5.71 ( ( ord_less_nat @ A @ B )
% 5.48/5.71 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono1
% 5.48/5.71 thf(fact_344_add__mono1,axiom,
% 5.48/5.71 ! [A: int,B: int] :
% 5.48/5.71 ( ( ord_less_int @ A @ B )
% 5.48/5.71 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono1
% 5.48/5.71 thf(fact_345_less__add__one,axiom,
% 5.48/5.71 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_add_one
% 5.48/5.71 thf(fact_346_less__add__one,axiom,
% 5.48/5.71 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_add_one
% 5.48/5.71 thf(fact_347_less__add__one,axiom,
% 5.48/5.71 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_add_one
% 5.48/5.71 thf(fact_348_less__add__one,axiom,
% 5.48/5.71 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_add_one
% 5.48/5.71 thf(fact_349_mono__nat__linear__lb,axiom,
% 5.48/5.71 ! [F: nat > nat,M: nat,K: nat] :
% 5.48/5.71 ( ! [M4: nat,N2: nat] :
% 5.48/5.71 ( ( ord_less_nat @ M4 @ N2 )
% 5.48/5.71 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N2 ) ) )
% 5.48/5.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mono_nat_linear_lb
% 5.48/5.71 thf(fact_350_discrete,axiom,
% 5.48/5.71 ( ord_less_nat
% 5.48/5.71 = ( ^ [A4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A4 @ one_one_nat ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % discrete
% 5.48/5.71 thf(fact_351_discrete,axiom,
% 5.48/5.71 ( ord_less_int
% 5.48/5.71 = ( ^ [A4: int] : ( ord_less_eq_int @ ( plus_plus_int @ A4 @ one_one_int ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % discrete
% 5.48/5.71 thf(fact_352_less__half__sum,axiom,
% 5.48/5.71 ! [A: real,B: real] :
% 5.48/5.71 ( ( ord_less_real @ A @ B )
% 5.48/5.71 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_half_sum
% 5.48/5.71 thf(fact_353_less__half__sum,axiom,
% 5.48/5.71 ! [A: rat,B: rat] :
% 5.48/5.71 ( ( ord_less_rat @ A @ B )
% 5.48/5.71 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_half_sum
% 5.48/5.71 thf(fact_354_gt__half__sum,axiom,
% 5.48/5.71 ! [A: real,B: real] :
% 5.48/5.71 ( ( ord_less_real @ A @ B )
% 5.48/5.71 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % gt_half_sum
% 5.48/5.71 thf(fact_355_gt__half__sum,axiom,
% 5.48/5.71 ! [A: rat,B: rat] :
% 5.48/5.71 ( ( ord_less_rat @ A @ B )
% 5.48/5.71 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % gt_half_sum
% 5.48/5.71 thf(fact_356_not__numeral__less__one,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.48/5.71
% 5.48/5.71 % not_numeral_less_one
% 5.48/5.71 thf(fact_357_not__numeral__less__one,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.48/5.71
% 5.48/5.71 % not_numeral_less_one
% 5.48/5.71 thf(fact_358_not__numeral__less__one,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.48/5.71
% 5.48/5.71 % not_numeral_less_one
% 5.48/5.71 thf(fact_359_not__numeral__less__one,axiom,
% 5.48/5.71 ! [N: num] :
% 5.48/5.71 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.48/5.71
% 5.48/5.71 % not_numeral_less_one
% 5.48/5.71 thf(fact_360_less__mult__imp__div__less,axiom,
% 5.48/5.71 ! [M: nat,I: nat,N: nat] :
% 5.48/5.71 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 5.48/5.71 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_mult_imp_div_less
% 5.48/5.71 thf(fact_361_Nat_Oex__has__greatest__nat,axiom,
% 5.48/5.71 ! [P: nat > $o,K: nat,B: nat] :
% 5.48/5.71 ( ( P @ K )
% 5.48/5.71 => ( ! [Y3: nat] :
% 5.48/5.71 ( ( P @ Y3 )
% 5.48/5.71 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.48/5.71 => ? [X4: nat] :
% 5.48/5.71 ( ( P @ X4 )
% 5.48/5.71 & ! [Y4: nat] :
% 5.48/5.71 ( ( P @ Y4 )
% 5.48/5.71 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % Nat.ex_has_greatest_nat
% 5.48/5.71 thf(fact_362_nat__le__linear,axiom,
% 5.48/5.71 ! [M: nat,N: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.71 | ( ord_less_eq_nat @ N @ M ) ) ).
% 5.48/5.71
% 5.48/5.71 % nat_le_linear
% 5.48/5.71 thf(fact_363_le__antisym,axiom,
% 5.48/5.71 ! [M: nat,N: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.71 => ( ( ord_less_eq_nat @ N @ M )
% 5.48/5.71 => ( M = N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % le_antisym
% 5.48/5.71 thf(fact_364_eq__imp__le,axiom,
% 5.48/5.71 ! [M: nat,N: nat] :
% 5.48/5.71 ( ( M = N )
% 5.48/5.71 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % eq_imp_le
% 5.48/5.71 thf(fact_365_le__trans,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.71 => ( ( ord_less_eq_nat @ J @ K )
% 5.48/5.71 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % le_trans
% 5.48/5.71 thf(fact_366_le__refl,axiom,
% 5.48/5.71 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.48/5.71
% 5.48/5.71 % le_refl
% 5.48/5.71 thf(fact_367_size__neq__size__imp__neq,axiom,
% 5.48/5.71 ! [X2: list_VEBT_VEBT,Y2: list_VEBT_VEBT] :
% 5.48/5.71 ( ( ( size_s6755466524823107622T_VEBT @ X2 )
% 5.48/5.71 != ( size_s6755466524823107622T_VEBT @ Y2 ) )
% 5.48/5.71 => ( X2 != Y2 ) ) ).
% 5.48/5.71
% 5.48/5.71 % size_neq_size_imp_neq
% 5.48/5.71 thf(fact_368_size__neq__size__imp__neq,axiom,
% 5.48/5.71 ! [X2: num,Y2: num] :
% 5.48/5.71 ( ( ( size_size_num @ X2 )
% 5.48/5.71 != ( size_size_num @ Y2 ) )
% 5.48/5.71 => ( X2 != Y2 ) ) ).
% 5.48/5.71
% 5.48/5.71 % size_neq_size_imp_neq
% 5.48/5.71 thf(fact_369_size__neq__size__imp__neq,axiom,
% 5.48/5.71 ! [X2: list_o,Y2: list_o] :
% 5.48/5.71 ( ( ( size_size_list_o @ X2 )
% 5.48/5.71 != ( size_size_list_o @ Y2 ) )
% 5.48/5.71 => ( X2 != Y2 ) ) ).
% 5.48/5.71
% 5.48/5.71 % size_neq_size_imp_neq
% 5.48/5.71 thf(fact_370_size__neq__size__imp__neq,axiom,
% 5.48/5.71 ! [X2: list_nat,Y2: list_nat] :
% 5.48/5.71 ( ( ( size_size_list_nat @ X2 )
% 5.48/5.71 != ( size_size_list_nat @ Y2 ) )
% 5.48/5.71 => ( X2 != Y2 ) ) ).
% 5.48/5.71
% 5.48/5.71 % size_neq_size_imp_neq
% 5.48/5.71 thf(fact_371_size__neq__size__imp__neq,axiom,
% 5.48/5.71 ! [X2: vEBT_VEBT,Y2: vEBT_VEBT] :
% 5.48/5.71 ( ( ( size_size_VEBT_VEBT @ X2 )
% 5.48/5.71 != ( size_size_VEBT_VEBT @ Y2 ) )
% 5.48/5.71 => ( X2 != Y2 ) ) ).
% 5.48/5.71
% 5.48/5.71 % size_neq_size_imp_neq
% 5.48/5.71 thf(fact_372_combine__common__factor,axiom,
% 5.48/5.71 ! [A: complex,E: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ C ) )
% 5.48/5.71 = ( plus_plus_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ E ) @ C ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_common_factor
% 5.48/5.71 thf(fact_373_combine__common__factor,axiom,
% 5.48/5.71 ! [A: real,E: real,B: real,C: real] :
% 5.48/5.71 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 5.48/5.71 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_common_factor
% 5.48/5.71 thf(fact_374_combine__common__factor,axiom,
% 5.48/5.71 ! [A: rat,E: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 5.48/5.71 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_common_factor
% 5.48/5.71 thf(fact_375_combine__common__factor,axiom,
% 5.48/5.71 ! [A: nat,E: nat,B: nat,C: nat] :
% 5.48/5.71 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 5.48/5.71 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_common_factor
% 5.48/5.71 thf(fact_376_combine__common__factor,axiom,
% 5.48/5.71 ! [A: int,E: int,B: int,C: int] :
% 5.48/5.71 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 5.48/5.71 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 5.48/5.71
% 5.48/5.71 % combine_common_factor
% 5.48/5.71 thf(fact_377_distrib__right,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % distrib_right
% 5.48/5.71 thf(fact_378_distrib__right,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % distrib_right
% 5.48/5.71 thf(fact_379_distrib__right,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % distrib_right
% 5.48/5.71 thf(fact_380_distrib__right,axiom,
% 5.48/5.71 ! [A: nat,B: nat,C: nat] :
% 5.48/5.71 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % distrib_right
% 5.48/5.71 thf(fact_381_distrib__right,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % distrib_right
% 5.48/5.71 thf(fact_382_distrib__left,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.48/5.71 = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % distrib_left
% 5.48/5.71 thf(fact_383_distrib__left,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.48/5.71 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % distrib_left
% 5.48/5.71 thf(fact_384_distrib__left,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.48/5.71 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % distrib_left
% 5.48/5.71 thf(fact_385_distrib__left,axiom,
% 5.48/5.71 ! [A: nat,B: nat,C: nat] :
% 5.48/5.71 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.48/5.71 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % distrib_left
% 5.48/5.71 thf(fact_386_distrib__left,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.48/5.71 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % distrib_left
% 5.48/5.71 thf(fact_387_comm__semiring__class_Odistrib,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % comm_semiring_class.distrib
% 5.48/5.71 thf(fact_388_comm__semiring__class_Odistrib,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % comm_semiring_class.distrib
% 5.48/5.71 thf(fact_389_comm__semiring__class_Odistrib,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % comm_semiring_class.distrib
% 5.48/5.71 thf(fact_390_comm__semiring__class_Odistrib,axiom,
% 5.48/5.71 ! [A: nat,B: nat,C: nat] :
% 5.48/5.71 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % comm_semiring_class.distrib
% 5.48/5.71 thf(fact_391_comm__semiring__class_Odistrib,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % comm_semiring_class.distrib
% 5.48/5.71 thf(fact_392_ring__class_Oring__distribs_I1_J,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.48/5.71 = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ring_class.ring_distribs(1)
% 5.48/5.71 thf(fact_393_ring__class_Oring__distribs_I1_J,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.48/5.71 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ring_class.ring_distribs(1)
% 5.48/5.71 thf(fact_394_ring__class_Oring__distribs_I1_J,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.48/5.71 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ring_class.ring_distribs(1)
% 5.48/5.71 thf(fact_395_ring__class_Oring__distribs_I1_J,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.48/5.71 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ring_class.ring_distribs(1)
% 5.48/5.71 thf(fact_396_ring__class_Oring__distribs_I2_J,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ring_class.ring_distribs(2)
% 5.48/5.71 thf(fact_397_ring__class_Oring__distribs_I2_J,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ring_class.ring_distribs(2)
% 5.48/5.71 thf(fact_398_ring__class_Oring__distribs_I2_J,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ring_class.ring_distribs(2)
% 5.48/5.71 thf(fact_399_ring__class_Oring__distribs_I2_J,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ring_class.ring_distribs(2)
% 5.48/5.71 thf(fact_400_divide__divide__eq__left_H,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.48/5.71 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_divide_eq_left'
% 5.48/5.71 thf(fact_401_divide__divide__eq__left_H,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.48/5.71 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_divide_eq_left'
% 5.48/5.71 thf(fact_402_divide__divide__eq__left_H,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.48/5.71 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_divide_eq_left'
% 5.48/5.71 thf(fact_403_divide__divide__times__eq,axiom,
% 5.48/5.71 ! [X2: complex,Y2: complex,Z: complex,W: complex] :
% 5.48/5.71 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X2 @ Y2 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.48/5.71 = ( divide1717551699836669952omplex @ ( times_times_complex @ X2 @ W ) @ ( times_times_complex @ Y2 @ Z ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_divide_times_eq
% 5.48/5.71 thf(fact_404_divide__divide__times__eq,axiom,
% 5.48/5.71 ! [X2: real,Y2: real,Z: real,W: real] :
% 5.48/5.71 ( ( divide_divide_real @ ( divide_divide_real @ X2 @ Y2 ) @ ( divide_divide_real @ Z @ W ) )
% 5.48/5.71 = ( divide_divide_real @ ( times_times_real @ X2 @ W ) @ ( times_times_real @ Y2 @ Z ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_divide_times_eq
% 5.48/5.71 thf(fact_405_divide__divide__times__eq,axiom,
% 5.48/5.71 ! [X2: rat,Y2: rat,Z: rat,W: rat] :
% 5.48/5.71 ( ( divide_divide_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.48/5.71 = ( divide_divide_rat @ ( times_times_rat @ X2 @ W ) @ ( times_times_rat @ Y2 @ Z ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % divide_divide_times_eq
% 5.48/5.71 thf(fact_406_times__divide__times__eq,axiom,
% 5.48/5.71 ! [X2: complex,Y2: complex,Z: complex,W: complex] :
% 5.48/5.71 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X2 @ Y2 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.48/5.71 = ( divide1717551699836669952omplex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ Y2 @ W ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % times_divide_times_eq
% 5.48/5.71 thf(fact_407_times__divide__times__eq,axiom,
% 5.48/5.71 ! [X2: real,Y2: real,Z: real,W: real] :
% 5.48/5.71 ( ( times_times_real @ ( divide_divide_real @ X2 @ Y2 ) @ ( divide_divide_real @ Z @ W ) )
% 5.48/5.71 = ( divide_divide_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y2 @ W ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % times_divide_times_eq
% 5.48/5.71 thf(fact_408_times__divide__times__eq,axiom,
% 5.48/5.71 ! [X2: rat,Y2: rat,Z: rat,W: rat] :
% 5.48/5.71 ( ( times_times_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.48/5.71 = ( divide_divide_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y2 @ W ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % times_divide_times_eq
% 5.48/5.71 thf(fact_409_add__divide__distrib,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_divide_distrib
% 5.48/5.71 thf(fact_410_add__divide__distrib,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_divide_distrib
% 5.48/5.71 thf(fact_411_add__divide__distrib,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_divide_distrib
% 5.48/5.71 thf(fact_412_nat__le__iff__add,axiom,
% 5.48/5.71 ( ord_less_eq_nat
% 5.48/5.71 = ( ^ [M3: nat,N3: nat] :
% 5.48/5.71 ? [K2: nat] :
% 5.48/5.71 ( N3
% 5.48/5.71 = ( plus_plus_nat @ M3 @ K2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % nat_le_iff_add
% 5.48/5.71 thf(fact_413_trans__le__add2,axiom,
% 5.48/5.71 ! [I: nat,J: nat,M: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.71 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % trans_le_add2
% 5.48/5.71 thf(fact_414_trans__le__add1,axiom,
% 5.48/5.71 ! [I: nat,J: nat,M: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.71 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % trans_le_add1
% 5.48/5.71 thf(fact_415_add__le__mono1,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_le_mono1
% 5.48/5.71 thf(fact_416_add__le__mono,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.71 => ( ( ord_less_eq_nat @ K @ L )
% 5.48/5.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_le_mono
% 5.48/5.71 thf(fact_417_le__Suc__ex,axiom,
% 5.48/5.71 ! [K: nat,L: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ K @ L )
% 5.48/5.71 => ? [N2: nat] :
% 5.48/5.71 ( L
% 5.48/5.71 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % le_Suc_ex
% 5.48/5.71 thf(fact_418_add__leD2,axiom,
% 5.48/5.71 ! [M: nat,K: nat,N: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.48/5.71 => ( ord_less_eq_nat @ K @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_leD2
% 5.48/5.71 thf(fact_419_add__leD1,axiom,
% 5.48/5.71 ! [M: nat,K: nat,N: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.48/5.71 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_leD1
% 5.48/5.71 thf(fact_420_le__add2,axiom,
% 5.48/5.71 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % le_add2
% 5.48/5.71 thf(fact_421_le__add1,axiom,
% 5.48/5.71 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 5.48/5.71
% 5.48/5.71 % le_add1
% 5.48/5.71 thf(fact_422_add__leE,axiom,
% 5.48/5.71 ! [M: nat,K: nat,N: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.48/5.71 => ~ ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.71 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_leE
% 5.48/5.71 thf(fact_423_mult__le__mono2,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.71 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_le_mono2
% 5.48/5.71 thf(fact_424_mult__le__mono1,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.71 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_le_mono1
% 5.48/5.71 thf(fact_425_mult__le__mono,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.71 => ( ( ord_less_eq_nat @ K @ L )
% 5.48/5.71 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult_le_mono
% 5.48/5.71 thf(fact_426_le__square,axiom,
% 5.48/5.71 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.48/5.71
% 5.48/5.71 % le_square
% 5.48/5.71 thf(fact_427_le__cube,axiom,
% 5.48/5.71 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % le_cube
% 5.48/5.71 thf(fact_428_add__mult__distrib2,axiom,
% 5.48/5.71 ! [K: nat,M: nat,N: nat] :
% 5.48/5.71 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 5.48/5.71 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mult_distrib2
% 5.48/5.71 thf(fact_429_add__mult__distrib,axiom,
% 5.48/5.71 ! [M: nat,N: nat,K: nat] :
% 5.48/5.71 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 5.48/5.71 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mult_distrib
% 5.48/5.71 thf(fact_430_nat__mult__1__right,axiom,
% 5.48/5.71 ! [N: nat] :
% 5.48/5.71 ( ( times_times_nat @ N @ one_one_nat )
% 5.48/5.71 = N ) ).
% 5.48/5.71
% 5.48/5.71 % nat_mult_1_right
% 5.48/5.71 thf(fact_431_nat__mult__1,axiom,
% 5.48/5.71 ! [N: nat] :
% 5.48/5.71 ( ( times_times_nat @ one_one_nat @ N )
% 5.48/5.71 = N ) ).
% 5.48/5.71
% 5.48/5.71 % nat_mult_1
% 5.48/5.71 thf(fact_432_greater__shift,axiom,
% 5.48/5.71 ( ord_less_nat
% 5.48/5.71 = ( ^ [Y: nat,X: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % greater_shift
% 5.48/5.71 thf(fact_433_field__less__half__sum,axiom,
% 5.48/5.71 ! [X2: real,Y2: real] :
% 5.48/5.71 ( ( ord_less_real @ X2 @ Y2 )
% 5.48/5.71 => ( ord_less_real @ X2 @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % field_less_half_sum
% 5.48/5.71 thf(fact_434_field__less__half__sum,axiom,
% 5.48/5.71 ! [X2: rat,Y2: rat] :
% 5.48/5.71 ( ( ord_less_rat @ X2 @ Y2 )
% 5.48/5.71 => ( ord_less_rat @ X2 @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % field_less_half_sum
% 5.48/5.71 thf(fact_435_high__inv,axiom,
% 5.48/5.71 ! [X2: nat,N: nat,Y2: nat] :
% 5.48/5.71 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.71 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X2 ) @ N )
% 5.48/5.71 = Y2 ) ) ).
% 5.48/5.71
% 5.48/5.71 % high_inv
% 5.48/5.71 thf(fact_436_field__sum__of__halves,axiom,
% 5.48/5.71 ! [X2: real] :
% 5.48/5.71 ( ( plus_plus_real @ ( divide_divide_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.48/5.71 = X2 ) ).
% 5.48/5.71
% 5.48/5.71 % field_sum_of_halves
% 5.48/5.71 thf(fact_437_field__sum__of__halves,axiom,
% 5.48/5.71 ! [X2: rat] :
% 5.48/5.71 ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.48/5.71 = X2 ) ).
% 5.48/5.71
% 5.48/5.71 % field_sum_of_halves
% 5.48/5.71 thf(fact_438_mult__1,axiom,
% 5.48/5.71 ! [A: complex] :
% 5.48/5.71 ( ( times_times_complex @ one_one_complex @ A )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult_1
% 5.48/5.71 thf(fact_439_mult__1,axiom,
% 5.48/5.71 ! [A: real] :
% 5.48/5.71 ( ( times_times_real @ one_one_real @ A )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult_1
% 5.48/5.71 thf(fact_440_mult__1,axiom,
% 5.48/5.71 ! [A: rat] :
% 5.48/5.71 ( ( times_times_rat @ one_one_rat @ A )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult_1
% 5.48/5.71 thf(fact_441_mult__1,axiom,
% 5.48/5.71 ! [A: nat] :
% 5.48/5.71 ( ( times_times_nat @ one_one_nat @ A )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult_1
% 5.48/5.71 thf(fact_442_mult__1,axiom,
% 5.48/5.71 ! [A: int] :
% 5.48/5.71 ( ( times_times_int @ one_one_int @ A )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult_1
% 5.48/5.71 thf(fact_443_mult_Oright__neutral,axiom,
% 5.48/5.71 ! [A: complex] :
% 5.48/5.71 ( ( times_times_complex @ A @ one_one_complex )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult.right_neutral
% 5.48/5.71 thf(fact_444_mult_Oright__neutral,axiom,
% 5.48/5.71 ! [A: real] :
% 5.48/5.71 ( ( times_times_real @ A @ one_one_real )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult.right_neutral
% 5.48/5.71 thf(fact_445_mult_Oright__neutral,axiom,
% 5.48/5.71 ! [A: rat] :
% 5.48/5.71 ( ( times_times_rat @ A @ one_one_rat )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult.right_neutral
% 5.48/5.71 thf(fact_446_mult_Oright__neutral,axiom,
% 5.48/5.71 ! [A: nat] :
% 5.48/5.71 ( ( times_times_nat @ A @ one_one_nat )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult.right_neutral
% 5.48/5.71 thf(fact_447_mult_Oright__neutral,axiom,
% 5.48/5.71 ! [A: int] :
% 5.48/5.71 ( ( times_times_int @ A @ one_one_int )
% 5.48/5.71 = A ) ).
% 5.48/5.71
% 5.48/5.71 % mult.right_neutral
% 5.48/5.71 thf(fact_448_add__less__cancel__right,axiom,
% 5.48/5.71 ! [A: real,C: real,B: real] :
% 5.48/5.71 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.48/5.71 = ( ord_less_real @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_less_cancel_right
% 5.48/5.71 thf(fact_449_add__less__cancel__right,axiom,
% 5.48/5.71 ! [A: rat,C: rat,B: rat] :
% 5.48/5.71 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.48/5.71 = ( ord_less_rat @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_less_cancel_right
% 5.48/5.71 thf(fact_450_add__less__cancel__right,axiom,
% 5.48/5.71 ! [A: nat,C: nat,B: nat] :
% 5.48/5.71 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.48/5.71 = ( ord_less_nat @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_less_cancel_right
% 5.48/5.71 thf(fact_451_add__less__cancel__right,axiom,
% 5.48/5.71 ! [A: int,C: int,B: int] :
% 5.48/5.71 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.48/5.71 = ( ord_less_int @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_less_cancel_right
% 5.48/5.71 thf(fact_452_add__less__cancel__left,axiom,
% 5.48/5.71 ! [C: real,A: real,B: real] :
% 5.48/5.71 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.48/5.71 = ( ord_less_real @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_less_cancel_left
% 5.48/5.71 thf(fact_453_add__less__cancel__left,axiom,
% 5.48/5.71 ! [C: rat,A: rat,B: rat] :
% 5.48/5.71 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.48/5.71 = ( ord_less_rat @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_less_cancel_left
% 5.48/5.71 thf(fact_454_add__less__cancel__left,axiom,
% 5.48/5.71 ! [C: nat,A: nat,B: nat] :
% 5.48/5.71 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.48/5.71 = ( ord_less_nat @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_less_cancel_left
% 5.48/5.71 thf(fact_455_add__less__cancel__left,axiom,
% 5.48/5.71 ! [C: int,A: int,B: int] :
% 5.48/5.71 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.48/5.71 = ( ord_less_int @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_less_cancel_left
% 5.48/5.71 thf(fact_456_add__le__cancel__right,axiom,
% 5.48/5.71 ! [A: real,C: real,B: real] :
% 5.48/5.71 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.48/5.71 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_le_cancel_right
% 5.48/5.71 thf(fact_457_add__le__cancel__right,axiom,
% 5.48/5.71 ! [A: rat,C: rat,B: rat] :
% 5.48/5.71 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.48/5.71 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_le_cancel_right
% 5.48/5.71 thf(fact_458_add__le__cancel__right,axiom,
% 5.48/5.71 ! [A: nat,C: nat,B: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.48/5.71 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_le_cancel_right
% 5.48/5.71 thf(fact_459_add__le__cancel__right,axiom,
% 5.48/5.71 ! [A: int,C: int,B: int] :
% 5.48/5.71 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.48/5.71 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_le_cancel_right
% 5.48/5.71 thf(fact_460_add__le__cancel__left,axiom,
% 5.48/5.71 ! [C: real,A: real,B: real] :
% 5.48/5.71 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.48/5.71 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_le_cancel_left
% 5.48/5.71 thf(fact_461_add__le__cancel__left,axiom,
% 5.48/5.71 ! [C: rat,A: rat,B: rat] :
% 5.48/5.71 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.48/5.71 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_le_cancel_left
% 5.48/5.71 thf(fact_462_add__le__cancel__left,axiom,
% 5.48/5.71 ! [C: nat,A: nat,B: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.48/5.71 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_le_cancel_left
% 5.48/5.71 thf(fact_463_add__le__cancel__left,axiom,
% 5.48/5.71 ! [C: int,A: int,B: int] :
% 5.48/5.71 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.48/5.71 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_le_cancel_left
% 5.48/5.71 thf(fact_464_mul__shift,axiom,
% 5.48/5.71 ! [X2: nat,Y2: nat,Z: nat] :
% 5.48/5.71 ( ( ( times_times_nat @ X2 @ Y2 )
% 5.48/5.71 = Z )
% 5.48/5.71 = ( ( vEBT_VEBT_mul @ ( some_nat @ X2 ) @ ( some_nat @ Y2 ) )
% 5.48/5.71 = ( some_nat @ Z ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mul_shift
% 5.48/5.71 thf(fact_465_add__shift,axiom,
% 5.48/5.71 ! [X2: nat,Y2: nat,Z: nat] :
% 5.48/5.71 ( ( ( plus_plus_nat @ X2 @ Y2 )
% 5.48/5.71 = Z )
% 5.48/5.71 = ( ( vEBT_VEBT_add @ ( some_nat @ X2 ) @ ( some_nat @ Y2 ) )
% 5.48/5.71 = ( some_nat @ Z ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_shift
% 5.48/5.71 thf(fact_466_power__shift,axiom,
% 5.48/5.71 ! [X2: nat,Y2: nat,Z: nat] :
% 5.48/5.71 ( ( ( power_power_nat @ X2 @ Y2 )
% 5.48/5.71 = Z )
% 5.48/5.71 = ( ( vEBT_VEBT_power @ ( some_nat @ X2 ) @ ( some_nat @ Y2 ) )
% 5.48/5.71 = ( some_nat @ Z ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % power_shift
% 5.48/5.71 thf(fact_467_add__left__cancel,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( ( plus_plus_real @ A @ B )
% 5.48/5.71 = ( plus_plus_real @ A @ C ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_cancel
% 5.48/5.71 thf(fact_468_add__left__cancel,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( ( plus_plus_rat @ A @ B )
% 5.48/5.71 = ( plus_plus_rat @ A @ C ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_cancel
% 5.48/5.71 thf(fact_469_add__left__cancel,axiom,
% 5.48/5.71 ! [A: nat,B: nat,C: nat] :
% 5.48/5.71 ( ( ( plus_plus_nat @ A @ B )
% 5.48/5.71 = ( plus_plus_nat @ A @ C ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_cancel
% 5.48/5.71 thf(fact_470_add__left__cancel,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( ( plus_plus_int @ A @ B )
% 5.48/5.71 = ( plus_plus_int @ A @ C ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_cancel
% 5.48/5.71 thf(fact_471_add__left__cancel,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( ( plus_plus_complex @ A @ B )
% 5.48/5.71 = ( plus_plus_complex @ A @ C ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_cancel
% 5.48/5.71 thf(fact_472_add__right__cancel,axiom,
% 5.48/5.71 ! [B: real,A: real,C: real] :
% 5.48/5.71 ( ( ( plus_plus_real @ B @ A )
% 5.48/5.71 = ( plus_plus_real @ C @ A ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_right_cancel
% 5.48/5.71 thf(fact_473_add__right__cancel,axiom,
% 5.48/5.71 ! [B: rat,A: rat,C: rat] :
% 5.48/5.71 ( ( ( plus_plus_rat @ B @ A )
% 5.48/5.71 = ( plus_plus_rat @ C @ A ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_right_cancel
% 5.48/5.71 thf(fact_474_add__right__cancel,axiom,
% 5.48/5.71 ! [B: nat,A: nat,C: nat] :
% 5.48/5.71 ( ( ( plus_plus_nat @ B @ A )
% 5.48/5.71 = ( plus_plus_nat @ C @ A ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_right_cancel
% 5.48/5.71 thf(fact_475_add__right__cancel,axiom,
% 5.48/5.71 ! [B: int,A: int,C: int] :
% 5.48/5.71 ( ( ( plus_plus_int @ B @ A )
% 5.48/5.71 = ( plus_plus_int @ C @ A ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_right_cancel
% 5.48/5.71 thf(fact_476_add__right__cancel,axiom,
% 5.48/5.71 ! [B: complex,A: complex,C: complex] :
% 5.48/5.71 ( ( ( plus_plus_complex @ B @ A )
% 5.48/5.71 = ( plus_plus_complex @ C @ A ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_right_cancel
% 5.48/5.71 thf(fact_477_pow__sum,axiom,
% 5.48/5.71 ! [A: nat,B: nat] :
% 5.48/5.71 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.48/5.71 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.48/5.71
% 5.48/5.71 % pow_sum
% 5.48/5.71 thf(fact_478_high__def,axiom,
% 5.48/5.71 ( vEBT_VEBT_high
% 5.48/5.71 = ( ^ [X: nat,N3: nat] : ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % high_def
% 5.48/5.71 thf(fact_479_high__bound__aux,axiom,
% 5.48/5.71 ! [Ma: nat,N: nat,M: nat] :
% 5.48/5.71 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.48/5.71 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % high_bound_aux
% 5.48/5.71 thf(fact_480__C5_Ohyps_C_I2_J,axiom,
% 5.48/5.71 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.48/5.71 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.48/5.71
% 5.48/5.71 % "5.hyps"(2)
% 5.48/5.71 thf(fact_481_semiring__norm_I78_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.48/5.71 = ( ord_less_num @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(78)
% 5.48/5.71 thf(fact_482_semiring__norm_I75_J,axiom,
% 5.48/5.71 ! [M: num] :
% 5.48/5.71 ~ ( ord_less_num @ M @ one ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(75)
% 5.48/5.71 thf(fact_483_semiring__norm_I80_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.48/5.71 = ( ord_less_num @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(80)
% 5.48/5.71 thf(fact_484_bit__concat__def,axiom,
% 5.48/5.71 ( vEBT_VEBT_bit_concat
% 5.48/5.71 = ( ^ [H: nat,L2: nat,D: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D ) ) @ L2 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % bit_concat_def
% 5.48/5.71 thf(fact_485_semiring__norm_I76_J,axiom,
% 5.48/5.71 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(76)
% 5.48/5.71 thf(fact_486_semiring__norm_I81_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.48/5.71 = ( ord_less_num @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(81)
% 5.48/5.71 thf(fact_487_semiring__norm_I77_J,axiom,
% 5.48/5.71 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(77)
% 5.48/5.71 thf(fact_488_enat__ord__number_I2_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.48/5.71 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % enat_ord_number(2)
% 5.48/5.71 thf(fact_489_semiring__norm_I79_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.48/5.71 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(79)
% 5.48/5.71 thf(fact_490_semiring__norm_I74_J,axiom,
% 5.48/5.71 ! [M: num,N: num] :
% 5.48/5.71 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.48/5.71 = ( ord_less_num @ M @ N ) ) ).
% 5.48/5.71
% 5.48/5.71 % semiring_norm(74)
% 5.48/5.71 thf(fact_491_add__def,axiom,
% 5.48/5.71 ( vEBT_VEBT_add
% 5.48/5.71 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_def
% 5.48/5.71 thf(fact_492_mul__def,axiom,
% 5.48/5.71 ( vEBT_VEBT_mul
% 5.48/5.71 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.48/5.71
% 5.48/5.71 % mul_def
% 5.48/5.71 thf(fact_493_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.48/5.71 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ab_semigroup_mult_class.mult_ac(1)
% 5.48/5.71 thf(fact_494_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.48/5.71 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ab_semigroup_mult_class.mult_ac(1)
% 5.48/5.71 thf(fact_495_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.48/5.71 ! [A: nat,B: nat,C: nat] :
% 5.48/5.71 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.48/5.71 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ab_semigroup_mult_class.mult_ac(1)
% 5.48/5.71 thf(fact_496_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.48/5.71 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ab_semigroup_mult_class.mult_ac(1)
% 5.48/5.71 thf(fact_497_mult_Oassoc,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.48/5.71 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult.assoc
% 5.48/5.71 thf(fact_498_mult_Oassoc,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.48/5.71 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult.assoc
% 5.48/5.71 thf(fact_499_mult_Oassoc,axiom,
% 5.48/5.71 ! [A: nat,B: nat,C: nat] :
% 5.48/5.71 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.48/5.71 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult.assoc
% 5.48/5.71 thf(fact_500_mult_Oassoc,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.48/5.71 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult.assoc
% 5.48/5.71 thf(fact_501_mult_Ocommute,axiom,
% 5.48/5.71 ( times_times_real
% 5.48/5.71 = ( ^ [A4: real,B3: real] : ( times_times_real @ B3 @ A4 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult.commute
% 5.48/5.71 thf(fact_502_mult_Ocommute,axiom,
% 5.48/5.71 ( times_times_rat
% 5.48/5.71 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ B3 @ A4 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult.commute
% 5.48/5.71 thf(fact_503_mult_Ocommute,axiom,
% 5.48/5.71 ( times_times_nat
% 5.48/5.71 = ( ^ [A4: nat,B3: nat] : ( times_times_nat @ B3 @ A4 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult.commute
% 5.48/5.71 thf(fact_504_mult_Ocommute,axiom,
% 5.48/5.71 ( times_times_int
% 5.48/5.71 = ( ^ [A4: int,B3: int] : ( times_times_int @ B3 @ A4 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult.commute
% 5.48/5.71 thf(fact_505_mult_Oleft__commute,axiom,
% 5.48/5.71 ! [B: real,A: real,C: real] :
% 5.48/5.71 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.48/5.71 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult.left_commute
% 5.48/5.71 thf(fact_506_mult_Oleft__commute,axiom,
% 5.48/5.71 ! [B: rat,A: rat,C: rat] :
% 5.48/5.71 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 5.48/5.71 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult.left_commute
% 5.48/5.71 thf(fact_507_mult_Oleft__commute,axiom,
% 5.48/5.71 ! [B: nat,A: nat,C: nat] :
% 5.48/5.71 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.48/5.71 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult.left_commute
% 5.48/5.71 thf(fact_508_mult_Oleft__commute,axiom,
% 5.48/5.71 ! [B: int,A: int,C: int] :
% 5.48/5.71 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.48/5.71 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % mult.left_commute
% 5.48/5.71 thf(fact_509_one__reorient,axiom,
% 5.48/5.71 ! [X2: complex] :
% 5.48/5.71 ( ( one_one_complex = X2 )
% 5.48/5.71 = ( X2 = one_one_complex ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_reorient
% 5.48/5.71 thf(fact_510_one__reorient,axiom,
% 5.48/5.71 ! [X2: real] :
% 5.48/5.71 ( ( one_one_real = X2 )
% 5.48/5.71 = ( X2 = one_one_real ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_reorient
% 5.48/5.71 thf(fact_511_one__reorient,axiom,
% 5.48/5.71 ! [X2: rat] :
% 5.48/5.71 ( ( one_one_rat = X2 )
% 5.48/5.71 = ( X2 = one_one_rat ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_reorient
% 5.48/5.71 thf(fact_512_one__reorient,axiom,
% 5.48/5.71 ! [X2: nat] :
% 5.48/5.71 ( ( one_one_nat = X2 )
% 5.48/5.71 = ( X2 = one_one_nat ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_reorient
% 5.48/5.71 thf(fact_513_one__reorient,axiom,
% 5.48/5.71 ! [X2: int] :
% 5.48/5.71 ( ( one_one_int = X2 )
% 5.48/5.71 = ( X2 = one_one_int ) ) ).
% 5.48/5.71
% 5.48/5.71 % one_reorient
% 5.48/5.71 thf(fact_514_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ab_semigroup_add_class.add_ac(1)
% 5.48/5.71 thf(fact_515_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ab_semigroup_add_class.add_ac(1)
% 5.48/5.71 thf(fact_516_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.48/5.71 ! [A: nat,B: nat,C: nat] :
% 5.48/5.71 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ab_semigroup_add_class.add_ac(1)
% 5.48/5.71 thf(fact_517_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ab_semigroup_add_class.add_ac(1)
% 5.48/5.71 thf(fact_518_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % ab_semigroup_add_class.add_ac(1)
% 5.48/5.71 thf(fact_519_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.48/5.71 ! [I: real,J: real,K: real,L: real] :
% 5.48/5.71 ( ( ( I = J )
% 5.48/5.71 & ( K = L ) )
% 5.48/5.71 => ( ( plus_plus_real @ I @ K )
% 5.48/5.71 = ( plus_plus_real @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(4)
% 5.48/5.71 thf(fact_520_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.48/5.71 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.48/5.71 ( ( ( I = J )
% 5.48/5.71 & ( K = L ) )
% 5.48/5.71 => ( ( plus_plus_rat @ I @ K )
% 5.48/5.71 = ( plus_plus_rat @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(4)
% 5.48/5.71 thf(fact_521_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.48/5.71 ( ( ( I = J )
% 5.48/5.71 & ( K = L ) )
% 5.48/5.71 => ( ( plus_plus_nat @ I @ K )
% 5.48/5.71 = ( plus_plus_nat @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(4)
% 5.48/5.71 thf(fact_522_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.48/5.71 ! [I: int,J: int,K: int,L: int] :
% 5.48/5.71 ( ( ( I = J )
% 5.48/5.71 & ( K = L ) )
% 5.48/5.71 => ( ( plus_plus_int @ I @ K )
% 5.48/5.71 = ( plus_plus_int @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(4)
% 5.48/5.71 thf(fact_523_group__cancel_Oadd1,axiom,
% 5.48/5.71 ! [A2: real,K: real,A: real,B: real] :
% 5.48/5.71 ( ( A2
% 5.48/5.71 = ( plus_plus_real @ K @ A ) )
% 5.48/5.71 => ( ( plus_plus_real @ A2 @ B )
% 5.48/5.71 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % group_cancel.add1
% 5.48/5.71 thf(fact_524_group__cancel_Oadd1,axiom,
% 5.48/5.71 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.48/5.71 ( ( A2
% 5.48/5.71 = ( plus_plus_rat @ K @ A ) )
% 5.48/5.71 => ( ( plus_plus_rat @ A2 @ B )
% 5.48/5.71 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % group_cancel.add1
% 5.48/5.71 thf(fact_525_group__cancel_Oadd1,axiom,
% 5.48/5.71 ! [A2: nat,K: nat,A: nat,B: nat] :
% 5.48/5.71 ( ( A2
% 5.48/5.71 = ( plus_plus_nat @ K @ A ) )
% 5.48/5.71 => ( ( plus_plus_nat @ A2 @ B )
% 5.48/5.71 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % group_cancel.add1
% 5.48/5.71 thf(fact_526_group__cancel_Oadd1,axiom,
% 5.48/5.71 ! [A2: int,K: int,A: int,B: int] :
% 5.48/5.71 ( ( A2
% 5.48/5.71 = ( plus_plus_int @ K @ A ) )
% 5.48/5.71 => ( ( plus_plus_int @ A2 @ B )
% 5.48/5.71 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % group_cancel.add1
% 5.48/5.71 thf(fact_527_group__cancel_Oadd1,axiom,
% 5.48/5.71 ! [A2: complex,K: complex,A: complex,B: complex] :
% 5.48/5.71 ( ( A2
% 5.48/5.71 = ( plus_plus_complex @ K @ A ) )
% 5.48/5.71 => ( ( plus_plus_complex @ A2 @ B )
% 5.48/5.71 = ( plus_plus_complex @ K @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % group_cancel.add1
% 5.48/5.71 thf(fact_528_group__cancel_Oadd2,axiom,
% 5.48/5.71 ! [B4: real,K: real,B: real,A: real] :
% 5.48/5.71 ( ( B4
% 5.48/5.71 = ( plus_plus_real @ K @ B ) )
% 5.48/5.71 => ( ( plus_plus_real @ A @ B4 )
% 5.48/5.71 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % group_cancel.add2
% 5.48/5.71 thf(fact_529_group__cancel_Oadd2,axiom,
% 5.48/5.71 ! [B4: rat,K: rat,B: rat,A: rat] :
% 5.48/5.71 ( ( B4
% 5.48/5.71 = ( plus_plus_rat @ K @ B ) )
% 5.48/5.71 => ( ( plus_plus_rat @ A @ B4 )
% 5.48/5.71 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % group_cancel.add2
% 5.48/5.71 thf(fact_530_group__cancel_Oadd2,axiom,
% 5.48/5.71 ! [B4: nat,K: nat,B: nat,A: nat] :
% 5.48/5.71 ( ( B4
% 5.48/5.71 = ( plus_plus_nat @ K @ B ) )
% 5.48/5.71 => ( ( plus_plus_nat @ A @ B4 )
% 5.48/5.71 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % group_cancel.add2
% 5.48/5.71 thf(fact_531_group__cancel_Oadd2,axiom,
% 5.48/5.71 ! [B4: int,K: int,B: int,A: int] :
% 5.48/5.71 ( ( B4
% 5.48/5.71 = ( plus_plus_int @ K @ B ) )
% 5.48/5.71 => ( ( plus_plus_int @ A @ B4 )
% 5.48/5.71 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % group_cancel.add2
% 5.48/5.71 thf(fact_532_group__cancel_Oadd2,axiom,
% 5.48/5.71 ! [B4: complex,K: complex,B: complex,A: complex] :
% 5.48/5.71 ( ( B4
% 5.48/5.71 = ( plus_plus_complex @ K @ B ) )
% 5.48/5.71 => ( ( plus_plus_complex @ A @ B4 )
% 5.48/5.71 = ( plus_plus_complex @ K @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % group_cancel.add2
% 5.48/5.71 thf(fact_533_add_Oassoc,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.assoc
% 5.48/5.71 thf(fact_534_add_Oassoc,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.assoc
% 5.48/5.71 thf(fact_535_add_Oassoc,axiom,
% 5.48/5.71 ! [A: nat,B: nat,C: nat] :
% 5.48/5.71 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.assoc
% 5.48/5.71 thf(fact_536_add_Oassoc,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.assoc
% 5.48/5.71 thf(fact_537_add_Oassoc,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.48/5.71 = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.assoc
% 5.48/5.71 thf(fact_538_add_Oleft__cancel,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( ( plus_plus_real @ A @ B )
% 5.48/5.71 = ( plus_plus_real @ A @ C ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.left_cancel
% 5.48/5.71 thf(fact_539_add_Oleft__cancel,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( ( plus_plus_rat @ A @ B )
% 5.48/5.71 = ( plus_plus_rat @ A @ C ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.left_cancel
% 5.48/5.71 thf(fact_540_add_Oleft__cancel,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( ( plus_plus_int @ A @ B )
% 5.48/5.71 = ( plus_plus_int @ A @ C ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.left_cancel
% 5.48/5.71 thf(fact_541_add_Oleft__cancel,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( ( plus_plus_complex @ A @ B )
% 5.48/5.71 = ( plus_plus_complex @ A @ C ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.left_cancel
% 5.48/5.71 thf(fact_542_add_Oright__cancel,axiom,
% 5.48/5.71 ! [B: real,A: real,C: real] :
% 5.48/5.71 ( ( ( plus_plus_real @ B @ A )
% 5.48/5.71 = ( plus_plus_real @ C @ A ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.right_cancel
% 5.48/5.71 thf(fact_543_add_Oright__cancel,axiom,
% 5.48/5.71 ! [B: rat,A: rat,C: rat] :
% 5.48/5.71 ( ( ( plus_plus_rat @ B @ A )
% 5.48/5.71 = ( plus_plus_rat @ C @ A ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.right_cancel
% 5.48/5.71 thf(fact_544_add_Oright__cancel,axiom,
% 5.48/5.71 ! [B: int,A: int,C: int] :
% 5.48/5.71 ( ( ( plus_plus_int @ B @ A )
% 5.48/5.71 = ( plus_plus_int @ C @ A ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.right_cancel
% 5.48/5.71 thf(fact_545_add_Oright__cancel,axiom,
% 5.48/5.71 ! [B: complex,A: complex,C: complex] :
% 5.48/5.71 ( ( ( plus_plus_complex @ B @ A )
% 5.48/5.71 = ( plus_plus_complex @ C @ A ) )
% 5.48/5.71 = ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.right_cancel
% 5.48/5.71 thf(fact_546_add_Ocommute,axiom,
% 5.48/5.71 ( plus_plus_real
% 5.48/5.71 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ B3 @ A4 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.commute
% 5.48/5.71 thf(fact_547_add_Ocommute,axiom,
% 5.48/5.71 ( plus_plus_rat
% 5.48/5.71 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ B3 @ A4 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.commute
% 5.48/5.71 thf(fact_548_add_Ocommute,axiom,
% 5.48/5.71 ( plus_plus_nat
% 5.48/5.71 = ( ^ [A4: nat,B3: nat] : ( plus_plus_nat @ B3 @ A4 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.commute
% 5.48/5.71 thf(fact_549_add_Ocommute,axiom,
% 5.48/5.71 ( plus_plus_int
% 5.48/5.71 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ B3 @ A4 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.commute
% 5.48/5.71 thf(fact_550_add_Ocommute,axiom,
% 5.48/5.71 ( plus_plus_complex
% 5.48/5.71 = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ B3 @ A4 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.commute
% 5.48/5.71 thf(fact_551_add_Oleft__commute,axiom,
% 5.48/5.71 ! [B: real,A: real,C: real] :
% 5.48/5.71 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.48/5.71 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.left_commute
% 5.48/5.71 thf(fact_552_add_Oleft__commute,axiom,
% 5.48/5.71 ! [B: rat,A: rat,C: rat] :
% 5.48/5.71 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 5.48/5.71 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.left_commute
% 5.48/5.71 thf(fact_553_add_Oleft__commute,axiom,
% 5.48/5.71 ! [B: nat,A: nat,C: nat] :
% 5.48/5.71 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.48/5.71 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.left_commute
% 5.48/5.71 thf(fact_554_add_Oleft__commute,axiom,
% 5.48/5.71 ! [B: int,A: int,C: int] :
% 5.48/5.71 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.48/5.71 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.left_commute
% 5.48/5.71 thf(fact_555_add_Oleft__commute,axiom,
% 5.48/5.71 ! [B: complex,A: complex,C: complex] :
% 5.48/5.71 ( ( plus_plus_complex @ B @ ( plus_plus_complex @ A @ C ) )
% 5.48/5.71 = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add.left_commute
% 5.48/5.71 thf(fact_556_add__left__imp__eq,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( ( plus_plus_real @ A @ B )
% 5.48/5.71 = ( plus_plus_real @ A @ C ) )
% 5.48/5.71 => ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_imp_eq
% 5.48/5.71 thf(fact_557_add__left__imp__eq,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( ( plus_plus_rat @ A @ B )
% 5.48/5.71 = ( plus_plus_rat @ A @ C ) )
% 5.48/5.71 => ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_imp_eq
% 5.48/5.71 thf(fact_558_add__left__imp__eq,axiom,
% 5.48/5.71 ! [A: nat,B: nat,C: nat] :
% 5.48/5.71 ( ( ( plus_plus_nat @ A @ B )
% 5.48/5.71 = ( plus_plus_nat @ A @ C ) )
% 5.48/5.71 => ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_imp_eq
% 5.48/5.71 thf(fact_559_add__left__imp__eq,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( ( plus_plus_int @ A @ B )
% 5.48/5.71 = ( plus_plus_int @ A @ C ) )
% 5.48/5.71 => ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_imp_eq
% 5.48/5.71 thf(fact_560_add__left__imp__eq,axiom,
% 5.48/5.71 ! [A: complex,B: complex,C: complex] :
% 5.48/5.71 ( ( ( plus_plus_complex @ A @ B )
% 5.48/5.71 = ( plus_plus_complex @ A @ C ) )
% 5.48/5.71 => ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_imp_eq
% 5.48/5.71 thf(fact_561_add__right__imp__eq,axiom,
% 5.48/5.71 ! [B: real,A: real,C: real] :
% 5.48/5.71 ( ( ( plus_plus_real @ B @ A )
% 5.48/5.71 = ( plus_plus_real @ C @ A ) )
% 5.48/5.71 => ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_right_imp_eq
% 5.48/5.71 thf(fact_562_add__right__imp__eq,axiom,
% 5.48/5.71 ! [B: rat,A: rat,C: rat] :
% 5.48/5.71 ( ( ( plus_plus_rat @ B @ A )
% 5.48/5.71 = ( plus_plus_rat @ C @ A ) )
% 5.48/5.71 => ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_right_imp_eq
% 5.48/5.71 thf(fact_563_add__right__imp__eq,axiom,
% 5.48/5.71 ! [B: nat,A: nat,C: nat] :
% 5.48/5.71 ( ( ( plus_plus_nat @ B @ A )
% 5.48/5.71 = ( plus_plus_nat @ C @ A ) )
% 5.48/5.71 => ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_right_imp_eq
% 5.48/5.71 thf(fact_564_add__right__imp__eq,axiom,
% 5.48/5.71 ! [B: int,A: int,C: int] :
% 5.48/5.71 ( ( ( plus_plus_int @ B @ A )
% 5.48/5.71 = ( plus_plus_int @ C @ A ) )
% 5.48/5.71 => ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_right_imp_eq
% 5.48/5.71 thf(fact_565_add__right__imp__eq,axiom,
% 5.48/5.71 ! [B: complex,A: complex,C: complex] :
% 5.48/5.71 ( ( ( plus_plus_complex @ B @ A )
% 5.48/5.71 = ( plus_plus_complex @ C @ A ) )
% 5.48/5.71 => ( B = C ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_right_imp_eq
% 5.48/5.71 thf(fact_566_div__exp__eq,axiom,
% 5.48/5.71 ! [A: nat,M: nat,N: nat] :
% 5.48/5.71 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.71 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % div_exp_eq
% 5.48/5.71 thf(fact_567_div__exp__eq,axiom,
% 5.48/5.71 ! [A: int,M: nat,N: nat] :
% 5.48/5.71 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.71 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % div_exp_eq
% 5.48/5.71 thf(fact_568_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.48/5.71 ! [I: real,J: real,K: real,L: real] :
% 5.48/5.71 ( ( ( ord_less_eq_real @ I @ J )
% 5.48/5.71 & ( K = L ) )
% 5.48/5.71 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(3)
% 5.48/5.71 thf(fact_569_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.48/5.71 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.48/5.71 ( ( ( ord_less_eq_rat @ I @ J )
% 5.48/5.71 & ( K = L ) )
% 5.48/5.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(3)
% 5.48/5.71 thf(fact_570_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.48/5.71 ( ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.71 & ( K = L ) )
% 5.48/5.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(3)
% 5.48/5.71 thf(fact_571_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.48/5.71 ! [I: int,J: int,K: int,L: int] :
% 5.48/5.71 ( ( ( ord_less_eq_int @ I @ J )
% 5.48/5.71 & ( K = L ) )
% 5.48/5.71 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(3)
% 5.48/5.71 thf(fact_572_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.48/5.71 ! [I: real,J: real,K: real,L: real] :
% 5.48/5.71 ( ( ( I = J )
% 5.48/5.71 & ( ord_less_eq_real @ K @ L ) )
% 5.48/5.71 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(2)
% 5.48/5.71 thf(fact_573_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.48/5.71 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.48/5.71 ( ( ( I = J )
% 5.48/5.71 & ( ord_less_eq_rat @ K @ L ) )
% 5.48/5.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(2)
% 5.48/5.71 thf(fact_574_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.48/5.71 ( ( ( I = J )
% 5.48/5.71 & ( ord_less_eq_nat @ K @ L ) )
% 5.48/5.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(2)
% 5.48/5.71 thf(fact_575_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.48/5.71 ! [I: int,J: int,K: int,L: int] :
% 5.48/5.71 ( ( ( I = J )
% 5.48/5.71 & ( ord_less_eq_int @ K @ L ) )
% 5.48/5.71 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(2)
% 5.48/5.71 thf(fact_576_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.48/5.71 ! [I: real,J: real,K: real,L: real] :
% 5.48/5.71 ( ( ( ord_less_eq_real @ I @ J )
% 5.48/5.71 & ( ord_less_eq_real @ K @ L ) )
% 5.48/5.71 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(1)
% 5.48/5.71 thf(fact_577_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.48/5.71 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.48/5.71 ( ( ( ord_less_eq_rat @ I @ J )
% 5.48/5.71 & ( ord_less_eq_rat @ K @ L ) )
% 5.48/5.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(1)
% 5.48/5.71 thf(fact_578_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.48/5.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.48/5.71 ( ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.71 & ( ord_less_eq_nat @ K @ L ) )
% 5.48/5.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(1)
% 5.48/5.71 thf(fact_579_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.48/5.71 ! [I: int,J: int,K: int,L: int] :
% 5.48/5.71 ( ( ( ord_less_eq_int @ I @ J )
% 5.48/5.71 & ( ord_less_eq_int @ K @ L ) )
% 5.48/5.71 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono_thms_linordered_semiring(1)
% 5.48/5.71 thf(fact_580_add__mono,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real,D2: real] :
% 5.48/5.71 ( ( ord_less_eq_real @ A @ B )
% 5.48/5.71 => ( ( ord_less_eq_real @ C @ D2 )
% 5.48/5.71 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono
% 5.48/5.71 thf(fact_581_add__mono,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.48/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.48/5.71 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.48/5.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono
% 5.48/5.71 thf(fact_582_add__mono,axiom,
% 5.48/5.71 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.71 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.48/5.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono
% 5.48/5.71 thf(fact_583_add__mono,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int,D2: int] :
% 5.48/5.71 ( ( ord_less_eq_int @ A @ B )
% 5.48/5.71 => ( ( ord_less_eq_int @ C @ D2 )
% 5.48/5.71 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_mono
% 5.48/5.71 thf(fact_584_add__left__mono,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( ord_less_eq_real @ A @ B )
% 5.48/5.71 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_mono
% 5.48/5.71 thf(fact_585_add__left__mono,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.48/5.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_mono
% 5.48/5.71 thf(fact_586_add__left__mono,axiom,
% 5.48/5.71 ! [A: nat,B: nat,C: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_mono
% 5.48/5.71 thf(fact_587_add__left__mono,axiom,
% 5.48/5.71 ! [A: int,B: int,C: int] :
% 5.48/5.71 ( ( ord_less_eq_int @ A @ B )
% 5.48/5.71 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_left_mono
% 5.48/5.71 thf(fact_588_less__eqE,axiom,
% 5.48/5.71 ! [A: nat,B: nat] :
% 5.48/5.71 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.71 => ~ ! [C2: nat] :
% 5.48/5.71 ( B
% 5.48/5.71 != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % less_eqE
% 5.48/5.71 thf(fact_589_add__right__mono,axiom,
% 5.48/5.71 ! [A: real,B: real,C: real] :
% 5.48/5.71 ( ( ord_less_eq_real @ A @ B )
% 5.48/5.71 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.48/5.71
% 5.48/5.71 % add_right_mono
% 5.48/5.71 thf(fact_590_add__right__mono,axiom,
% 5.48/5.71 ! [A: rat,B: rat,C: rat] :
% 5.48/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.48/5.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_right_mono
% 5.48/5.72 thf(fact_591_add__right__mono,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_right_mono
% 5.48/5.72 thf(fact_592_add__right__mono,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ A @ B )
% 5.48/5.72 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_right_mono
% 5.48/5.72 thf(fact_593_le__iff__add,axiom,
% 5.48/5.72 ( ord_less_eq_nat
% 5.48/5.72 = ( ^ [A4: nat,B3: nat] :
% 5.48/5.72 ? [C3: nat] :
% 5.48/5.72 ( B3
% 5.48/5.72 = ( plus_plus_nat @ A4 @ C3 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_iff_add
% 5.48/5.72 thf(fact_594_add__le__imp__le__left,axiom,
% 5.48/5.72 ! [C: real,A: real,B: real] :
% 5.48/5.72 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.48/5.72 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_imp_le_left
% 5.48/5.72 thf(fact_595_add__le__imp__le__left,axiom,
% 5.48/5.72 ! [C: rat,A: rat,B: rat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.48/5.72 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_imp_le_left
% 5.48/5.72 thf(fact_596_add__le__imp__le__left,axiom,
% 5.48/5.72 ! [C: nat,A: nat,B: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.48/5.72 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_imp_le_left
% 5.48/5.72 thf(fact_597_add__le__imp__le__left,axiom,
% 5.48/5.72 ! [C: int,A: int,B: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.48/5.72 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_imp_le_left
% 5.48/5.72 thf(fact_598_add__le__imp__le__right,axiom,
% 5.48/5.72 ! [A: real,C: real,B: real] :
% 5.48/5.72 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.48/5.72 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_imp_le_right
% 5.48/5.72 thf(fact_599_add__le__imp__le__right,axiom,
% 5.48/5.72 ! [A: rat,C: rat,B: rat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.48/5.72 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_imp_le_right
% 5.48/5.72 thf(fact_600_add__le__imp__le__right,axiom,
% 5.48/5.72 ! [A: nat,C: nat,B: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.48/5.72 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_imp_le_right
% 5.48/5.72 thf(fact_601_add__le__imp__le__right,axiom,
% 5.48/5.72 ! [A: int,C: int,B: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.48/5.72 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_imp_le_right
% 5.48/5.72 thf(fact_602_add__mono__thms__linordered__field_I5_J,axiom,
% 5.48/5.72 ! [I: real,J: real,K: real,L: real] :
% 5.48/5.72 ( ( ( ord_less_real @ I @ J )
% 5.48/5.72 & ( ord_less_real @ K @ L ) )
% 5.48/5.72 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(5)
% 5.48/5.72 thf(fact_603_add__mono__thms__linordered__field_I5_J,axiom,
% 5.48/5.72 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.48/5.72 ( ( ( ord_less_rat @ I @ J )
% 5.48/5.72 & ( ord_less_rat @ K @ L ) )
% 5.48/5.72 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(5)
% 5.48/5.72 thf(fact_604_add__mono__thms__linordered__field_I5_J,axiom,
% 5.48/5.72 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.48/5.72 ( ( ( ord_less_nat @ I @ J )
% 5.48/5.72 & ( ord_less_nat @ K @ L ) )
% 5.48/5.72 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(5)
% 5.48/5.72 thf(fact_605_add__mono__thms__linordered__field_I5_J,axiom,
% 5.48/5.72 ! [I: int,J: int,K: int,L: int] :
% 5.48/5.72 ( ( ( ord_less_int @ I @ J )
% 5.48/5.72 & ( ord_less_int @ K @ L ) )
% 5.48/5.72 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(5)
% 5.48/5.72 thf(fact_606_add__mono__thms__linordered__field_I2_J,axiom,
% 5.48/5.72 ! [I: real,J: real,K: real,L: real] :
% 5.48/5.72 ( ( ( I = J )
% 5.48/5.72 & ( ord_less_real @ K @ L ) )
% 5.48/5.72 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(2)
% 5.48/5.72 thf(fact_607_add__mono__thms__linordered__field_I2_J,axiom,
% 5.48/5.72 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.48/5.72 ( ( ( I = J )
% 5.48/5.72 & ( ord_less_rat @ K @ L ) )
% 5.48/5.72 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(2)
% 5.48/5.72 thf(fact_608_add__mono__thms__linordered__field_I2_J,axiom,
% 5.48/5.72 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.48/5.72 ( ( ( I = J )
% 5.48/5.72 & ( ord_less_nat @ K @ L ) )
% 5.48/5.72 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(2)
% 5.48/5.72 thf(fact_609_add__mono__thms__linordered__field_I2_J,axiom,
% 5.48/5.72 ! [I: int,J: int,K: int,L: int] :
% 5.48/5.72 ( ( ( I = J )
% 5.48/5.72 & ( ord_less_int @ K @ L ) )
% 5.48/5.72 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(2)
% 5.48/5.72 thf(fact_610_add__mono__thms__linordered__field_I1_J,axiom,
% 5.48/5.72 ! [I: real,J: real,K: real,L: real] :
% 5.48/5.72 ( ( ( ord_less_real @ I @ J )
% 5.48/5.72 & ( K = L ) )
% 5.48/5.72 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(1)
% 5.48/5.72 thf(fact_611_add__mono__thms__linordered__field_I1_J,axiom,
% 5.48/5.72 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.48/5.72 ( ( ( ord_less_rat @ I @ J )
% 5.48/5.72 & ( K = L ) )
% 5.48/5.72 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(1)
% 5.48/5.72 thf(fact_612_add__mono__thms__linordered__field_I1_J,axiom,
% 5.48/5.72 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.48/5.72 ( ( ( ord_less_nat @ I @ J )
% 5.48/5.72 & ( K = L ) )
% 5.48/5.72 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(1)
% 5.48/5.72 thf(fact_613_add__mono__thms__linordered__field_I1_J,axiom,
% 5.48/5.72 ! [I: int,J: int,K: int,L: int] :
% 5.48/5.72 ( ( ( ord_less_int @ I @ J )
% 5.48/5.72 & ( K = L ) )
% 5.48/5.72 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(1)
% 5.48/5.72 thf(fact_614_add__strict__mono,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real,D2: real] :
% 5.48/5.72 ( ( ord_less_real @ A @ B )
% 5.48/5.72 => ( ( ord_less_real @ C @ D2 )
% 5.48/5.72 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_strict_mono
% 5.48/5.72 thf(fact_615_add__strict__mono,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.48/5.72 ( ( ord_less_rat @ A @ B )
% 5.48/5.72 => ( ( ord_less_rat @ C @ D2 )
% 5.48/5.72 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_strict_mono
% 5.48/5.72 thf(fact_616_add__strict__mono,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.48/5.72 ( ( ord_less_nat @ A @ B )
% 5.48/5.72 => ( ( ord_less_nat @ C @ D2 )
% 5.48/5.72 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_strict_mono
% 5.48/5.72 thf(fact_617_add__strict__mono,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int,D2: int] :
% 5.48/5.72 ( ( ord_less_int @ A @ B )
% 5.48/5.72 => ( ( ord_less_int @ C @ D2 )
% 5.48/5.72 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_strict_mono
% 5.48/5.72 thf(fact_618_add__strict__left__mono,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( ord_less_real @ A @ B )
% 5.48/5.72 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_strict_left_mono
% 5.48/5.72 thf(fact_619_add__strict__left__mono,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( ord_less_rat @ A @ B )
% 5.48/5.72 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_strict_left_mono
% 5.48/5.72 thf(fact_620_add__strict__left__mono,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( ord_less_nat @ A @ B )
% 5.48/5.72 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_strict_left_mono
% 5.48/5.72 thf(fact_621_add__strict__left__mono,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( ord_less_int @ A @ B )
% 5.48/5.72 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_strict_left_mono
% 5.48/5.72 thf(fact_622_add__strict__right__mono,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( ord_less_real @ A @ B )
% 5.48/5.72 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_strict_right_mono
% 5.48/5.72 thf(fact_623_add__strict__right__mono,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( ord_less_rat @ A @ B )
% 5.48/5.72 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_strict_right_mono
% 5.48/5.72 thf(fact_624_add__strict__right__mono,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( ord_less_nat @ A @ B )
% 5.48/5.72 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_strict_right_mono
% 5.48/5.72 thf(fact_625_add__strict__right__mono,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( ord_less_int @ A @ B )
% 5.48/5.72 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_strict_right_mono
% 5.48/5.72 thf(fact_626_add__less__imp__less__left,axiom,
% 5.48/5.72 ! [C: real,A: real,B: real] :
% 5.48/5.72 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.48/5.72 => ( ord_less_real @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_less_imp_less_left
% 5.48/5.72 thf(fact_627_add__less__imp__less__left,axiom,
% 5.48/5.72 ! [C: rat,A: rat,B: rat] :
% 5.48/5.72 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.48/5.72 => ( ord_less_rat @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_less_imp_less_left
% 5.48/5.72 thf(fact_628_add__less__imp__less__left,axiom,
% 5.48/5.72 ! [C: nat,A: nat,B: nat] :
% 5.48/5.72 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.48/5.72 => ( ord_less_nat @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_less_imp_less_left
% 5.48/5.72 thf(fact_629_add__less__imp__less__left,axiom,
% 5.48/5.72 ! [C: int,A: int,B: int] :
% 5.48/5.72 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.48/5.72 => ( ord_less_int @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_less_imp_less_left
% 5.48/5.72 thf(fact_630_add__less__imp__less__right,axiom,
% 5.48/5.72 ! [A: real,C: real,B: real] :
% 5.48/5.72 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.48/5.72 => ( ord_less_real @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_less_imp_less_right
% 5.48/5.72 thf(fact_631_add__less__imp__less__right,axiom,
% 5.48/5.72 ! [A: rat,C: rat,B: rat] :
% 5.48/5.72 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.48/5.72 => ( ord_less_rat @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_less_imp_less_right
% 5.48/5.72 thf(fact_632_add__less__imp__less__right,axiom,
% 5.48/5.72 ! [A: nat,C: nat,B: nat] :
% 5.48/5.72 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.48/5.72 => ( ord_less_nat @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_less_imp_less_right
% 5.48/5.72 thf(fact_633_add__less__imp__less__right,axiom,
% 5.48/5.72 ! [A: int,C: int,B: int] :
% 5.48/5.72 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.48/5.72 => ( ord_less_int @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_less_imp_less_right
% 5.48/5.72 thf(fact_634_comm__monoid__mult__class_Omult__1,axiom,
% 5.48/5.72 ! [A: complex] :
% 5.48/5.72 ( ( times_times_complex @ one_one_complex @ A )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % comm_monoid_mult_class.mult_1
% 5.48/5.72 thf(fact_635_comm__monoid__mult__class_Omult__1,axiom,
% 5.48/5.72 ! [A: real] :
% 5.48/5.72 ( ( times_times_real @ one_one_real @ A )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % comm_monoid_mult_class.mult_1
% 5.48/5.72 thf(fact_636_comm__monoid__mult__class_Omult__1,axiom,
% 5.48/5.72 ! [A: rat] :
% 5.48/5.72 ( ( times_times_rat @ one_one_rat @ A )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % comm_monoid_mult_class.mult_1
% 5.48/5.72 thf(fact_637_comm__monoid__mult__class_Omult__1,axiom,
% 5.48/5.72 ! [A: nat] :
% 5.48/5.72 ( ( times_times_nat @ one_one_nat @ A )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % comm_monoid_mult_class.mult_1
% 5.48/5.72 thf(fact_638_comm__monoid__mult__class_Omult__1,axiom,
% 5.48/5.72 ! [A: int] :
% 5.48/5.72 ( ( times_times_int @ one_one_int @ A )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % comm_monoid_mult_class.mult_1
% 5.48/5.72 thf(fact_639_mult_Ocomm__neutral,axiom,
% 5.48/5.72 ! [A: complex] :
% 5.48/5.72 ( ( times_times_complex @ A @ one_one_complex )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % mult.comm_neutral
% 5.48/5.72 thf(fact_640_mult_Ocomm__neutral,axiom,
% 5.48/5.72 ! [A: real] :
% 5.48/5.72 ( ( times_times_real @ A @ one_one_real )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % mult.comm_neutral
% 5.48/5.72 thf(fact_641_mult_Ocomm__neutral,axiom,
% 5.48/5.72 ! [A: rat] :
% 5.48/5.72 ( ( times_times_rat @ A @ one_one_rat )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % mult.comm_neutral
% 5.48/5.72 thf(fact_642_mult_Ocomm__neutral,axiom,
% 5.48/5.72 ! [A: nat] :
% 5.48/5.72 ( ( times_times_nat @ A @ one_one_nat )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % mult.comm_neutral
% 5.48/5.72 thf(fact_643_mult_Ocomm__neutral,axiom,
% 5.48/5.72 ! [A: int] :
% 5.48/5.72 ( ( times_times_int @ A @ one_one_int )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % mult.comm_neutral
% 5.48/5.72 thf(fact_644_add__mono__thms__linordered__field_I4_J,axiom,
% 5.48/5.72 ! [I: real,J: real,K: real,L: real] :
% 5.48/5.72 ( ( ( ord_less_eq_real @ I @ J )
% 5.48/5.72 & ( ord_less_real @ K @ L ) )
% 5.48/5.72 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(4)
% 5.48/5.72 thf(fact_645_add__mono__thms__linordered__field_I4_J,axiom,
% 5.48/5.72 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.48/5.72 ( ( ( ord_less_eq_rat @ I @ J )
% 5.48/5.72 & ( ord_less_rat @ K @ L ) )
% 5.48/5.72 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(4)
% 5.48/5.72 thf(fact_646_add__mono__thms__linordered__field_I4_J,axiom,
% 5.48/5.72 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.48/5.72 ( ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.72 & ( ord_less_nat @ K @ L ) )
% 5.48/5.72 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(4)
% 5.48/5.72 thf(fact_647_add__mono__thms__linordered__field_I4_J,axiom,
% 5.48/5.72 ! [I: int,J: int,K: int,L: int] :
% 5.48/5.72 ( ( ( ord_less_eq_int @ I @ J )
% 5.48/5.72 & ( ord_less_int @ K @ L ) )
% 5.48/5.72 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(4)
% 5.48/5.72 thf(fact_648_add__mono__thms__linordered__field_I3_J,axiom,
% 5.48/5.72 ! [I: real,J: real,K: real,L: real] :
% 5.48/5.72 ( ( ( ord_less_real @ I @ J )
% 5.48/5.72 & ( ord_less_eq_real @ K @ L ) )
% 5.48/5.72 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(3)
% 5.48/5.72 thf(fact_649_add__mono__thms__linordered__field_I3_J,axiom,
% 5.48/5.72 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.48/5.72 ( ( ( ord_less_rat @ I @ J )
% 5.48/5.72 & ( ord_less_eq_rat @ K @ L ) )
% 5.48/5.72 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(3)
% 5.48/5.72 thf(fact_650_add__mono__thms__linordered__field_I3_J,axiom,
% 5.48/5.72 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.48/5.72 ( ( ( ord_less_nat @ I @ J )
% 5.48/5.72 & ( ord_less_eq_nat @ K @ L ) )
% 5.48/5.72 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(3)
% 5.48/5.72 thf(fact_651_add__mono__thms__linordered__field_I3_J,axiom,
% 5.48/5.72 ! [I: int,J: int,K: int,L: int] :
% 5.48/5.72 ( ( ( ord_less_int @ I @ J )
% 5.48/5.72 & ( ord_less_eq_int @ K @ L ) )
% 5.48/5.72 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_mono_thms_linordered_field(3)
% 5.48/5.72 thf(fact_652_add__le__less__mono,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real,D2: real] :
% 5.48/5.72 ( ( ord_less_eq_real @ A @ B )
% 5.48/5.72 => ( ( ord_less_real @ C @ D2 )
% 5.48/5.72 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_less_mono
% 5.48/5.72 thf(fact_653_add__le__less__mono,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ A @ B )
% 5.48/5.72 => ( ( ord_less_rat @ C @ D2 )
% 5.48/5.72 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_less_mono
% 5.48/5.72 thf(fact_654_add__le__less__mono,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ( ord_less_nat @ C @ D2 )
% 5.48/5.72 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_less_mono
% 5.48/5.72 thf(fact_655_add__le__less__mono,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int,D2: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ A @ B )
% 5.48/5.72 => ( ( ord_less_int @ C @ D2 )
% 5.48/5.72 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_less_mono
% 5.48/5.72 thf(fact_656_add__less__le__mono,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real,D2: real] :
% 5.48/5.72 ( ( ord_less_real @ A @ B )
% 5.48/5.72 => ( ( ord_less_eq_real @ C @ D2 )
% 5.48/5.72 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_less_le_mono
% 5.48/5.72 thf(fact_657_add__less__le__mono,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.48/5.72 ( ( ord_less_rat @ A @ B )
% 5.48/5.72 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.48/5.72 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_less_le_mono
% 5.48/5.72 thf(fact_658_add__less__le__mono,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.48/5.72 ( ( ord_less_nat @ A @ B )
% 5.48/5.72 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.48/5.72 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_less_le_mono
% 5.48/5.72 thf(fact_659_add__less__le__mono,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int,D2: int] :
% 5.48/5.72 ( ( ord_less_int @ A @ B )
% 5.48/5.72 => ( ( ord_less_eq_int @ C @ D2 )
% 5.48/5.72 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_less_le_mono
% 5.48/5.72 thf(fact_660_power__increasing__iff,axiom,
% 5.48/5.72 ! [B: real,X2: nat,Y2: nat] :
% 5.48/5.72 ( ( ord_less_real @ one_one_real @ B )
% 5.48/5.72 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X2 ) @ ( power_power_real @ B @ Y2 ) )
% 5.48/5.72 = ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_increasing_iff
% 5.48/5.72 thf(fact_661_power__increasing__iff,axiom,
% 5.48/5.72 ! [B: rat,X2: nat,Y2: nat] :
% 5.48/5.72 ( ( ord_less_rat @ one_one_rat @ B )
% 5.48/5.72 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y2 ) )
% 5.48/5.72 = ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_increasing_iff
% 5.48/5.72 thf(fact_662_power__increasing__iff,axiom,
% 5.48/5.72 ! [B: nat,X2: nat,Y2: nat] :
% 5.48/5.72 ( ( ord_less_nat @ one_one_nat @ B )
% 5.48/5.72 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y2 ) )
% 5.48/5.72 = ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_increasing_iff
% 5.48/5.72 thf(fact_663_power__increasing__iff,axiom,
% 5.48/5.72 ! [B: int,X2: nat,Y2: nat] :
% 5.48/5.72 ( ( ord_less_int @ one_one_int @ B )
% 5.48/5.72 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y2 ) )
% 5.48/5.72 = ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_increasing_iff
% 5.48/5.72 thf(fact_664_power__add__numeral,axiom,
% 5.48/5.72 ! [A: complex,M: num,N: num] :
% 5.48/5.72 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.48/5.72 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add_numeral
% 5.48/5.72 thf(fact_665_power__add__numeral,axiom,
% 5.48/5.72 ! [A: real,M: num,N: num] :
% 5.48/5.72 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.48/5.72 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add_numeral
% 5.48/5.72 thf(fact_666_power__add__numeral,axiom,
% 5.48/5.72 ! [A: rat,M: num,N: num] :
% 5.48/5.72 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.48/5.72 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add_numeral
% 5.48/5.72 thf(fact_667_power__add__numeral,axiom,
% 5.48/5.72 ! [A: nat,M: num,N: num] :
% 5.48/5.72 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.48/5.72 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add_numeral
% 5.48/5.72 thf(fact_668_power__add__numeral,axiom,
% 5.48/5.72 ! [A: int,M: num,N: num] :
% 5.48/5.72 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.48/5.72 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add_numeral
% 5.48/5.72 thf(fact_669_power__add__numeral2,axiom,
% 5.48/5.72 ! [A: complex,M: num,N: num,B: complex] :
% 5.48/5.72 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.48/5.72 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add_numeral2
% 5.48/5.72 thf(fact_670_power__add__numeral2,axiom,
% 5.48/5.72 ! [A: real,M: num,N: num,B: real] :
% 5.48/5.72 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.48/5.72 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add_numeral2
% 5.48/5.72 thf(fact_671_power__add__numeral2,axiom,
% 5.48/5.72 ! [A: rat,M: num,N: num,B: rat] :
% 5.48/5.72 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.48/5.72 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add_numeral2
% 5.48/5.72 thf(fact_672_power__add__numeral2,axiom,
% 5.48/5.72 ! [A: nat,M: num,N: num,B: nat] :
% 5.48/5.72 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.48/5.72 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add_numeral2
% 5.48/5.72 thf(fact_673_power__add__numeral2,axiom,
% 5.48/5.72 ! [A: int,M: num,N: num,B: int] :
% 5.48/5.72 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.48/5.72 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add_numeral2
% 5.48/5.72 thf(fact_674_power__strict__increasing__iff,axiom,
% 5.48/5.72 ! [B: real,X2: nat,Y2: nat] :
% 5.48/5.72 ( ( ord_less_real @ one_one_real @ B )
% 5.48/5.72 => ( ( ord_less_real @ ( power_power_real @ B @ X2 ) @ ( power_power_real @ B @ Y2 ) )
% 5.48/5.72 = ( ord_less_nat @ X2 @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_strict_increasing_iff
% 5.48/5.72 thf(fact_675_power__strict__increasing__iff,axiom,
% 5.48/5.72 ! [B: rat,X2: nat,Y2: nat] :
% 5.48/5.72 ( ( ord_less_rat @ one_one_rat @ B )
% 5.48/5.72 => ( ( ord_less_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y2 ) )
% 5.48/5.72 = ( ord_less_nat @ X2 @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_strict_increasing_iff
% 5.48/5.72 thf(fact_676_power__strict__increasing__iff,axiom,
% 5.48/5.72 ! [B: nat,X2: nat,Y2: nat] :
% 5.48/5.72 ( ( ord_less_nat @ one_one_nat @ B )
% 5.48/5.72 => ( ( ord_less_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y2 ) )
% 5.48/5.72 = ( ord_less_nat @ X2 @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_strict_increasing_iff
% 5.48/5.72 thf(fact_677_power__strict__increasing__iff,axiom,
% 5.48/5.72 ! [B: int,X2: nat,Y2: nat] :
% 5.48/5.72 ( ( ord_less_int @ one_one_int @ B )
% 5.48/5.72 => ( ( ord_less_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y2 ) )
% 5.48/5.72 = ( ord_less_nat @ X2 @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_strict_increasing_iff
% 5.48/5.72 thf(fact_678_ex__power__ivl1,axiom,
% 5.48/5.72 ! [B: nat,K: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.48/5.72 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.48/5.72 => ? [N2: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.48/5.72 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % ex_power_ivl1
% 5.48/5.72 thf(fact_679_ex__power__ivl2,axiom,
% 5.48/5.72 ! [B: nat,K: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.48/5.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.48/5.72 => ? [N2: nat] :
% 5.48/5.72 ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.48/5.72 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % ex_power_ivl2
% 5.48/5.72 thf(fact_680_power__mult__numeral,axiom,
% 5.48/5.72 ! [A: nat,M: num,N: num] :
% 5.48/5.72 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.48/5.72 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult_numeral
% 5.48/5.72 thf(fact_681_power__mult__numeral,axiom,
% 5.48/5.72 ! [A: real,M: num,N: num] :
% 5.48/5.72 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.48/5.72 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult_numeral
% 5.48/5.72 thf(fact_682_power__mult__numeral,axiom,
% 5.48/5.72 ! [A: int,M: num,N: num] :
% 5.48/5.72 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.48/5.72 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult_numeral
% 5.48/5.72 thf(fact_683_power__mult__numeral,axiom,
% 5.48/5.72 ! [A: complex,M: num,N: num] :
% 5.48/5.72 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.48/5.72 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult_numeral
% 5.48/5.72 thf(fact_684_sum__squares__bound,axiom,
% 5.48/5.72 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % sum_squares_bound
% 5.48/5.72 thf(fact_685_sum__squares__bound,axiom,
% 5.48/5.72 ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % sum_squares_bound
% 5.48/5.72 thf(fact_686_power__inject__exp,axiom,
% 5.48/5.72 ! [A: real,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_real @ one_one_real @ A )
% 5.48/5.72 => ( ( ( power_power_real @ A @ M )
% 5.48/5.72 = ( power_power_real @ A @ N ) )
% 5.48/5.72 = ( M = N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_inject_exp
% 5.48/5.72 thf(fact_687_power__inject__exp,axiom,
% 5.48/5.72 ! [A: rat,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_rat @ one_one_rat @ A )
% 5.48/5.72 => ( ( ( power_power_rat @ A @ M )
% 5.48/5.72 = ( power_power_rat @ A @ N ) )
% 5.48/5.72 = ( M = N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_inject_exp
% 5.48/5.72 thf(fact_688_power__inject__exp,axiom,
% 5.48/5.72 ! [A: nat,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_nat @ one_one_nat @ A )
% 5.48/5.72 => ( ( ( power_power_nat @ A @ M )
% 5.48/5.72 = ( power_power_nat @ A @ N ) )
% 5.48/5.72 = ( M = N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_inject_exp
% 5.48/5.72 thf(fact_689_power__inject__exp,axiom,
% 5.48/5.72 ! [A: int,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_int @ one_one_int @ A )
% 5.48/5.72 => ( ( ( power_power_int @ A @ M )
% 5.48/5.72 = ( power_power_int @ A @ N ) )
% 5.48/5.72 = ( M = N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_inject_exp
% 5.48/5.72 thf(fact_690_power2__sum,axiom,
% 5.48/5.72 ! [X2: complex,Y2: complex] :
% 5.48/5.72 ( ( power_power_complex @ ( plus_plus_complex @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power2_sum
% 5.48/5.72 thf(fact_691_power2__sum,axiom,
% 5.48/5.72 ! [X2: real,Y2: real] :
% 5.48/5.72 ( ( power_power_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power2_sum
% 5.48/5.72 thf(fact_692_power2__sum,axiom,
% 5.48/5.72 ! [X2: rat,Y2: rat] :
% 5.48/5.72 ( ( power_power_rat @ ( plus_plus_rat @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power2_sum
% 5.48/5.72 thf(fact_693_power2__sum,axiom,
% 5.48/5.72 ! [X2: nat,Y2: nat] :
% 5.48/5.72 ( ( power_power_nat @ ( plus_plus_nat @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power2_sum
% 5.48/5.72 thf(fact_694_power2__sum,axiom,
% 5.48/5.72 ! [X2: int,Y2: int] :
% 5.48/5.72 ( ( power_power_int @ ( plus_plus_int @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power2_sum
% 5.48/5.72 thf(fact_695_mi__ma__2__deg,axiom,
% 5.48/5.72 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.48/5.72 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.48/5.72 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % mi_ma_2_deg
% 5.48/5.72 thf(fact_696_deg__deg__n,axiom,
% 5.48/5.72 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.48/5.72 => ( Deg = N ) ) ).
% 5.48/5.72
% 5.48/5.72 % deg_deg_n
% 5.48/5.72 thf(fact_697__C5_Ohyps_C_I1_J,axiom,
% 5.48/5.72 vEBT_invar_vebt @ summary @ m ).
% 5.48/5.72
% 5.48/5.72 % "5.hyps"(1)
% 5.48/5.72 thf(fact_698_local_Opower__def,axiom,
% 5.48/5.72 ( vEBT_VEBT_power
% 5.48/5.72 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.48/5.72
% 5.48/5.72 % local.power_def
% 5.48/5.72 thf(fact_699__C5_Ohyps_C_I4_J,axiom,
% 5.48/5.72 ( deg
% 5.48/5.72 = ( plus_plus_nat @ na @ m ) ) ).
% 5.48/5.72
% 5.48/5.72 % "5.hyps"(4)
% 5.48/5.72 thf(fact_700_geqmaxNone,axiom,
% 5.48/5.72 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.48/5.72 => ( ( ord_less_eq_nat @ Ma @ X2 )
% 5.48/5.72 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.48/5.72 = none_nat ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % geqmaxNone
% 5.48/5.72 thf(fact_701_power__one,axiom,
% 5.48/5.72 ! [N: nat] :
% 5.48/5.72 ( ( power_power_rat @ one_one_rat @ N )
% 5.48/5.72 = one_one_rat ) ).
% 5.48/5.72
% 5.48/5.72 % power_one
% 5.48/5.72 thf(fact_702_power__one,axiom,
% 5.48/5.72 ! [N: nat] :
% 5.48/5.72 ( ( power_power_nat @ one_one_nat @ N )
% 5.48/5.72 = one_one_nat ) ).
% 5.48/5.72
% 5.48/5.72 % power_one
% 5.48/5.72 thf(fact_703_power__one,axiom,
% 5.48/5.72 ! [N: nat] :
% 5.48/5.72 ( ( power_power_real @ one_one_real @ N )
% 5.48/5.72 = one_one_real ) ).
% 5.48/5.72
% 5.48/5.72 % power_one
% 5.48/5.72 thf(fact_704_power__one,axiom,
% 5.48/5.72 ! [N: nat] :
% 5.48/5.72 ( ( power_power_int @ one_one_int @ N )
% 5.48/5.72 = one_one_int ) ).
% 5.48/5.72
% 5.48/5.72 % power_one
% 5.48/5.72 thf(fact_705_power__one,axiom,
% 5.48/5.72 ! [N: nat] :
% 5.48/5.72 ( ( power_power_complex @ one_one_complex @ N )
% 5.48/5.72 = one_one_complex ) ).
% 5.48/5.72
% 5.48/5.72 % power_one
% 5.48/5.72 thf(fact_706_two__powr__height__bound__deg,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_VEBT_height @ T ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % two_powr_height_bound_deg
% 5.48/5.72 thf(fact_707_helpyd,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,X2: nat,Y2: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.48/5.72 = ( some_nat @ Y2 ) )
% 5.48/5.72 => ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % helpyd
% 5.48/5.72 thf(fact_708_power__one__right,axiom,
% 5.48/5.72 ! [A: nat] :
% 5.48/5.72 ( ( power_power_nat @ A @ one_one_nat )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % power_one_right
% 5.48/5.72 thf(fact_709_power__one__right,axiom,
% 5.48/5.72 ! [A: real] :
% 5.48/5.72 ( ( power_power_real @ A @ one_one_nat )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % power_one_right
% 5.48/5.72 thf(fact_710_power__one__right,axiom,
% 5.48/5.72 ! [A: int] :
% 5.48/5.72 ( ( power_power_int @ A @ one_one_nat )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % power_one_right
% 5.48/5.72 thf(fact_711_power__one__right,axiom,
% 5.48/5.72 ! [A: complex] :
% 5.48/5.72 ( ( power_power_complex @ A @ one_one_nat )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % power_one_right
% 5.48/5.72 thf(fact_712_helpypredd,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,X2: nat,Y2: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.48/5.72 = ( some_nat @ Y2 ) )
% 5.48/5.72 => ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % helpypredd
% 5.48/5.72 thf(fact_713__C5_Ohyps_C_I5_J,axiom,
% 5.48/5.72 ! [I3: nat] :
% 5.48/5.72 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.48/5.72 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I3 ) @ X7 ) )
% 5.48/5.72 = ( vEBT_V8194947554948674370ptions @ summary @ I3 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % "5.hyps"(5)
% 5.48/5.72 thf(fact_714_enat__less__induct,axiom,
% 5.48/5.72 ! [P: extended_enat > $o,N: extended_enat] :
% 5.48/5.72 ( ! [N2: extended_enat] :
% 5.48/5.72 ( ! [M2: extended_enat] :
% 5.48/5.72 ( ( ord_le72135733267957522d_enat @ M2 @ N2 )
% 5.48/5.72 => ( P @ M2 ) )
% 5.48/5.72 => ( P @ N2 ) )
% 5.48/5.72 => ( P @ N ) ) ).
% 5.48/5.72
% 5.48/5.72 % enat_less_induct
% 5.48/5.72 thf(fact_715_L2__set__mult__ineq__lemma,axiom,
% 5.48/5.72 ! [A: real,C: real,B: real,D2: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ D2 ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % L2_set_mult_ineq_lemma
% 5.48/5.72 thf(fact_716_four__x__squared,axiom,
% 5.48/5.72 ! [X2: real] :
% 5.48/5.72 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.48/5.72 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % four_x_squared
% 5.48/5.72 thf(fact_717_two__realpow__ge__one,axiom,
% 5.48/5.72 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.48/5.72
% 5.48/5.72 % two_realpow_ge_one
% 5.48/5.72 thf(fact_718_height__node,axiom,
% 5.48/5.72 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.48/5.72 => ( ord_less_eq_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % height_node
% 5.48/5.72 thf(fact_719_power__commuting__commutes,axiom,
% 5.48/5.72 ! [X2: complex,Y2: complex,N: nat] :
% 5.48/5.72 ( ( ( times_times_complex @ X2 @ Y2 )
% 5.48/5.72 = ( times_times_complex @ Y2 @ X2 ) )
% 5.48/5.72 => ( ( times_times_complex @ ( power_power_complex @ X2 @ N ) @ Y2 )
% 5.48/5.72 = ( times_times_complex @ Y2 @ ( power_power_complex @ X2 @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_commuting_commutes
% 5.48/5.72 thf(fact_720_power__commuting__commutes,axiom,
% 5.48/5.72 ! [X2: real,Y2: real,N: nat] :
% 5.48/5.72 ( ( ( times_times_real @ X2 @ Y2 )
% 5.48/5.72 = ( times_times_real @ Y2 @ X2 ) )
% 5.48/5.72 => ( ( times_times_real @ ( power_power_real @ X2 @ N ) @ Y2 )
% 5.48/5.72 = ( times_times_real @ Y2 @ ( power_power_real @ X2 @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_commuting_commutes
% 5.48/5.72 thf(fact_721_power__commuting__commutes,axiom,
% 5.48/5.72 ! [X2: rat,Y2: rat,N: nat] :
% 5.48/5.72 ( ( ( times_times_rat @ X2 @ Y2 )
% 5.48/5.72 = ( times_times_rat @ Y2 @ X2 ) )
% 5.48/5.72 => ( ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ Y2 )
% 5.48/5.72 = ( times_times_rat @ Y2 @ ( power_power_rat @ X2 @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_commuting_commutes
% 5.48/5.72 thf(fact_722_power__commuting__commutes,axiom,
% 5.48/5.72 ! [X2: nat,Y2: nat,N: nat] :
% 5.48/5.72 ( ( ( times_times_nat @ X2 @ Y2 )
% 5.48/5.72 = ( times_times_nat @ Y2 @ X2 ) )
% 5.48/5.72 => ( ( times_times_nat @ ( power_power_nat @ X2 @ N ) @ Y2 )
% 5.48/5.72 = ( times_times_nat @ Y2 @ ( power_power_nat @ X2 @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_commuting_commutes
% 5.48/5.72 thf(fact_723_power__commuting__commutes,axiom,
% 5.48/5.72 ! [X2: int,Y2: int,N: nat] :
% 5.48/5.72 ( ( ( times_times_int @ X2 @ Y2 )
% 5.48/5.72 = ( times_times_int @ Y2 @ X2 ) )
% 5.48/5.72 => ( ( times_times_int @ ( power_power_int @ X2 @ N ) @ Y2 )
% 5.48/5.72 = ( times_times_int @ Y2 @ ( power_power_int @ X2 @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_commuting_commutes
% 5.48/5.72 thf(fact_724_power__mult__distrib,axiom,
% 5.48/5.72 ! [A: complex,B: complex,N: nat] :
% 5.48/5.72 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 5.48/5.72 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult_distrib
% 5.48/5.72 thf(fact_725_power__mult__distrib,axiom,
% 5.48/5.72 ! [A: real,B: real,N: nat] :
% 5.48/5.72 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 5.48/5.72 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult_distrib
% 5.48/5.72 thf(fact_726_power__mult__distrib,axiom,
% 5.48/5.72 ! [A: rat,B: rat,N: nat] :
% 5.48/5.72 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 5.48/5.72 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult_distrib
% 5.48/5.72 thf(fact_727_power__mult__distrib,axiom,
% 5.48/5.72 ! [A: nat,B: nat,N: nat] :
% 5.48/5.72 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 5.48/5.72 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult_distrib
% 5.48/5.72 thf(fact_728_power__mult__distrib,axiom,
% 5.48/5.72 ! [A: int,B: int,N: nat] :
% 5.48/5.72 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 5.48/5.72 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult_distrib
% 5.48/5.72 thf(fact_729_power__commutes,axiom,
% 5.48/5.72 ! [A: complex,N: nat] :
% 5.48/5.72 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 5.48/5.72 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_commutes
% 5.48/5.72 thf(fact_730_power__commutes,axiom,
% 5.48/5.72 ! [A: real,N: nat] :
% 5.48/5.72 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 5.48/5.72 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_commutes
% 5.48/5.72 thf(fact_731_power__commutes,axiom,
% 5.48/5.72 ! [A: rat,N: nat] :
% 5.48/5.72 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 5.48/5.72 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_commutes
% 5.48/5.72 thf(fact_732_power__commutes,axiom,
% 5.48/5.72 ! [A: nat,N: nat] :
% 5.48/5.72 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 5.48/5.72 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_commutes
% 5.48/5.72 thf(fact_733_power__commutes,axiom,
% 5.48/5.72 ! [A: int,N: nat] :
% 5.48/5.72 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 5.48/5.72 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_commutes
% 5.48/5.72 thf(fact_734_power__divide,axiom,
% 5.48/5.72 ! [A: complex,B: complex,N: nat] :
% 5.48/5.72 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 5.48/5.72 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_divide
% 5.48/5.72 thf(fact_735_power__divide,axiom,
% 5.48/5.72 ! [A: real,B: real,N: nat] :
% 5.48/5.72 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 5.48/5.72 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_divide
% 5.48/5.72 thf(fact_736_power__divide,axiom,
% 5.48/5.72 ! [A: rat,B: rat,N: nat] :
% 5.48/5.72 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 5.48/5.72 = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_divide
% 5.48/5.72 thf(fact_737_power__mult,axiom,
% 5.48/5.72 ! [A: nat,M: nat,N: nat] :
% 5.48/5.72 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 5.48/5.72 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult
% 5.48/5.72 thf(fact_738_power__mult,axiom,
% 5.48/5.72 ! [A: real,M: nat,N: nat] :
% 5.48/5.72 ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 5.48/5.72 = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult
% 5.48/5.72 thf(fact_739_power__mult,axiom,
% 5.48/5.72 ! [A: int,M: nat,N: nat] :
% 5.48/5.72 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 5.48/5.72 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult
% 5.48/5.72 thf(fact_740_power__mult,axiom,
% 5.48/5.72 ! [A: complex,M: nat,N: nat] :
% 5.48/5.72 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 5.48/5.72 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_mult
% 5.48/5.72 thf(fact_741_one__le__power,axiom,
% 5.48/5.72 ! [A: real,N: nat] :
% 5.48/5.72 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.48/5.72 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % one_le_power
% 5.48/5.72 thf(fact_742_one__le__power,axiom,
% 5.48/5.72 ! [A: rat,N: nat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.48/5.72 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % one_le_power
% 5.48/5.72 thf(fact_743_one__le__power,axiom,
% 5.48/5.72 ! [A: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.48/5.72 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % one_le_power
% 5.48/5.72 thf(fact_744_one__le__power,axiom,
% 5.48/5.72 ! [A: int,N: nat] :
% 5.48/5.72 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.48/5.72 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % one_le_power
% 5.48/5.72 thf(fact_745_left__right__inverse__power,axiom,
% 5.48/5.72 ! [X2: complex,Y2: complex,N: nat] :
% 5.48/5.72 ( ( ( times_times_complex @ X2 @ Y2 )
% 5.48/5.72 = one_one_complex )
% 5.48/5.72 => ( ( times_times_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y2 @ N ) )
% 5.48/5.72 = one_one_complex ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_right_inverse_power
% 5.48/5.72 thf(fact_746_left__right__inverse__power,axiom,
% 5.48/5.72 ! [X2: real,Y2: real,N: nat] :
% 5.48/5.72 ( ( ( times_times_real @ X2 @ Y2 )
% 5.48/5.72 = one_one_real )
% 5.48/5.72 => ( ( times_times_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y2 @ N ) )
% 5.48/5.72 = one_one_real ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_right_inverse_power
% 5.48/5.72 thf(fact_747_left__right__inverse__power,axiom,
% 5.48/5.72 ! [X2: rat,Y2: rat,N: nat] :
% 5.48/5.72 ( ( ( times_times_rat @ X2 @ Y2 )
% 5.48/5.72 = one_one_rat )
% 5.48/5.72 => ( ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ Y2 @ N ) )
% 5.48/5.72 = one_one_rat ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_right_inverse_power
% 5.48/5.72 thf(fact_748_left__right__inverse__power,axiom,
% 5.48/5.72 ! [X2: nat,Y2: nat,N: nat] :
% 5.48/5.72 ( ( ( times_times_nat @ X2 @ Y2 )
% 5.48/5.72 = one_one_nat )
% 5.48/5.72 => ( ( times_times_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y2 @ N ) )
% 5.48/5.72 = one_one_nat ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_right_inverse_power
% 5.48/5.72 thf(fact_749_left__right__inverse__power,axiom,
% 5.48/5.72 ! [X2: int,Y2: int,N: nat] :
% 5.48/5.72 ( ( ( times_times_int @ X2 @ Y2 )
% 5.48/5.72 = one_one_int )
% 5.48/5.72 => ( ( times_times_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y2 @ N ) )
% 5.48/5.72 = one_one_int ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_right_inverse_power
% 5.48/5.72 thf(fact_750_power__one__over,axiom,
% 5.48/5.72 ! [A: complex,N: nat] :
% 5.48/5.72 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 5.48/5.72 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_one_over
% 5.48/5.72 thf(fact_751_power__one__over,axiom,
% 5.48/5.72 ! [A: real,N: nat] :
% 5.48/5.72 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 5.48/5.72 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_one_over
% 5.48/5.72 thf(fact_752_power__one__over,axiom,
% 5.48/5.72 ! [A: rat,N: nat] :
% 5.48/5.72 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 5.48/5.72 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_one_over
% 5.48/5.72 thf(fact_753_power__add,axiom,
% 5.48/5.72 ! [A: complex,M: nat,N: nat] :
% 5.48/5.72 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 5.48/5.72 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add
% 5.48/5.72 thf(fact_754_power__add,axiom,
% 5.48/5.72 ! [A: real,M: nat,N: nat] :
% 5.48/5.72 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 5.48/5.72 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add
% 5.48/5.72 thf(fact_755_power__add,axiom,
% 5.48/5.72 ! [A: rat,M: nat,N: nat] :
% 5.48/5.72 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.48/5.72 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add
% 5.48/5.72 thf(fact_756_power__add,axiom,
% 5.48/5.72 ! [A: nat,M: nat,N: nat] :
% 5.48/5.72 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.48/5.72 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add
% 5.48/5.72 thf(fact_757_power__add,axiom,
% 5.48/5.72 ! [A: int,M: nat,N: nat] :
% 5.48/5.72 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 5.48/5.72 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_add
% 5.48/5.72 thf(fact_758_power__less__power__Suc,axiom,
% 5.48/5.72 ! [A: real,N: nat] :
% 5.48/5.72 ( ( ord_less_real @ one_one_real @ A )
% 5.48/5.72 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_less_power_Suc
% 5.48/5.72 thf(fact_759_power__less__power__Suc,axiom,
% 5.48/5.72 ! [A: rat,N: nat] :
% 5.48/5.72 ( ( ord_less_rat @ one_one_rat @ A )
% 5.48/5.72 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_less_power_Suc
% 5.48/5.72 thf(fact_760_power__less__power__Suc,axiom,
% 5.48/5.72 ! [A: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_nat @ one_one_nat @ A )
% 5.48/5.72 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_less_power_Suc
% 5.48/5.72 thf(fact_761_power__less__power__Suc,axiom,
% 5.48/5.72 ! [A: int,N: nat] :
% 5.48/5.72 ( ( ord_less_int @ one_one_int @ A )
% 5.48/5.72 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_less_power_Suc
% 5.48/5.72 thf(fact_762_power__gt1__lemma,axiom,
% 5.48/5.72 ! [A: real,N: nat] :
% 5.48/5.72 ( ( ord_less_real @ one_one_real @ A )
% 5.48/5.72 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_gt1_lemma
% 5.48/5.72 thf(fact_763_power__gt1__lemma,axiom,
% 5.48/5.72 ! [A: rat,N: nat] :
% 5.48/5.72 ( ( ord_less_rat @ one_one_rat @ A )
% 5.48/5.72 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_gt1_lemma
% 5.48/5.72 thf(fact_764_power__gt1__lemma,axiom,
% 5.48/5.72 ! [A: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_nat @ one_one_nat @ A )
% 5.48/5.72 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_gt1_lemma
% 5.48/5.72 thf(fact_765_power__gt1__lemma,axiom,
% 5.48/5.72 ! [A: int,N: nat] :
% 5.48/5.72 ( ( ord_less_int @ one_one_int @ A )
% 5.48/5.72 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_gt1_lemma
% 5.48/5.72 thf(fact_766_power__strict__increasing,axiom,
% 5.48/5.72 ! [N: nat,N4: nat,A: real] :
% 5.48/5.72 ( ( ord_less_nat @ N @ N4 )
% 5.48/5.72 => ( ( ord_less_real @ one_one_real @ A )
% 5.48/5.72 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_strict_increasing
% 5.48/5.72 thf(fact_767_power__strict__increasing,axiom,
% 5.48/5.72 ! [N: nat,N4: nat,A: rat] :
% 5.48/5.72 ( ( ord_less_nat @ N @ N4 )
% 5.48/5.72 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.48/5.72 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_strict_increasing
% 5.48/5.72 thf(fact_768_power__strict__increasing,axiom,
% 5.48/5.72 ! [N: nat,N4: nat,A: nat] :
% 5.48/5.72 ( ( ord_less_nat @ N @ N4 )
% 5.48/5.72 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.48/5.72 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_strict_increasing
% 5.48/5.72 thf(fact_769_power__strict__increasing,axiom,
% 5.48/5.72 ! [N: nat,N4: nat,A: int] :
% 5.48/5.72 ( ( ord_less_nat @ N @ N4 )
% 5.48/5.72 => ( ( ord_less_int @ one_one_int @ A )
% 5.48/5.72 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_strict_increasing
% 5.48/5.72 thf(fact_770_power__less__imp__less__exp,axiom,
% 5.48/5.72 ! [A: real,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_real @ one_one_real @ A )
% 5.48/5.72 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.48/5.72 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_less_imp_less_exp
% 5.48/5.72 thf(fact_771_power__less__imp__less__exp,axiom,
% 5.48/5.72 ! [A: rat,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_rat @ one_one_rat @ A )
% 5.48/5.72 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.48/5.72 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_less_imp_less_exp
% 5.48/5.72 thf(fact_772_power__less__imp__less__exp,axiom,
% 5.48/5.72 ! [A: nat,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_nat @ one_one_nat @ A )
% 5.48/5.72 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.48/5.72 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_less_imp_less_exp
% 5.48/5.72 thf(fact_773_power__less__imp__less__exp,axiom,
% 5.48/5.72 ! [A: int,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_int @ one_one_int @ A )
% 5.48/5.72 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.48/5.72 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_less_imp_less_exp
% 5.48/5.72 thf(fact_774_power__increasing,axiom,
% 5.48/5.72 ! [N: nat,N4: nat,A: real] :
% 5.48/5.72 ( ( ord_less_eq_nat @ N @ N4 )
% 5.48/5.72 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.48/5.72 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_increasing
% 5.48/5.72 thf(fact_775_power__increasing,axiom,
% 5.48/5.72 ! [N: nat,N4: nat,A: rat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ N @ N4 )
% 5.48/5.72 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.48/5.72 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_increasing
% 5.48/5.72 thf(fact_776_power__increasing,axiom,
% 5.48/5.72 ! [N: nat,N4: nat,A: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ N @ N4 )
% 5.48/5.72 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.48/5.72 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_increasing
% 5.48/5.72 thf(fact_777_power__increasing,axiom,
% 5.48/5.72 ! [N: nat,N4: nat,A: int] :
% 5.48/5.72 ( ( ord_less_eq_nat @ N @ N4 )
% 5.48/5.72 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.48/5.72 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_increasing
% 5.48/5.72 thf(fact_778_power__le__imp__le__exp,axiom,
% 5.48/5.72 ! [A: real,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_real @ one_one_real @ A )
% 5.48/5.72 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.48/5.72 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_le_imp_le_exp
% 5.48/5.72 thf(fact_779_power__le__imp__le__exp,axiom,
% 5.48/5.72 ! [A: rat,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_rat @ one_one_rat @ A )
% 5.48/5.72 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.48/5.72 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_le_imp_le_exp
% 5.48/5.72 thf(fact_780_power__le__imp__le__exp,axiom,
% 5.48/5.72 ! [A: nat,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_nat @ one_one_nat @ A )
% 5.48/5.72 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.48/5.72 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_le_imp_le_exp
% 5.48/5.72 thf(fact_781_power__le__imp__le__exp,axiom,
% 5.48/5.72 ! [A: int,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_int @ one_one_int @ A )
% 5.48/5.72 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.48/5.72 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_le_imp_le_exp
% 5.48/5.72 thf(fact_782_power2__eq__square,axiom,
% 5.48/5.72 ! [A: complex] :
% 5.48/5.72 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = ( times_times_complex @ A @ A ) ) ).
% 5.48/5.72
% 5.48/5.72 % power2_eq_square
% 5.48/5.72 thf(fact_783_power2__eq__square,axiom,
% 5.48/5.72 ! [A: real] :
% 5.48/5.72 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = ( times_times_real @ A @ A ) ) ).
% 5.48/5.72
% 5.48/5.72 % power2_eq_square
% 5.48/5.72 thf(fact_784_power2__eq__square,axiom,
% 5.48/5.72 ! [A: rat] :
% 5.48/5.72 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = ( times_times_rat @ A @ A ) ) ).
% 5.48/5.72
% 5.48/5.72 % power2_eq_square
% 5.48/5.72 thf(fact_785_power2__eq__square,axiom,
% 5.48/5.72 ! [A: nat] :
% 5.48/5.72 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = ( times_times_nat @ A @ A ) ) ).
% 5.48/5.72
% 5.48/5.72 % power2_eq_square
% 5.48/5.72 thf(fact_786_power2__eq__square,axiom,
% 5.48/5.72 ! [A: int] :
% 5.48/5.72 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = ( times_times_int @ A @ A ) ) ).
% 5.48/5.72
% 5.48/5.72 % power2_eq_square
% 5.48/5.72 thf(fact_787_power4__eq__xxxx,axiom,
% 5.48/5.72 ! [X2: complex] :
% 5.48/5.72 ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.48/5.72 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.48/5.72
% 5.48/5.72 % power4_eq_xxxx
% 5.48/5.72 thf(fact_788_power4__eq__xxxx,axiom,
% 5.48/5.72 ! [X2: real] :
% 5.48/5.72 ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.48/5.72 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.48/5.72
% 5.48/5.72 % power4_eq_xxxx
% 5.48/5.72 thf(fact_789_power4__eq__xxxx,axiom,
% 5.48/5.72 ! [X2: rat] :
% 5.48/5.72 ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.48/5.72 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.48/5.72
% 5.48/5.72 % power4_eq_xxxx
% 5.48/5.72 thf(fact_790_power4__eq__xxxx,axiom,
% 5.48/5.72 ! [X2: nat] :
% 5.48/5.72 ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.48/5.72 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.48/5.72
% 5.48/5.72 % power4_eq_xxxx
% 5.48/5.72 thf(fact_791_power4__eq__xxxx,axiom,
% 5.48/5.72 ! [X2: int] :
% 5.48/5.72 ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.48/5.72 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.48/5.72
% 5.48/5.72 % power4_eq_xxxx
% 5.48/5.72 thf(fact_792_one__power2,axiom,
% 5.48/5.72 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = one_one_rat ) ).
% 5.48/5.72
% 5.48/5.72 % one_power2
% 5.48/5.72 thf(fact_793_one__power2,axiom,
% 5.48/5.72 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = one_one_nat ) ).
% 5.48/5.72
% 5.48/5.72 % one_power2
% 5.48/5.72 thf(fact_794_one__power2,axiom,
% 5.48/5.72 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = one_one_real ) ).
% 5.48/5.72
% 5.48/5.72 % one_power2
% 5.48/5.72 thf(fact_795_one__power2,axiom,
% 5.48/5.72 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = one_one_int ) ).
% 5.48/5.72
% 5.48/5.72 % one_power2
% 5.48/5.72 thf(fact_796_one__power2,axiom,
% 5.48/5.72 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.72 = one_one_complex ) ).
% 5.48/5.72
% 5.48/5.72 % one_power2
% 5.48/5.72 thf(fact_797_power3__eq__cube,axiom,
% 5.48/5.72 ! [A: complex] :
% 5.48/5.72 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.48/5.72 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.48/5.72
% 5.48/5.72 % power3_eq_cube
% 5.48/5.72 thf(fact_798_power3__eq__cube,axiom,
% 5.48/5.72 ! [A: real] :
% 5.48/5.72 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.48/5.72 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.48/5.72
% 5.48/5.72 % power3_eq_cube
% 5.48/5.72 thf(fact_799_power3__eq__cube,axiom,
% 5.48/5.72 ! [A: rat] :
% 5.48/5.72 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.48/5.72 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.48/5.72
% 5.48/5.72 % power3_eq_cube
% 5.48/5.72 thf(fact_800_power3__eq__cube,axiom,
% 5.48/5.72 ! [A: nat] :
% 5.48/5.72 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.48/5.72 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.48/5.72
% 5.48/5.72 % power3_eq_cube
% 5.48/5.72 thf(fact_801_power3__eq__cube,axiom,
% 5.48/5.72 ! [A: int] :
% 5.48/5.72 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.48/5.72 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.48/5.72
% 5.48/5.72 % power3_eq_cube
% 5.48/5.72 thf(fact_802_power__even__eq,axiom,
% 5.48/5.72 ! [A: nat,N: nat] :
% 5.48/5.72 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.72 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_even_eq
% 5.48/5.72 thf(fact_803_power__even__eq,axiom,
% 5.48/5.72 ! [A: real,N: nat] :
% 5.48/5.72 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.72 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_even_eq
% 5.48/5.72 thf(fact_804_power__even__eq,axiom,
% 5.48/5.72 ! [A: int,N: nat] :
% 5.48/5.72 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.72 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_even_eq
% 5.48/5.72 thf(fact_805_power__even__eq,axiom,
% 5.48/5.72 ! [A: complex,N: nat] :
% 5.48/5.72 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.72 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_even_eq
% 5.48/5.72 thf(fact_806_less__exp,axiom,
% 5.48/5.72 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.48/5.72
% 5.48/5.72 % less_exp
% 5.48/5.72 thf(fact_807_power2__nat__le__imp__le,axiom,
% 5.48/5.72 ! [M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.48/5.72 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.48/5.72
% 5.48/5.72 % power2_nat_le_imp_le
% 5.48/5.72 thf(fact_808_power2__nat__le__eq__le,axiom,
% 5.48/5.72 ! [M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.48/5.72 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.48/5.72
% 5.48/5.72 % power2_nat_le_eq_le
% 5.48/5.72 thf(fact_809_self__le__ge2__pow,axiom,
% 5.48/5.72 ! [K: nat,M: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.48/5.72 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % self_le_ge2_pow
% 5.48/5.72 thf(fact_810_summaxma,axiom,
% 5.48/5.72 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.48/5.72 => ( ( Mi != Ma )
% 5.48/5.72 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.48/5.72 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % summaxma
% 5.48/5.72 thf(fact_811_misiz,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,M: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( ( some_nat @ M )
% 5.48/5.72 = ( vEBT_vebt_mint @ T ) )
% 5.48/5.72 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % misiz
% 5.48/5.72 thf(fact_812_post__member__pre__member,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,X2: nat,Y2: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.72 => ( ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.72 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X2 ) @ Y2 )
% 5.48/5.72 => ( ( vEBT_vebt_member @ T @ Y2 )
% 5.48/5.72 | ( X2 = Y2 ) ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % post_member_pre_member
% 5.48/5.72 thf(fact_813__C5_OIH_C_I1_J,axiom,
% 5.48/5.72 ! [X6: vEBT_VEBT] :
% 5.48/5.72 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.48/5.72 => ( ( vEBT_invar_vebt @ X6 @ na )
% 5.48/5.72 & ! [Xa: nat] : ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c @ X6 @ Xa ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ X6 ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % "5.IH"(1)
% 5.48/5.72 thf(fact_814_member__bound,axiom,
% 5.48/5.72 ! [Tree: vEBT_VEBT,X2: nat,N: nat] :
% 5.48/5.72 ( ( vEBT_vebt_member @ Tree @ X2 )
% 5.48/5.72 => ( ( vEBT_invar_vebt @ Tree @ N )
% 5.48/5.72 => ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % member_bound
% 5.48/5.72 thf(fact_815_set__n__deg__not__0,axiom,
% 5.48/5.72 ! [TreeList: list_VEBT_VEBT,N: nat,M: nat] :
% 5.48/5.72 ( ! [X4: vEBT_VEBT] :
% 5.48/5.72 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.48/5.72 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.48/5.72 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.48/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.48/5.72 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % set_n_deg_not_0
% 5.48/5.72 thf(fact_816_power__minus__is__div,axiom,
% 5.48/5.72 ! [B: nat,A: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ B @ A )
% 5.48/5.72 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 5.48/5.72 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % power_minus_is_div
% 5.48/5.72 thf(fact_817_vebt__pred_Osimps_I4_J,axiom,
% 5.48/5.72 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.48/5.72 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.48/5.72 = none_nat ) ).
% 5.48/5.72
% 5.48/5.72 % vebt_pred.simps(4)
% 5.48/5.72 thf(fact_818_vebt__succ_Osimps_I3_J,axiom,
% 5.48/5.72 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.48/5.72 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.48/5.72 = none_nat ) ).
% 5.48/5.72
% 5.48/5.72 % vebt_succ.simps(3)
% 5.48/5.72 thf(fact_819_valid__insert__both__member__options__pres,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,X2: nat,Y2: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.72 => ( ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.72 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.48/5.72 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y2 ) @ X2 ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % valid_insert_both_member_options_pres
% 5.48/5.72 thf(fact_820_valid__insert__both__member__options__add,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.72 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X2 ) @ X2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % valid_insert_both_member_options_add
% 5.48/5.72 thf(fact_821_maxbmo,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,X2: nat] :
% 5.48/5.72 ( ( ( vEBT_vebt_maxt @ T )
% 5.48/5.72 = ( some_nat @ X2 ) )
% 5.48/5.72 => ( vEBT_V8194947554948674370ptions @ T @ X2 ) ) ).
% 5.48/5.72
% 5.48/5.72 % maxbmo
% 5.48/5.72 thf(fact_822_valid__member__both__member__options,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.48/5.72 => ( vEBT_vebt_member @ T @ X2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % valid_member_both_member_options
% 5.48/5.72 thf(fact_823_both__member__options__equiv__member,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.48/5.72 = ( vEBT_vebt_member @ T @ X2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % both_member_options_equiv_member
% 5.48/5.72 thf(fact_824_inthall,axiom,
% 5.48/5.72 ! [Xs2: list_option_nat,P: option_nat > $o,N: nat] :
% 5.48/5.72 ( ! [X4: option_nat] :
% 5.48/5.72 ( ( member_option_nat @ X4 @ ( set_option_nat2 @ Xs2 ) )
% 5.48/5.72 => ( P @ X4 ) )
% 5.48/5.72 => ( ( ord_less_nat @ N @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 5.48/5.72 => ( P @ ( nth_option_nat @ Xs2 @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % inthall
% 5.48/5.72 thf(fact_825_inthall,axiom,
% 5.48/5.72 ! [Xs2: list_real,P: real > $o,N: nat] :
% 5.48/5.72 ( ! [X4: real] :
% 5.48/5.72 ( ( member_real @ X4 @ ( set_real2 @ Xs2 ) )
% 5.48/5.72 => ( P @ X4 ) )
% 5.48/5.72 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.48/5.72 => ( P @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % inthall
% 5.48/5.72 thf(fact_826_inthall,axiom,
% 5.48/5.72 ! [Xs2: list_set_nat_rat,P: set_nat_rat > $o,N: nat] :
% 5.48/5.72 ( ! [X4: set_nat_rat] :
% 5.48/5.72 ( ( member_set_nat_rat @ X4 @ ( set_set_nat_rat2 @ Xs2 ) )
% 5.48/5.72 => ( P @ X4 ) )
% 5.48/5.72 => ( ( ord_less_nat @ N @ ( size_s3959913991096427681at_rat @ Xs2 ) )
% 5.48/5.72 => ( P @ ( nth_set_nat_rat @ Xs2 @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % inthall
% 5.48/5.72 thf(fact_827_inthall,axiom,
% 5.48/5.72 ! [Xs2: list_int,P: int > $o,N: nat] :
% 5.48/5.72 ( ! [X4: int] :
% 5.48/5.72 ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 5.48/5.72 => ( P @ X4 ) )
% 5.48/5.72 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.48/5.72 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % inthall
% 5.48/5.72 thf(fact_828_inthall,axiom,
% 5.48/5.72 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 5.48/5.72 ( ! [X4: vEBT_VEBT] :
% 5.48/5.72 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.48/5.72 => ( P @ X4 ) )
% 5.48/5.72 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.48/5.72 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % inthall
% 5.48/5.72 thf(fact_829_inthall,axiom,
% 5.48/5.72 ! [Xs2: list_o,P: $o > $o,N: nat] :
% 5.48/5.72 ( ! [X4: $o] :
% 5.48/5.72 ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 5.48/5.72 => ( P @ X4 ) )
% 5.48/5.72 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.48/5.72 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % inthall
% 5.48/5.72 thf(fact_830_inthall,axiom,
% 5.48/5.72 ! [Xs2: list_nat,P: nat > $o,N: nat] :
% 5.48/5.72 ( ! [X4: nat] :
% 5.48/5.72 ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 5.48/5.72 => ( P @ X4 ) )
% 5.48/5.72 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.48/5.72 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % inthall
% 5.48/5.72 thf(fact_831__C5_Ohyps_C_I6_J,axiom,
% 5.48/5.72 ( ( mi = ma )
% 5.48/5.72 => ! [X6: vEBT_VEBT] :
% 5.48/5.72 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.48/5.72 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % "5.hyps"(6)
% 5.48/5.72 thf(fact_832_maxt__member,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( ( vEBT_vebt_maxt @ T )
% 5.48/5.72 = ( some_nat @ Maxi ) )
% 5.48/5.72 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % maxt_member
% 5.48/5.72 thf(fact_833_mint__member,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( ( vEBT_vebt_mint @ T )
% 5.48/5.72 = ( some_nat @ Maxi ) )
% 5.48/5.72 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % mint_member
% 5.48/5.72 thf(fact_834_real__divide__square__eq,axiom,
% 5.48/5.72 ! [R: real,A: real] :
% 5.48/5.72 ( ( divide_divide_real @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ R ) )
% 5.48/5.72 = ( divide_divide_real @ A @ R ) ) ).
% 5.48/5.72
% 5.48/5.72 % real_divide_square_eq
% 5.48/5.72 thf(fact_835_maxt__corr__help,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X2: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( ( vEBT_vebt_maxt @ T )
% 5.48/5.72 = ( some_nat @ Maxi ) )
% 5.48/5.72 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.48/5.72 => ( ord_less_eq_nat @ X2 @ Maxi ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % maxt_corr_help
% 5.48/5.72 thf(fact_836_mint__corr__help,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,Mini: nat,X2: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( ( vEBT_vebt_mint @ T )
% 5.48/5.72 = ( some_nat @ Mini ) )
% 5.48/5.72 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.48/5.72 => ( ord_less_eq_nat @ Mini @ X2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % mint_corr_help
% 5.48/5.72 thf(fact_837_height__compose__child,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,Summary: vEBT_VEBT] :
% 5.48/5.72 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.48/5.72 => ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % height_compose_child
% 5.48/5.72 thf(fact_838_mi__eq__ma__no__ch,axiom,
% 5.48/5.72 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.48/5.72 => ( ( Mi = Ma )
% 5.48/5.72 => ( ! [X6: vEBT_VEBT] :
% 5.48/5.72 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.48/5.72 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) )
% 5.48/5.72 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % mi_eq_ma_no_ch
% 5.48/5.72 thf(fact_839_add__diff__cancel,axiom,
% 5.48/5.72 ! [A: complex,B: complex] :
% 5.48/5.72 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel
% 5.48/5.72 thf(fact_840_add__diff__cancel,axiom,
% 5.48/5.72 ! [A: real,B: real] :
% 5.48/5.72 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel
% 5.48/5.72 thf(fact_841_add__diff__cancel,axiom,
% 5.48/5.72 ! [A: rat,B: rat] :
% 5.48/5.72 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel
% 5.48/5.72 thf(fact_842_add__diff__cancel,axiom,
% 5.48/5.72 ! [A: int,B: int] :
% 5.48/5.72 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel
% 5.48/5.72 thf(fact_843_diff__add__cancel,axiom,
% 5.48/5.72 ! [A: complex,B: complex] :
% 5.48/5.72 ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_cancel
% 5.48/5.72 thf(fact_844_diff__add__cancel,axiom,
% 5.48/5.72 ! [A: real,B: real] :
% 5.48/5.72 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_cancel
% 5.48/5.72 thf(fact_845_diff__add__cancel,axiom,
% 5.48/5.72 ! [A: rat,B: rat] :
% 5.48/5.72 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_cancel
% 5.48/5.72 thf(fact_846_diff__add__cancel,axiom,
% 5.48/5.72 ! [A: int,B: int] :
% 5.48/5.72 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_cancel
% 5.48/5.72 thf(fact_847_add__diff__cancel__left,axiom,
% 5.48/5.72 ! [C: complex,A: complex,B: complex] :
% 5.48/5.72 ( ( minus_minus_complex @ ( plus_plus_complex @ C @ A ) @ ( plus_plus_complex @ C @ B ) )
% 5.48/5.72 = ( minus_minus_complex @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_left
% 5.48/5.72 thf(fact_848_add__diff__cancel__left,axiom,
% 5.48/5.72 ! [C: real,A: real,B: real] :
% 5.48/5.72 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.48/5.72 = ( minus_minus_real @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_left
% 5.48/5.72 thf(fact_849_add__diff__cancel__left,axiom,
% 5.48/5.72 ! [C: rat,A: rat,B: rat] :
% 5.48/5.72 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.48/5.72 = ( minus_minus_rat @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_left
% 5.48/5.72 thf(fact_850_add__diff__cancel__left,axiom,
% 5.48/5.72 ! [C: nat,A: nat,B: nat] :
% 5.48/5.72 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.48/5.72 = ( minus_minus_nat @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_left
% 5.48/5.72 thf(fact_851_add__diff__cancel__left,axiom,
% 5.48/5.72 ! [C: int,A: int,B: int] :
% 5.48/5.72 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.48/5.72 = ( minus_minus_int @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_left
% 5.48/5.72 thf(fact_852_add__diff__cancel__left_H,axiom,
% 5.48/5.72 ! [A: complex,B: complex] :
% 5.48/5.72 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ A )
% 5.48/5.72 = B ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_left'
% 5.48/5.72 thf(fact_853_add__diff__cancel__left_H,axiom,
% 5.48/5.72 ! [A: real,B: real] :
% 5.48/5.72 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.48/5.72 = B ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_left'
% 5.48/5.72 thf(fact_854_add__diff__cancel__left_H,axiom,
% 5.48/5.72 ! [A: rat,B: rat] :
% 5.48/5.72 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.48/5.72 = B ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_left'
% 5.48/5.72 thf(fact_855_add__diff__cancel__left_H,axiom,
% 5.48/5.72 ! [A: nat,B: nat] :
% 5.48/5.72 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.48/5.72 = B ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_left'
% 5.48/5.72 thf(fact_856_add__diff__cancel__left_H,axiom,
% 5.48/5.72 ! [A: int,B: int] :
% 5.48/5.72 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.48/5.72 = B ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_left'
% 5.48/5.72 thf(fact_857_add__diff__cancel__right,axiom,
% 5.48/5.72 ! [A: complex,C: complex,B: complex] :
% 5.48/5.72 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ C ) )
% 5.48/5.72 = ( minus_minus_complex @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_right
% 5.48/5.72 thf(fact_858_add__diff__cancel__right,axiom,
% 5.48/5.72 ! [A: real,C: real,B: real] :
% 5.48/5.72 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.48/5.72 = ( minus_minus_real @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_right
% 5.48/5.72 thf(fact_859_add__diff__cancel__right,axiom,
% 5.48/5.72 ! [A: rat,C: rat,B: rat] :
% 5.48/5.72 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.48/5.72 = ( minus_minus_rat @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_right
% 5.48/5.72 thf(fact_860_add__diff__cancel__right,axiom,
% 5.48/5.72 ! [A: nat,C: nat,B: nat] :
% 5.48/5.72 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.48/5.72 = ( minus_minus_nat @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_right
% 5.48/5.72 thf(fact_861_add__diff__cancel__right,axiom,
% 5.48/5.72 ! [A: int,C: int,B: int] :
% 5.48/5.72 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.48/5.72 = ( minus_minus_int @ A @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_right
% 5.48/5.72 thf(fact_862_add__diff__cancel__right_H,axiom,
% 5.48/5.72 ! [A: complex,B: complex] :
% 5.48/5.72 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_right'
% 5.48/5.72 thf(fact_863_add__diff__cancel__right_H,axiom,
% 5.48/5.72 ! [A: real,B: real] :
% 5.48/5.72 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_right'
% 5.48/5.72 thf(fact_864_add__diff__cancel__right_H,axiom,
% 5.48/5.72 ! [A: rat,B: rat] :
% 5.48/5.72 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_right'
% 5.48/5.72 thf(fact_865_add__diff__cancel__right_H,axiom,
% 5.48/5.72 ! [A: nat,B: nat] :
% 5.48/5.72 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_right'
% 5.48/5.72 thf(fact_866_add__diff__cancel__right_H,axiom,
% 5.48/5.72 ! [A: int,B: int] :
% 5.48/5.72 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.48/5.72 = A ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_cancel_right'
% 5.48/5.72 thf(fact_867_diff__diff__cancel,axiom,
% 5.48/5.72 ! [I: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ I @ N )
% 5.48/5.72 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 5.48/5.72 = I ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_diff_cancel
% 5.48/5.72 thf(fact_868_diff__diff__left,axiom,
% 5.48/5.72 ! [I: nat,J: nat,K: nat] :
% 5.48/5.72 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.48/5.72 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_diff_left
% 5.48/5.72 thf(fact_869_member__correct,axiom,
% 5.48/5.72 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.72 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.48/5.72 = ( member_nat @ X2 @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % member_correct
% 5.48/5.72 thf(fact_870_le__add__diff__inverse,axiom,
% 5.48/5.72 ! [B: real,A: real] :
% 5.48/5.72 ( ( ord_less_eq_real @ B @ A )
% 5.48/5.72 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.48/5.72 = A ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_add_diff_inverse
% 5.48/5.72 thf(fact_871_le__add__diff__inverse,axiom,
% 5.48/5.72 ! [B: rat,A: rat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ B @ A )
% 5.48/5.72 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.48/5.72 = A ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_add_diff_inverse
% 5.48/5.72 thf(fact_872_le__add__diff__inverse,axiom,
% 5.48/5.72 ! [B: nat,A: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ B @ A )
% 5.48/5.72 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.48/5.72 = A ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_add_diff_inverse
% 5.48/5.72 thf(fact_873_le__add__diff__inverse,axiom,
% 5.48/5.72 ! [B: int,A: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ B @ A )
% 5.48/5.72 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.48/5.72 = A ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_add_diff_inverse
% 5.48/5.72 thf(fact_874_le__add__diff__inverse2,axiom,
% 5.48/5.72 ! [B: real,A: real] :
% 5.48/5.72 ( ( ord_less_eq_real @ B @ A )
% 5.48/5.72 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.48/5.72 = A ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_add_diff_inverse2
% 5.48/5.72 thf(fact_875_le__add__diff__inverse2,axiom,
% 5.48/5.72 ! [B: rat,A: rat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ B @ A )
% 5.48/5.72 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.48/5.72 = A ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_add_diff_inverse2
% 5.48/5.72 thf(fact_876_le__add__diff__inverse2,axiom,
% 5.48/5.72 ! [B: nat,A: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ B @ A )
% 5.48/5.72 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.48/5.72 = A ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_add_diff_inverse2
% 5.48/5.72 thf(fact_877_le__add__diff__inverse2,axiom,
% 5.48/5.72 ! [B: int,A: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ B @ A )
% 5.48/5.72 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.48/5.72 = A ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_add_diff_inverse2
% 5.48/5.72 thf(fact_878_left__diff__distrib__numeral,axiom,
% 5.48/5.72 ! [A: complex,B: complex,V: num] :
% 5.48/5.72 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.48/5.72 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib_numeral
% 5.48/5.72 thf(fact_879_left__diff__distrib__numeral,axiom,
% 5.48/5.72 ! [A: real,B: real,V: num] :
% 5.48/5.72 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.48/5.72 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib_numeral
% 5.48/5.72 thf(fact_880_left__diff__distrib__numeral,axiom,
% 5.48/5.72 ! [A: rat,B: rat,V: num] :
% 5.48/5.72 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.48/5.72 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib_numeral
% 5.48/5.72 thf(fact_881_left__diff__distrib__numeral,axiom,
% 5.48/5.72 ! [A: int,B: int,V: num] :
% 5.48/5.72 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.48/5.72 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib_numeral
% 5.48/5.72 thf(fact_882_right__diff__distrib__numeral,axiom,
% 5.48/5.72 ! [V: num,B: complex,C: complex] :
% 5.48/5.72 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.48/5.72 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib_numeral
% 5.48/5.72 thf(fact_883_right__diff__distrib__numeral,axiom,
% 5.48/5.72 ! [V: num,B: real,C: real] :
% 5.48/5.72 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.48/5.72 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib_numeral
% 5.48/5.72 thf(fact_884_right__diff__distrib__numeral,axiom,
% 5.48/5.72 ! [V: num,B: rat,C: rat] :
% 5.48/5.72 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.48/5.72 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib_numeral
% 5.48/5.72 thf(fact_885_right__diff__distrib__numeral,axiom,
% 5.48/5.72 ! [V: num,B: int,C: int] :
% 5.48/5.72 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.48/5.72 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib_numeral
% 5.48/5.72 thf(fact_886_Nat_Oadd__diff__assoc,axiom,
% 5.48/5.72 ! [K: nat,J: nat,I: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ K @ J )
% 5.48/5.72 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.48/5.72 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % Nat.add_diff_assoc
% 5.48/5.72 thf(fact_887_Nat_Oadd__diff__assoc2,axiom,
% 5.48/5.72 ! [K: nat,J: nat,I: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ K @ J )
% 5.48/5.72 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.48/5.72 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % Nat.add_diff_assoc2
% 5.48/5.72 thf(fact_888_Nat_Odiff__diff__right,axiom,
% 5.48/5.72 ! [K: nat,J: nat,I: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ K @ J )
% 5.48/5.72 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.48/5.72 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % Nat.diff_diff_right
% 5.48/5.72 thf(fact_889_mintlistlength,axiom,
% 5.48/5.72 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.48/5.72 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.48/5.72 => ( ( Mi != Ma )
% 5.48/5.72 => ( ( ord_less_nat @ Mi @ Ma )
% 5.48/5.72 & ? [M4: nat] :
% 5.48/5.72 ( ( ( some_nat @ M4 )
% 5.48/5.72 = ( vEBT_vebt_mint @ Summary ) )
% 5.48/5.72 & ( ord_less_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % mintlistlength
% 5.48/5.72 thf(fact_890__C5_Ohyps_C_I3_J,axiom,
% 5.48/5.72 ( m
% 5.48/5.72 = ( suc @ na ) ) ).
% 5.48/5.72
% 5.48/5.72 % "5.hyps"(3)
% 5.48/5.72 thf(fact_891__C5_Ohyps_C_I9_J,axiom,
% 5.48/5.72 ( ( mi != ma )
% 5.48/5.72 => ! [I3: nat] :
% 5.48/5.72 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.48/5.72 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.48/5.72 = I3 )
% 5.48/5.72 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I3 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.48/5.72 & ! [X6: nat] :
% 5.48/5.72 ( ( ( ( vEBT_VEBT_high @ X6 @ na )
% 5.48/5.72 = I3 )
% 5.48/5.72 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I3 ) @ ( vEBT_VEBT_low @ X6 @ na ) ) )
% 5.48/5.72 => ( ( ord_less_nat @ mi @ X6 )
% 5.48/5.72 & ( ord_less_eq_nat @ X6 @ ma ) ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % "5.hyps"(9)
% 5.48/5.72 thf(fact_892_less__eq__real__def,axiom,
% 5.48/5.72 ( ord_less_eq_real
% 5.48/5.72 = ( ^ [X: real,Y: real] :
% 5.48/5.72 ( ( ord_less_real @ X @ Y )
% 5.48/5.72 | ( X = Y ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % less_eq_real_def
% 5.48/5.72 thf(fact_893_real__arch__pow,axiom,
% 5.48/5.72 ! [X2: real,Y2: real] :
% 5.48/5.72 ( ( ord_less_real @ one_one_real @ X2 )
% 5.48/5.72 => ? [N2: nat] : ( ord_less_real @ Y2 @ ( power_power_real @ X2 @ N2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % real_arch_pow
% 5.48/5.72 thf(fact_894_diff__commute,axiom,
% 5.48/5.72 ! [I: nat,J: nat,K: nat] :
% 5.48/5.72 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.48/5.72 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_commute
% 5.48/5.72 thf(fact_895_diff__eq__diff__eq,axiom,
% 5.48/5.72 ! [A: complex,B: complex,C: complex,D2: complex] :
% 5.48/5.72 ( ( ( minus_minus_complex @ A @ B )
% 5.48/5.72 = ( minus_minus_complex @ C @ D2 ) )
% 5.48/5.72 => ( ( A = B )
% 5.48/5.72 = ( C = D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_diff_eq
% 5.48/5.72 thf(fact_896_diff__eq__diff__eq,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real,D2: real] :
% 5.48/5.72 ( ( ( minus_minus_real @ A @ B )
% 5.48/5.72 = ( minus_minus_real @ C @ D2 ) )
% 5.48/5.72 => ( ( A = B )
% 5.48/5.72 = ( C = D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_diff_eq
% 5.48/5.72 thf(fact_897_diff__eq__diff__eq,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.48/5.72 ( ( ( minus_minus_rat @ A @ B )
% 5.48/5.72 = ( minus_minus_rat @ C @ D2 ) )
% 5.48/5.72 => ( ( A = B )
% 5.48/5.72 = ( C = D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_diff_eq
% 5.48/5.72 thf(fact_898_diff__eq__diff__eq,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int,D2: int] :
% 5.48/5.72 ( ( ( minus_minus_int @ A @ B )
% 5.48/5.72 = ( minus_minus_int @ C @ D2 ) )
% 5.48/5.72 => ( ( A = B )
% 5.48/5.72 = ( C = D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_diff_eq
% 5.48/5.72 thf(fact_899_diff__right__commute,axiom,
% 5.48/5.72 ! [A: complex,C: complex,B: complex] :
% 5.48/5.72 ( ( minus_minus_complex @ ( minus_minus_complex @ A @ C ) @ B )
% 5.48/5.72 = ( minus_minus_complex @ ( minus_minus_complex @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_right_commute
% 5.48/5.72 thf(fact_900_diff__right__commute,axiom,
% 5.48/5.72 ! [A: real,C: real,B: real] :
% 5.48/5.72 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 5.48/5.72 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_right_commute
% 5.48/5.72 thf(fact_901_diff__right__commute,axiom,
% 5.48/5.72 ! [A: rat,C: rat,B: rat] :
% 5.48/5.72 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 5.48/5.72 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_right_commute
% 5.48/5.72 thf(fact_902_diff__right__commute,axiom,
% 5.48/5.72 ! [A: nat,C: nat,B: nat] :
% 5.48/5.72 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 5.48/5.72 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_right_commute
% 5.48/5.72 thf(fact_903_diff__right__commute,axiom,
% 5.48/5.72 ! [A: int,C: int,B: int] :
% 5.48/5.72 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 5.48/5.72 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_right_commute
% 5.48/5.72 thf(fact_904_diff__mono,axiom,
% 5.48/5.72 ! [A: real,B: real,D2: real,C: real] :
% 5.48/5.72 ( ( ord_less_eq_real @ A @ B )
% 5.48/5.72 => ( ( ord_less_eq_real @ D2 @ C )
% 5.48/5.72 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_mono
% 5.48/5.72 thf(fact_905_diff__mono,axiom,
% 5.48/5.72 ! [A: rat,B: rat,D2: rat,C: rat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ A @ B )
% 5.48/5.72 => ( ( ord_less_eq_rat @ D2 @ C )
% 5.48/5.72 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_mono
% 5.48/5.72 thf(fact_906_diff__mono,axiom,
% 5.48/5.72 ! [A: int,B: int,D2: int,C: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ A @ B )
% 5.48/5.72 => ( ( ord_less_eq_int @ D2 @ C )
% 5.48/5.72 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_mono
% 5.48/5.72 thf(fact_907_diff__left__mono,axiom,
% 5.48/5.72 ! [B: real,A: real,C: real] :
% 5.48/5.72 ( ( ord_less_eq_real @ B @ A )
% 5.48/5.72 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_left_mono
% 5.48/5.72 thf(fact_908_diff__left__mono,axiom,
% 5.48/5.72 ! [B: rat,A: rat,C: rat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ B @ A )
% 5.48/5.72 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_left_mono
% 5.48/5.72 thf(fact_909_diff__left__mono,axiom,
% 5.48/5.72 ! [B: int,A: int,C: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ B @ A )
% 5.48/5.72 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_left_mono
% 5.48/5.72 thf(fact_910_diff__right__mono,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( ord_less_eq_real @ A @ B )
% 5.48/5.72 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_right_mono
% 5.48/5.72 thf(fact_911_diff__right__mono,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ A @ B )
% 5.48/5.72 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_right_mono
% 5.48/5.72 thf(fact_912_diff__right__mono,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ A @ B )
% 5.48/5.72 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_right_mono
% 5.48/5.72 thf(fact_913_diff__eq__diff__less__eq,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real,D2: real] :
% 5.48/5.72 ( ( ( minus_minus_real @ A @ B )
% 5.48/5.72 = ( minus_minus_real @ C @ D2 ) )
% 5.48/5.72 => ( ( ord_less_eq_real @ A @ B )
% 5.48/5.72 = ( ord_less_eq_real @ C @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_diff_less_eq
% 5.48/5.72 thf(fact_914_diff__eq__diff__less__eq,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.48/5.72 ( ( ( minus_minus_rat @ A @ B )
% 5.48/5.72 = ( minus_minus_rat @ C @ D2 ) )
% 5.48/5.72 => ( ( ord_less_eq_rat @ A @ B )
% 5.48/5.72 = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_diff_less_eq
% 5.48/5.72 thf(fact_915_diff__eq__diff__less__eq,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int,D2: int] :
% 5.48/5.72 ( ( ( minus_minus_int @ A @ B )
% 5.48/5.72 = ( minus_minus_int @ C @ D2 ) )
% 5.48/5.72 => ( ( ord_less_eq_int @ A @ B )
% 5.48/5.72 = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_diff_less_eq
% 5.48/5.72 thf(fact_916_diff__strict__right__mono,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( ord_less_real @ A @ B )
% 5.48/5.72 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_strict_right_mono
% 5.48/5.72 thf(fact_917_diff__strict__right__mono,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( ord_less_rat @ A @ B )
% 5.48/5.72 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_strict_right_mono
% 5.48/5.72 thf(fact_918_diff__strict__right__mono,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( ord_less_int @ A @ B )
% 5.48/5.72 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_strict_right_mono
% 5.48/5.72 thf(fact_919_diff__strict__left__mono,axiom,
% 5.48/5.72 ! [B: real,A: real,C: real] :
% 5.48/5.72 ( ( ord_less_real @ B @ A )
% 5.48/5.72 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_strict_left_mono
% 5.48/5.72 thf(fact_920_diff__strict__left__mono,axiom,
% 5.48/5.72 ! [B: rat,A: rat,C: rat] :
% 5.48/5.72 ( ( ord_less_rat @ B @ A )
% 5.48/5.72 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_strict_left_mono
% 5.48/5.72 thf(fact_921_diff__strict__left__mono,axiom,
% 5.48/5.72 ! [B: int,A: int,C: int] :
% 5.48/5.72 ( ( ord_less_int @ B @ A )
% 5.48/5.72 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_strict_left_mono
% 5.48/5.72 thf(fact_922_diff__eq__diff__less,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real,D2: real] :
% 5.48/5.72 ( ( ( minus_minus_real @ A @ B )
% 5.48/5.72 = ( minus_minus_real @ C @ D2 ) )
% 5.48/5.72 => ( ( ord_less_real @ A @ B )
% 5.48/5.72 = ( ord_less_real @ C @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_diff_less
% 5.48/5.72 thf(fact_923_diff__eq__diff__less,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.48/5.72 ( ( ( minus_minus_rat @ A @ B )
% 5.48/5.72 = ( minus_minus_rat @ C @ D2 ) )
% 5.48/5.72 => ( ( ord_less_rat @ A @ B )
% 5.48/5.72 = ( ord_less_rat @ C @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_diff_less
% 5.48/5.72 thf(fact_924_diff__eq__diff__less,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int,D2: int] :
% 5.48/5.72 ( ( ( minus_minus_int @ A @ B )
% 5.48/5.72 = ( minus_minus_int @ C @ D2 ) )
% 5.48/5.72 => ( ( ord_less_int @ A @ B )
% 5.48/5.72 = ( ord_less_int @ C @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_diff_less
% 5.48/5.72 thf(fact_925_diff__strict__mono,axiom,
% 5.48/5.72 ! [A: real,B: real,D2: real,C: real] :
% 5.48/5.72 ( ( ord_less_real @ A @ B )
% 5.48/5.72 => ( ( ord_less_real @ D2 @ C )
% 5.48/5.72 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_strict_mono
% 5.48/5.72 thf(fact_926_diff__strict__mono,axiom,
% 5.48/5.72 ! [A: rat,B: rat,D2: rat,C: rat] :
% 5.48/5.72 ( ( ord_less_rat @ A @ B )
% 5.48/5.72 => ( ( ord_less_rat @ D2 @ C )
% 5.48/5.72 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_strict_mono
% 5.48/5.72 thf(fact_927_diff__strict__mono,axiom,
% 5.48/5.72 ! [A: int,B: int,D2: int,C: int] :
% 5.48/5.72 ( ( ord_less_int @ A @ B )
% 5.48/5.72 => ( ( ord_less_int @ D2 @ C )
% 5.48/5.72 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_strict_mono
% 5.48/5.72 thf(fact_928_left__diff__distrib,axiom,
% 5.48/5.72 ! [A: complex,B: complex,C: complex] :
% 5.48/5.72 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib
% 5.48/5.72 thf(fact_929_left__diff__distrib,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib
% 5.48/5.72 thf(fact_930_left__diff__distrib,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib
% 5.48/5.72 thf(fact_931_left__diff__distrib,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib
% 5.48/5.72 thf(fact_932_right__diff__distrib,axiom,
% 5.48/5.72 ! [A: complex,B: complex,C: complex] :
% 5.48/5.72 ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 5.48/5.72 = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib
% 5.48/5.72 thf(fact_933_right__diff__distrib,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.48/5.72 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib
% 5.48/5.72 thf(fact_934_right__diff__distrib,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.48/5.72 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib
% 5.48/5.72 thf(fact_935_right__diff__distrib,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.48/5.72 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib
% 5.48/5.72 thf(fact_936_left__diff__distrib_H,axiom,
% 5.48/5.72 ! [B: complex,C: complex,A: complex] :
% 5.48/5.72 ( ( times_times_complex @ ( minus_minus_complex @ B @ C ) @ A )
% 5.48/5.72 = ( minus_minus_complex @ ( times_times_complex @ B @ A ) @ ( times_times_complex @ C @ A ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib'
% 5.48/5.72 thf(fact_937_left__diff__distrib_H,axiom,
% 5.48/5.72 ! [B: real,C: real,A: real] :
% 5.48/5.72 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.48/5.72 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib'
% 5.48/5.72 thf(fact_938_left__diff__distrib_H,axiom,
% 5.48/5.72 ! [B: rat,C: rat,A: rat] :
% 5.48/5.72 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.48/5.72 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib'
% 5.48/5.72 thf(fact_939_left__diff__distrib_H,axiom,
% 5.48/5.72 ! [B: nat,C: nat,A: nat] :
% 5.48/5.72 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.48/5.72 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib'
% 5.48/5.72 thf(fact_940_left__diff__distrib_H,axiom,
% 5.48/5.72 ! [B: int,C: int,A: int] :
% 5.48/5.72 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.48/5.72 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % left_diff_distrib'
% 5.48/5.72 thf(fact_941_right__diff__distrib_H,axiom,
% 5.48/5.72 ! [A: complex,B: complex,C: complex] :
% 5.48/5.72 ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 5.48/5.72 = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib'
% 5.48/5.72 thf(fact_942_right__diff__distrib_H,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.48/5.72 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib'
% 5.48/5.72 thf(fact_943_right__diff__distrib_H,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.48/5.72 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib'
% 5.48/5.72 thf(fact_944_right__diff__distrib_H,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.48/5.72 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib'
% 5.48/5.72 thf(fact_945_right__diff__distrib_H,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.48/5.72 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % right_diff_distrib'
% 5.48/5.72 thf(fact_946_group__cancel_Osub1,axiom,
% 5.48/5.72 ! [A2: complex,K: complex,A: complex,B: complex] :
% 5.48/5.72 ( ( A2
% 5.48/5.72 = ( plus_plus_complex @ K @ A ) )
% 5.48/5.72 => ( ( minus_minus_complex @ A2 @ B )
% 5.48/5.72 = ( plus_plus_complex @ K @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % group_cancel.sub1
% 5.48/5.72 thf(fact_947_group__cancel_Osub1,axiom,
% 5.48/5.72 ! [A2: real,K: real,A: real,B: real] :
% 5.48/5.72 ( ( A2
% 5.48/5.72 = ( plus_plus_real @ K @ A ) )
% 5.48/5.72 => ( ( minus_minus_real @ A2 @ B )
% 5.48/5.72 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % group_cancel.sub1
% 5.48/5.72 thf(fact_948_group__cancel_Osub1,axiom,
% 5.48/5.72 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.48/5.72 ( ( A2
% 5.48/5.72 = ( plus_plus_rat @ K @ A ) )
% 5.48/5.72 => ( ( minus_minus_rat @ A2 @ B )
% 5.48/5.72 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % group_cancel.sub1
% 5.48/5.72 thf(fact_949_group__cancel_Osub1,axiom,
% 5.48/5.72 ! [A2: int,K: int,A: int,B: int] :
% 5.48/5.72 ( ( A2
% 5.48/5.72 = ( plus_plus_int @ K @ A ) )
% 5.48/5.72 => ( ( minus_minus_int @ A2 @ B )
% 5.48/5.72 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % group_cancel.sub1
% 5.48/5.72 thf(fact_950_diff__eq__eq,axiom,
% 5.48/5.72 ! [A: complex,B: complex,C: complex] :
% 5.48/5.72 ( ( ( minus_minus_complex @ A @ B )
% 5.48/5.72 = C )
% 5.48/5.72 = ( A
% 5.48/5.72 = ( plus_plus_complex @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_eq
% 5.48/5.72 thf(fact_951_diff__eq__eq,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( ( minus_minus_real @ A @ B )
% 5.48/5.72 = C )
% 5.48/5.72 = ( A
% 5.48/5.72 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_eq
% 5.48/5.72 thf(fact_952_diff__eq__eq,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( ( minus_minus_rat @ A @ B )
% 5.48/5.72 = C )
% 5.48/5.72 = ( A
% 5.48/5.72 = ( plus_plus_rat @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_eq
% 5.48/5.72 thf(fact_953_diff__eq__eq,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( ( minus_minus_int @ A @ B )
% 5.48/5.72 = C )
% 5.48/5.72 = ( A
% 5.48/5.72 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_eq_eq
% 5.48/5.72 thf(fact_954_eq__diff__eq,axiom,
% 5.48/5.72 ! [A: complex,C: complex,B: complex] :
% 5.48/5.72 ( ( A
% 5.48/5.72 = ( minus_minus_complex @ C @ B ) )
% 5.48/5.72 = ( ( plus_plus_complex @ A @ B )
% 5.48/5.72 = C ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_diff_eq
% 5.48/5.72 thf(fact_955_eq__diff__eq,axiom,
% 5.48/5.72 ! [A: real,C: real,B: real] :
% 5.48/5.72 ( ( A
% 5.48/5.72 = ( minus_minus_real @ C @ B ) )
% 5.48/5.72 = ( ( plus_plus_real @ A @ B )
% 5.48/5.72 = C ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_diff_eq
% 5.48/5.72 thf(fact_956_eq__diff__eq,axiom,
% 5.48/5.72 ! [A: rat,C: rat,B: rat] :
% 5.48/5.72 ( ( A
% 5.48/5.72 = ( minus_minus_rat @ C @ B ) )
% 5.48/5.72 = ( ( plus_plus_rat @ A @ B )
% 5.48/5.72 = C ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_diff_eq
% 5.48/5.72 thf(fact_957_eq__diff__eq,axiom,
% 5.48/5.72 ! [A: int,C: int,B: int] :
% 5.48/5.72 ( ( A
% 5.48/5.72 = ( minus_minus_int @ C @ B ) )
% 5.48/5.72 = ( ( plus_plus_int @ A @ B )
% 5.48/5.72 = C ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_diff_eq
% 5.48/5.72 thf(fact_958_add__diff__eq,axiom,
% 5.48/5.72 ! [A: complex,B: complex,C: complex] :
% 5.48/5.72 ( ( plus_plus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 5.48/5.72 = ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_eq
% 5.48/5.72 thf(fact_959_add__diff__eq,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.48/5.72 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_eq
% 5.48/5.72 thf(fact_960_add__diff__eq,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.48/5.72 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_eq
% 5.48/5.72 thf(fact_961_add__diff__eq,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.48/5.72 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_eq
% 5.48/5.72 thf(fact_962_diff__diff__eq2,axiom,
% 5.48/5.72 ! [A: complex,B: complex,C: complex] :
% 5.48/5.72 ( ( minus_minus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 5.48/5.72 = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_diff_eq2
% 5.48/5.72 thf(fact_963_diff__diff__eq2,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.48/5.72 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_diff_eq2
% 5.48/5.72 thf(fact_964_diff__diff__eq2,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.48/5.72 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_diff_eq2
% 5.48/5.72 thf(fact_965_diff__diff__eq2,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.48/5.72 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_diff_eq2
% 5.48/5.72 thf(fact_966_diff__add__eq,axiom,
% 5.48/5.72 ! [A: complex,B: complex,C: complex] :
% 5.48/5.72 ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_eq
% 5.48/5.72 thf(fact_967_diff__add__eq,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_eq
% 5.48/5.72 thf(fact_968_diff__add__eq,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_eq
% 5.48/5.72 thf(fact_969_diff__add__eq,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_eq
% 5.48/5.72 thf(fact_970_diff__add__eq__diff__diff__swap,axiom,
% 5.48/5.72 ! [A: complex,B: complex,C: complex] :
% 5.48/5.72 ( ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.48/5.72 = ( minus_minus_complex @ ( minus_minus_complex @ A @ C ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_eq_diff_diff_swap
% 5.48/5.72 thf(fact_971_diff__add__eq__diff__diff__swap,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.48/5.72 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_eq_diff_diff_swap
% 5.48/5.72 thf(fact_972_diff__add__eq__diff__diff__swap,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.48/5.72 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_eq_diff_diff_swap
% 5.48/5.72 thf(fact_973_diff__add__eq__diff__diff__swap,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.48/5.72 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_eq_diff_diff_swap
% 5.48/5.72 thf(fact_974_add__implies__diff,axiom,
% 5.48/5.72 ! [C: complex,B: complex,A: complex] :
% 5.48/5.72 ( ( ( plus_plus_complex @ C @ B )
% 5.48/5.72 = A )
% 5.48/5.72 => ( C
% 5.48/5.72 = ( minus_minus_complex @ A @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_implies_diff
% 5.48/5.72 thf(fact_975_add__implies__diff,axiom,
% 5.48/5.72 ! [C: real,B: real,A: real] :
% 5.48/5.72 ( ( ( plus_plus_real @ C @ B )
% 5.48/5.72 = A )
% 5.48/5.72 => ( C
% 5.48/5.72 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_implies_diff
% 5.48/5.72 thf(fact_976_add__implies__diff,axiom,
% 5.48/5.72 ! [C: rat,B: rat,A: rat] :
% 5.48/5.72 ( ( ( plus_plus_rat @ C @ B )
% 5.48/5.72 = A )
% 5.48/5.72 => ( C
% 5.48/5.72 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_implies_diff
% 5.48/5.72 thf(fact_977_add__implies__diff,axiom,
% 5.48/5.72 ! [C: nat,B: nat,A: nat] :
% 5.48/5.72 ( ( ( plus_plus_nat @ C @ B )
% 5.48/5.72 = A )
% 5.48/5.72 => ( C
% 5.48/5.72 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_implies_diff
% 5.48/5.72 thf(fact_978_add__implies__diff,axiom,
% 5.48/5.72 ! [C: int,B: int,A: int] :
% 5.48/5.72 ( ( ( plus_plus_int @ C @ B )
% 5.48/5.72 = A )
% 5.48/5.72 => ( C
% 5.48/5.72 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_implies_diff
% 5.48/5.72 thf(fact_979_add__diff__add,axiom,
% 5.48/5.72 ! [A: complex,C: complex,B: complex,D2: complex] :
% 5.48/5.72 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ D2 ) )
% 5.48/5.72 = ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ ( minus_minus_complex @ C @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_add
% 5.48/5.72 thf(fact_980_add__diff__add,axiom,
% 5.48/5.72 ! [A: real,C: real,B: real,D2: real] :
% 5.48/5.72 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) )
% 5.48/5.72 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_add
% 5.48/5.72 thf(fact_981_add__diff__add,axiom,
% 5.48/5.72 ! [A: rat,C: rat,B: rat,D2: rat] :
% 5.48/5.72 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) )
% 5.48/5.72 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_add
% 5.48/5.72 thf(fact_982_add__diff__add,axiom,
% 5.48/5.72 ! [A: int,C: int,B: int,D2: int] :
% 5.48/5.72 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) )
% 5.48/5.72 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_add
% 5.48/5.72 thf(fact_983_diff__diff__eq,axiom,
% 5.48/5.72 ! [A: complex,B: complex,C: complex] :
% 5.48/5.72 ( ( minus_minus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_diff_eq
% 5.48/5.72 thf(fact_984_diff__diff__eq,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_diff_eq
% 5.48/5.72 thf(fact_985_diff__diff__eq,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_diff_eq
% 5.48/5.72 thf(fact_986_diff__diff__eq,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_diff_eq
% 5.48/5.72 thf(fact_987_diff__diff__eq,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_diff_eq
% 5.48/5.72 thf(fact_988_diff__divide__distrib,axiom,
% 5.48/5.72 ! [A: complex,B: complex,C: complex] :
% 5.48/5.72 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_divide_distrib
% 5.48/5.72 thf(fact_989_diff__divide__distrib,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_divide_distrib
% 5.48/5.72 thf(fact_990_diff__divide__distrib,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.48/5.72 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_divide_distrib
% 5.48/5.72 thf(fact_991_less__imp__diff__less,axiom,
% 5.48/5.72 ! [J: nat,K: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_nat @ J @ K )
% 5.48/5.72 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 5.48/5.72
% 5.48/5.72 % less_imp_diff_less
% 5.48/5.72 thf(fact_992_diff__less__mono2,axiom,
% 5.48/5.72 ! [M: nat,N: nat,L: nat] :
% 5.48/5.72 ( ( ord_less_nat @ M @ N )
% 5.48/5.72 => ( ( ord_less_nat @ M @ L )
% 5.48/5.72 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_less_mono2
% 5.48/5.72 thf(fact_993_eq__diff__iff,axiom,
% 5.48/5.72 ! [K: nat,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ K @ M )
% 5.48/5.72 => ( ( ord_less_eq_nat @ K @ N )
% 5.48/5.72 => ( ( ( minus_minus_nat @ M @ K )
% 5.48/5.72 = ( minus_minus_nat @ N @ K ) )
% 5.48/5.72 = ( M = N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_diff_iff
% 5.48/5.72 thf(fact_994_le__diff__iff,axiom,
% 5.48/5.72 ! [K: nat,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ K @ M )
% 5.48/5.72 => ( ( ord_less_eq_nat @ K @ N )
% 5.48/5.72 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.48/5.72 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_diff_iff
% 5.48/5.72 thf(fact_995_Nat_Odiff__diff__eq,axiom,
% 5.48/5.72 ! [K: nat,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ K @ M )
% 5.48/5.72 => ( ( ord_less_eq_nat @ K @ N )
% 5.48/5.72 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.48/5.72 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % Nat.diff_diff_eq
% 5.48/5.72 thf(fact_996_diff__le__mono,axiom,
% 5.48/5.72 ! [M: nat,N: nat,L: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.72 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_le_mono
% 5.48/5.72 thf(fact_997_diff__le__self,axiom,
% 5.48/5.72 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 5.48/5.72
% 5.48/5.72 % diff_le_self
% 5.48/5.72 thf(fact_998_le__diff__iff_H,axiom,
% 5.48/5.72 ! [A: nat,C: nat,B: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ C )
% 5.48/5.72 => ( ( ord_less_eq_nat @ B @ C )
% 5.48/5.72 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.48/5.72 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_diff_iff'
% 5.48/5.72 thf(fact_999_diff__le__mono2,axiom,
% 5.48/5.72 ! [M: nat,N: nat,L: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.72 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_le_mono2
% 5.48/5.72 thf(fact_1000_Nat_Odiff__cancel,axiom,
% 5.48/5.72 ! [K: nat,M: nat,N: nat] :
% 5.48/5.72 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.48/5.72 = ( minus_minus_nat @ M @ N ) ) ).
% 5.48/5.72
% 5.48/5.72 % Nat.diff_cancel
% 5.48/5.72 thf(fact_1001_diff__cancel2,axiom,
% 5.48/5.72 ! [M: nat,K: nat,N: nat] :
% 5.48/5.72 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 5.48/5.72 = ( minus_minus_nat @ M @ N ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_cancel2
% 5.48/5.72 thf(fact_1002_diff__add__inverse,axiom,
% 5.48/5.72 ! [N: nat,M: nat] :
% 5.48/5.72 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 5.48/5.72 = M ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_inverse
% 5.48/5.72 thf(fact_1003_diff__add__inverse2,axiom,
% 5.48/5.72 ! [M: nat,N: nat] :
% 5.48/5.72 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 5.48/5.72 = M ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add_inverse2
% 5.48/5.72 thf(fact_1004_diff__mult__distrib,axiom,
% 5.48/5.72 ! [M: nat,N: nat,K: nat] :
% 5.48/5.72 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 5.48/5.72 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_mult_distrib
% 5.48/5.72 thf(fact_1005_diff__mult__distrib2,axiom,
% 5.48/5.72 ! [K: nat,M: nat,N: nat] :
% 5.48/5.72 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.48/5.72 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_mult_distrib2
% 5.48/5.72 thf(fact_1006_diff__le__eq,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.48/5.72 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_le_eq
% 5.48/5.72 thf(fact_1007_diff__le__eq,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.48/5.72 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_le_eq
% 5.48/5.72 thf(fact_1008_diff__le__eq,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.48/5.72 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_le_eq
% 5.48/5.72 thf(fact_1009_le__diff__eq,axiom,
% 5.48/5.72 ! [A: real,C: real,B: real] :
% 5.48/5.72 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.48/5.72 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_diff_eq
% 5.48/5.72 thf(fact_1010_le__diff__eq,axiom,
% 5.48/5.72 ! [A: rat,C: rat,B: rat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.48/5.72 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_diff_eq
% 5.48/5.72 thf(fact_1011_le__diff__eq,axiom,
% 5.48/5.72 ! [A: int,C: int,B: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.48/5.72 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_diff_eq
% 5.48/5.72 thf(fact_1012_diff__add,axiom,
% 5.48/5.72 ! [A: nat,B: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.48/5.72 = B ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_add
% 5.48/5.72 thf(fact_1013_le__add__diff,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_add_diff
% 5.48/5.72 thf(fact_1014_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.48/5.72 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.48/5.72 thf(fact_1015_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.48/5.72 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.48/5.72 thf(fact_1016_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.48/5.72 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.48/5.72 thf(fact_1017_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.48/5.72 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.48/5.72 thf(fact_1018_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.48/5.72 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.48/5.72 thf(fact_1019_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.48/5.72 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.48/5.72 thf(fact_1020_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.48/5.72 ! [A: nat,B: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.48/5.72 = B ) ) ).
% 5.48/5.72
% 5.48/5.72 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.48/5.72 thf(fact_1021_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ( ord_less_eq_nat @ A @ B )
% 5.48/5.72 => ( ( ( minus_minus_nat @ B @ A )
% 5.48/5.72 = C )
% 5.48/5.72 = ( B
% 5.48/5.72 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.48/5.72 thf(fact_1022_add__le__imp__le__diff,axiom,
% 5.48/5.72 ! [I: real,K: real,N: real] :
% 5.48/5.72 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.48/5.72 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_imp_le_diff
% 5.48/5.72 thf(fact_1023_add__le__imp__le__diff,axiom,
% 5.48/5.72 ! [I: rat,K: rat,N: rat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.48/5.72 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_imp_le_diff
% 5.48/5.72 thf(fact_1024_add__le__imp__le__diff,axiom,
% 5.48/5.72 ! [I: nat,K: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.48/5.72 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_imp_le_diff
% 5.48/5.72 thf(fact_1025_add__le__imp__le__diff,axiom,
% 5.48/5.72 ! [I: int,K: int,N: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.48/5.72 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_imp_le_diff
% 5.48/5.72 thf(fact_1026_add__le__add__imp__diff__le,axiom,
% 5.48/5.72 ! [I: real,K: real,N: real,J: real] :
% 5.48/5.72 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.48/5.72 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.48/5.72 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.48/5.72 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.48/5.72 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_add_imp_diff_le
% 5.48/5.72 thf(fact_1027_add__le__add__imp__diff__le,axiom,
% 5.48/5.72 ! [I: rat,K: rat,N: rat,J: rat] :
% 5.48/5.72 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.48/5.72 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.48/5.72 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.48/5.72 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.48/5.72 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_add_imp_diff_le
% 5.48/5.72 thf(fact_1028_add__le__add__imp__diff__le,axiom,
% 5.48/5.72 ! [I: nat,K: nat,N: nat,J: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.48/5.72 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.48/5.72 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.48/5.72 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.48/5.72 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_add_imp_diff_le
% 5.48/5.72 thf(fact_1029_add__le__add__imp__diff__le,axiom,
% 5.48/5.72 ! [I: int,K: int,N: int,J: int] :
% 5.48/5.72 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.48/5.72 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.48/5.72 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.48/5.72 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.48/5.72 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_le_add_imp_diff_le
% 5.48/5.72 thf(fact_1030_diff__less__eq,axiom,
% 5.48/5.72 ! [A: real,B: real,C: real] :
% 5.48/5.72 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.48/5.72 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_less_eq
% 5.48/5.72 thf(fact_1031_diff__less__eq,axiom,
% 5.48/5.72 ! [A: rat,B: rat,C: rat] :
% 5.48/5.72 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.48/5.72 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_less_eq
% 5.48/5.72 thf(fact_1032_diff__less__eq,axiom,
% 5.48/5.72 ! [A: int,B: int,C: int] :
% 5.48/5.72 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.48/5.72 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_less_eq
% 5.48/5.72 thf(fact_1033_less__diff__eq,axiom,
% 5.48/5.72 ! [A: real,C: real,B: real] :
% 5.48/5.72 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.48/5.72 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % less_diff_eq
% 5.48/5.72 thf(fact_1034_less__diff__eq,axiom,
% 5.48/5.72 ! [A: rat,C: rat,B: rat] :
% 5.48/5.72 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.48/5.72 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % less_diff_eq
% 5.48/5.72 thf(fact_1035_less__diff__eq,axiom,
% 5.48/5.72 ! [A: int,C: int,B: int] :
% 5.48/5.72 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.48/5.72 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.48/5.72
% 5.48/5.72 % less_diff_eq
% 5.48/5.72 thf(fact_1036_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.48/5.72 ! [A: real,B: real] :
% 5.48/5.72 ( ~ ( ord_less_real @ A @ B )
% 5.48/5.72 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.48/5.72 = A ) ) ).
% 5.48/5.72
% 5.48/5.72 % linordered_semidom_class.add_diff_inverse
% 5.48/5.72 thf(fact_1037_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.48/5.72 ! [A: rat,B: rat] :
% 5.48/5.72 ( ~ ( ord_less_rat @ A @ B )
% 5.48/5.72 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.48/5.72 = A ) ) ).
% 5.48/5.72
% 5.48/5.72 % linordered_semidom_class.add_diff_inverse
% 5.48/5.72 thf(fact_1038_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.48/5.72 ! [A: nat,B: nat] :
% 5.48/5.72 ( ~ ( ord_less_nat @ A @ B )
% 5.48/5.72 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.48/5.72 = A ) ) ).
% 5.48/5.72
% 5.48/5.72 % linordered_semidom_class.add_diff_inverse
% 5.48/5.72 thf(fact_1039_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.48/5.72 ! [A: int,B: int] :
% 5.48/5.72 ( ~ ( ord_less_int @ A @ B )
% 5.48/5.72 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.48/5.72 = A ) ) ).
% 5.48/5.72
% 5.48/5.72 % linordered_semidom_class.add_diff_inverse
% 5.48/5.72 thf(fact_1040_mult__diff__mult,axiom,
% 5.48/5.72 ! [X2: complex,Y2: complex,A: complex,B: complex] :
% 5.48/5.72 ( ( minus_minus_complex @ ( times_times_complex @ X2 @ Y2 ) @ ( times_times_complex @ A @ B ) )
% 5.48/5.72 = ( plus_plus_complex @ ( times_times_complex @ X2 @ ( minus_minus_complex @ Y2 @ B ) ) @ ( times_times_complex @ ( minus_minus_complex @ X2 @ A ) @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % mult_diff_mult
% 5.48/5.72 thf(fact_1041_mult__diff__mult,axiom,
% 5.48/5.72 ! [X2: real,Y2: real,A: real,B: real] :
% 5.48/5.72 ( ( minus_minus_real @ ( times_times_real @ X2 @ Y2 ) @ ( times_times_real @ A @ B ) )
% 5.48/5.72 = ( plus_plus_real @ ( times_times_real @ X2 @ ( minus_minus_real @ Y2 @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X2 @ A ) @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % mult_diff_mult
% 5.48/5.72 thf(fact_1042_mult__diff__mult,axiom,
% 5.48/5.72 ! [X2: rat,Y2: rat,A: rat,B: rat] :
% 5.48/5.72 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ Y2 ) @ ( times_times_rat @ A @ B ) )
% 5.48/5.72 = ( plus_plus_rat @ ( times_times_rat @ X2 @ ( minus_minus_rat @ Y2 @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X2 @ A ) @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % mult_diff_mult
% 5.48/5.72 thf(fact_1043_mult__diff__mult,axiom,
% 5.48/5.72 ! [X2: int,Y2: int,A: int,B: int] :
% 5.48/5.72 ( ( minus_minus_int @ ( times_times_int @ X2 @ Y2 ) @ ( times_times_int @ A @ B ) )
% 5.48/5.72 = ( plus_plus_int @ ( times_times_int @ X2 @ ( minus_minus_int @ Y2 @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X2 @ A ) @ B ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % mult_diff_mult
% 5.48/5.72 thf(fact_1044_eq__add__iff1,axiom,
% 5.48/5.72 ! [A: complex,E: complex,C: complex,B: complex,D2: complex] :
% 5.48/5.72 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 5.48/5.72 = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D2 ) )
% 5.48/5.72 = ( ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ E ) @ C )
% 5.48/5.72 = D2 ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_add_iff1
% 5.48/5.72 thf(fact_1045_eq__add__iff1,axiom,
% 5.48/5.72 ! [A: real,E: real,C: real,B: real,D2: real] :
% 5.48/5.72 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.48/5.72 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 5.48/5.72 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 5.48/5.72 = D2 ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_add_iff1
% 5.48/5.72 thf(fact_1046_eq__add__iff1,axiom,
% 5.48/5.72 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.48/5.72 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.48/5.72 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.48/5.72 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 5.48/5.72 = D2 ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_add_iff1
% 5.48/5.72 thf(fact_1047_eq__add__iff1,axiom,
% 5.48/5.72 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.48/5.72 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.48/5.72 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.48/5.72 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 5.48/5.72 = D2 ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_add_iff1
% 5.48/5.72 thf(fact_1048_eq__add__iff2,axiom,
% 5.48/5.72 ! [A: complex,E: complex,C: complex,B: complex,D2: complex] :
% 5.48/5.72 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 5.48/5.72 = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D2 ) )
% 5.48/5.72 = ( C
% 5.48/5.72 = ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_add_iff2
% 5.48/5.72 thf(fact_1049_eq__add__iff2,axiom,
% 5.48/5.72 ! [A: real,E: real,C: real,B: real,D2: real] :
% 5.48/5.72 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.48/5.72 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 5.48/5.72 = ( C
% 5.48/5.72 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_add_iff2
% 5.48/5.72 thf(fact_1050_eq__add__iff2,axiom,
% 5.48/5.72 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.48/5.72 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.48/5.72 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.48/5.72 = ( C
% 5.48/5.72 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_add_iff2
% 5.48/5.72 thf(fact_1051_eq__add__iff2,axiom,
% 5.48/5.72 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.48/5.72 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.48/5.72 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.48/5.72 = ( C
% 5.48/5.72 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % eq_add_iff2
% 5.48/5.72 thf(fact_1052_square__diff__square__factored,axiom,
% 5.48/5.72 ! [X2: complex,Y2: complex] :
% 5.48/5.72 ( ( minus_minus_complex @ ( times_times_complex @ X2 @ X2 ) @ ( times_times_complex @ Y2 @ Y2 ) )
% 5.48/5.72 = ( times_times_complex @ ( plus_plus_complex @ X2 @ Y2 ) @ ( minus_minus_complex @ X2 @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % square_diff_square_factored
% 5.48/5.72 thf(fact_1053_square__diff__square__factored,axiom,
% 5.48/5.72 ! [X2: real,Y2: real] :
% 5.48/5.72 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) )
% 5.48/5.72 = ( times_times_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( minus_minus_real @ X2 @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % square_diff_square_factored
% 5.48/5.72 thf(fact_1054_square__diff__square__factored,axiom,
% 5.48/5.72 ! [X2: rat,Y2: rat] :
% 5.48/5.72 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y2 @ Y2 ) )
% 5.48/5.72 = ( times_times_rat @ ( plus_plus_rat @ X2 @ Y2 ) @ ( minus_minus_rat @ X2 @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % square_diff_square_factored
% 5.48/5.72 thf(fact_1055_square__diff__square__factored,axiom,
% 5.48/5.72 ! [X2: int,Y2: int] :
% 5.48/5.72 ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y2 @ Y2 ) )
% 5.48/5.72 = ( times_times_int @ ( plus_plus_int @ X2 @ Y2 ) @ ( minus_minus_int @ X2 @ Y2 ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % square_diff_square_factored
% 5.48/5.72 thf(fact_1056_less__diff__iff,axiom,
% 5.48/5.72 ! [K: nat,M: nat,N: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ K @ M )
% 5.48/5.72 => ( ( ord_less_eq_nat @ K @ N )
% 5.48/5.72 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.48/5.72 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % less_diff_iff
% 5.48/5.72 thf(fact_1057_diff__less__mono,axiom,
% 5.48/5.72 ! [A: nat,B: nat,C: nat] :
% 5.48/5.72 ( ( ord_less_nat @ A @ B )
% 5.48/5.72 => ( ( ord_less_eq_nat @ C @ A )
% 5.48/5.72 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % diff_less_mono
% 5.48/5.72 thf(fact_1058_less__diff__conv,axiom,
% 5.48/5.72 ! [I: nat,J: nat,K: nat] :
% 5.48/5.72 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.48/5.72 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 5.48/5.72
% 5.48/5.72 % less_diff_conv
% 5.48/5.72 thf(fact_1059_add__diff__inverse__nat,axiom,
% 5.48/5.72 ! [M: nat,N: nat] :
% 5.48/5.72 ( ~ ( ord_less_nat @ M @ N )
% 5.48/5.72 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 5.48/5.72 = M ) ) ).
% 5.48/5.72
% 5.48/5.72 % add_diff_inverse_nat
% 5.48/5.72 thf(fact_1060_le__diff__conv,axiom,
% 5.48/5.72 ! [J: nat,K: nat,I: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.48/5.72 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % le_diff_conv
% 5.48/5.72 thf(fact_1061_Nat_Ole__diff__conv2,axiom,
% 5.48/5.72 ! [K: nat,J: nat,I: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ K @ J )
% 5.48/5.72 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.48/5.72 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % Nat.le_diff_conv2
% 5.48/5.72 thf(fact_1062_Nat_Odiff__add__assoc,axiom,
% 5.48/5.72 ! [K: nat,J: nat,I: nat] :
% 5.48/5.72 ( ( ord_less_eq_nat @ K @ J )
% 5.48/5.72 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.48/5.72 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.48/5.72
% 5.48/5.72 % Nat.diff_add_assoc
% 5.48/5.72 thf(fact_1063_Nat_Odiff__add__assoc2,axiom,
% 5.48/5.72 ! [K: nat,J: nat,I: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ K @ J )
% 5.48/5.73 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 5.48/5.73 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Nat.diff_add_assoc2
% 5.48/5.73 thf(fact_1064_Nat_Ole__imp__diff__is__add,axiom,
% 5.48/5.73 ! [I: nat,J: nat,K: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.73 => ( ( ( minus_minus_nat @ J @ I )
% 5.48/5.73 = K )
% 5.48/5.73 = ( J
% 5.48/5.73 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Nat.le_imp_diff_is_add
% 5.48/5.73 thf(fact_1065_ordered__ring__class_Ole__add__iff1,axiom,
% 5.48/5.73 ! [A: real,E: real,C: real,B: real,D2: real] :
% 5.48/5.73 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 5.48/5.73 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.48/5.73
% 5.48/5.73 % ordered_ring_class.le_add_iff1
% 5.48/5.73 thf(fact_1066_ordered__ring__class_Ole__add__iff1,axiom,
% 5.48/5.73 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.48/5.73 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.48/5.73 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.48/5.73
% 5.48/5.73 % ordered_ring_class.le_add_iff1
% 5.48/5.73 thf(fact_1067_ordered__ring__class_Ole__add__iff1,axiom,
% 5.48/5.73 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.48/5.73 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.48/5.73 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.48/5.73
% 5.48/5.73 % ordered_ring_class.le_add_iff1
% 5.48/5.73 thf(fact_1068_ordered__ring__class_Ole__add__iff2,axiom,
% 5.48/5.73 ! [A: real,E: real,C: real,B: real,D2: real] :
% 5.48/5.73 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 5.48/5.73 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % ordered_ring_class.le_add_iff2
% 5.48/5.73 thf(fact_1069_ordered__ring__class_Ole__add__iff2,axiom,
% 5.48/5.73 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.48/5.73 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.48/5.73 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % ordered_ring_class.le_add_iff2
% 5.48/5.73 thf(fact_1070_ordered__ring__class_Ole__add__iff2,axiom,
% 5.48/5.73 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.48/5.73 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.48/5.73 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % ordered_ring_class.le_add_iff2
% 5.48/5.73 thf(fact_1071_less__add__iff1,axiom,
% 5.48/5.73 ! [A: real,E: real,C: real,B: real,D2: real] :
% 5.48/5.73 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 5.48/5.73 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_add_iff1
% 5.48/5.73 thf(fact_1072_less__add__iff1,axiom,
% 5.48/5.73 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.48/5.73 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.48/5.73 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_add_iff1
% 5.48/5.73 thf(fact_1073_less__add__iff1,axiom,
% 5.48/5.73 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.48/5.73 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.48/5.73 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_add_iff1
% 5.48/5.73 thf(fact_1074_less__add__iff2,axiom,
% 5.48/5.73 ! [A: real,E: real,C: real,B: real,D2: real] :
% 5.48/5.73 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 5.48/5.73 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_add_iff2
% 5.48/5.73 thf(fact_1075_less__add__iff2,axiom,
% 5.48/5.73 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.48/5.73 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.48/5.73 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_add_iff2
% 5.48/5.73 thf(fact_1076_less__add__iff2,axiom,
% 5.48/5.73 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.48/5.73 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.48/5.73 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_add_iff2
% 5.48/5.73 thf(fact_1077_square__diff__one__factored,axiom,
% 5.48/5.73 ! [X2: complex] :
% 5.48/5.73 ( ( minus_minus_complex @ ( times_times_complex @ X2 @ X2 ) @ one_one_complex )
% 5.48/5.73 = ( times_times_complex @ ( plus_plus_complex @ X2 @ one_one_complex ) @ ( minus_minus_complex @ X2 @ one_one_complex ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % square_diff_one_factored
% 5.48/5.73 thf(fact_1078_square__diff__one__factored,axiom,
% 5.48/5.73 ! [X2: real] :
% 5.48/5.73 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ one_one_real )
% 5.48/5.73 = ( times_times_real @ ( plus_plus_real @ X2 @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % square_diff_one_factored
% 5.48/5.73 thf(fact_1079_square__diff__one__factored,axiom,
% 5.48/5.73 ! [X2: rat] :
% 5.48/5.73 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ one_one_rat )
% 5.48/5.73 = ( times_times_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % square_diff_one_factored
% 5.48/5.73 thf(fact_1080_square__diff__one__factored,axiom,
% 5.48/5.73 ! [X2: int] :
% 5.48/5.73 ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ one_one_int )
% 5.48/5.73 = ( times_times_int @ ( plus_plus_int @ X2 @ one_one_int ) @ ( minus_minus_int @ X2 @ one_one_int ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % square_diff_one_factored
% 5.48/5.73 thf(fact_1081_less__diff__conv2,axiom,
% 5.48/5.73 ! [K: nat,J: nat,I: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ K @ J )
% 5.48/5.73 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.48/5.73 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_diff_conv2
% 5.48/5.73 thf(fact_1082_nat__eq__add__iff1,axiom,
% 5.48/5.73 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ J @ I )
% 5.48/5.73 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.48/5.73 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.48/5.73 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 5.48/5.73 = N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nat_eq_add_iff1
% 5.48/5.73 thf(fact_1083_nat__eq__add__iff2,axiom,
% 5.48/5.73 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.73 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.48/5.73 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.48/5.73 = ( M
% 5.48/5.73 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nat_eq_add_iff2
% 5.48/5.73 thf(fact_1084_nat__le__add__iff1,axiom,
% 5.48/5.73 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ J @ I )
% 5.48/5.73 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.48/5.73 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nat_le_add_iff1
% 5.48/5.73 thf(fact_1085_nat__le__add__iff2,axiom,
% 5.48/5.73 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.73 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.48/5.73 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nat_le_add_iff2
% 5.48/5.73 thf(fact_1086_nat__diff__add__eq1,axiom,
% 5.48/5.73 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ J @ I )
% 5.48/5.73 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.48/5.73 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nat_diff_add_eq1
% 5.48/5.73 thf(fact_1087_nat__diff__add__eq2,axiom,
% 5.48/5.73 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.73 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.48/5.73 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nat_diff_add_eq2
% 5.48/5.73 thf(fact_1088_power2__commute,axiom,
% 5.48/5.73 ! [X2: complex,Y2: complex] :
% 5.48/5.73 ( ( power_power_complex @ ( minus_minus_complex @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.73 = ( power_power_complex @ ( minus_minus_complex @ Y2 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power2_commute
% 5.48/5.73 thf(fact_1089_power2__commute,axiom,
% 5.48/5.73 ! [X2: real,Y2: real] :
% 5.48/5.73 ( ( power_power_real @ ( minus_minus_real @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.73 = ( power_power_real @ ( minus_minus_real @ Y2 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power2_commute
% 5.48/5.73 thf(fact_1090_power2__commute,axiom,
% 5.48/5.73 ! [X2: rat,Y2: rat] :
% 5.48/5.73 ( ( power_power_rat @ ( minus_minus_rat @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.73 = ( power_power_rat @ ( minus_minus_rat @ Y2 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power2_commute
% 5.48/5.73 thf(fact_1091_power2__commute,axiom,
% 5.48/5.73 ! [X2: int,Y2: int] :
% 5.48/5.73 ( ( power_power_int @ ( minus_minus_int @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.73 = ( power_power_int @ ( minus_minus_int @ Y2 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power2_commute
% 5.48/5.73 thf(fact_1092_nat__less__add__iff1,axiom,
% 5.48/5.73 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ J @ I )
% 5.48/5.73 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.48/5.73 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nat_less_add_iff1
% 5.48/5.73 thf(fact_1093_nat__less__add__iff2,axiom,
% 5.48/5.73 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.73 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.48/5.73 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nat_less_add_iff2
% 5.48/5.73 thf(fact_1094_diff__le__diff__pow,axiom,
% 5.48/5.73 ! [K: nat,M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.48/5.73 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % diff_le_diff_pow
% 5.48/5.73 thf(fact_1095_power2__diff,axiom,
% 5.48/5.73 ! [X2: complex,Y2: complex] :
% 5.48/5.73 ( ( power_power_complex @ ( minus_minus_complex @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.73 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power2_diff
% 5.48/5.73 thf(fact_1096_power2__diff,axiom,
% 5.48/5.73 ! [X2: real,Y2: real] :
% 5.48/5.73 ( ( power_power_real @ ( minus_minus_real @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.73 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power2_diff
% 5.48/5.73 thf(fact_1097_power2__diff,axiom,
% 5.48/5.73 ! [X2: rat,Y2: rat] :
% 5.48/5.73 ( ( power_power_rat @ ( minus_minus_rat @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.73 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power2_diff
% 5.48/5.73 thf(fact_1098_power2__diff,axiom,
% 5.48/5.73 ! [X2: int,Y2: int] :
% 5.48/5.73 ( ( power_power_int @ ( minus_minus_int @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.73 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power2_diff
% 5.48/5.73 thf(fact_1099_mint__sound,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 )
% 5.48/5.73 => ( ( vEBT_vebt_mint @ T )
% 5.48/5.73 = ( some_nat @ X2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mint_sound
% 5.48/5.73 thf(fact_1100_mint__corr,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( ( vEBT_vebt_mint @ T )
% 5.48/5.73 = ( some_nat @ X2 ) )
% 5.48/5.73 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mint_corr
% 5.48/5.73 thf(fact_1101_maxt__sound,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 )
% 5.48/5.73 => ( ( vEBT_vebt_maxt @ T )
% 5.48/5.73 = ( some_nat @ X2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % maxt_sound
% 5.48/5.73 thf(fact_1102_maxt__corr,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( ( vEBT_vebt_maxt @ T )
% 5.48/5.73 = ( some_nat @ X2 ) )
% 5.48/5.73 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % maxt_corr
% 5.48/5.73 thf(fact_1103_nested__mint,axiom,
% 5.48/5.73 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.48/5.73 => ( ( N
% 5.48/5.73 = ( suc @ ( suc @ Va ) ) )
% 5.48/5.73 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.48/5.73 => ( ( Ma != Mi )
% 5.48/5.73 => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nested_mint
% 5.48/5.73 thf(fact_1104_invar__vebt_Ointros_I2_J,axiom,
% 5.48/5.73 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.48/5.73 ( ! [X4: vEBT_VEBT] :
% 5.48/5.73 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.48/5.73 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.48/5.73 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.48/5.73 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.48/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.48/5.73 => ( ( M = N )
% 5.48/5.73 => ( ( Deg
% 5.48/5.73 = ( plus_plus_nat @ N @ M ) )
% 5.48/5.73 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.48/5.73 => ( ! [X4: vEBT_VEBT] :
% 5.48/5.73 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.48/5.73 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 5.48/5.73 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % invar_vebt.intros(2)
% 5.48/5.73 thf(fact_1105_divmod__step__eq,axiom,
% 5.48/5.73 ! [L: num,R: nat,Q2: nat] :
% 5.48/5.73 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R )
% 5.48/5.73 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.48/5.73 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L ) ) ) ) )
% 5.48/5.73 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R )
% 5.48/5.73 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.48/5.73 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % divmod_step_eq
% 5.48/5.73 thf(fact_1106_divmod__step__eq,axiom,
% 5.48/5.73 ! [L: num,R: int,Q2: int] :
% 5.48/5.73 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R )
% 5.48/5.73 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.48/5.73 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L ) ) ) ) )
% 5.48/5.73 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R )
% 5.48/5.73 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.48/5.73 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % divmod_step_eq
% 5.48/5.73 thf(fact_1107_divmod__step__eq,axiom,
% 5.48/5.73 ! [L: num,R: code_integer,Q2: code_integer] :
% 5.48/5.73 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R )
% 5.48/5.73 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 5.48/5.73 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 5.48/5.73 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R )
% 5.48/5.73 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 5.48/5.73 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % divmod_step_eq
% 5.48/5.73 thf(fact_1108_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.48/5.73 ! [X2: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.48/5.73 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.48/5.73 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % both_member_options_from_chilf_to_complete_tree
% 5.48/5.73 thf(fact_1109_member__inv,axiom,
% 5.48/5.73 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.48/5.73 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.48/5.73 & ( ( X2 = Mi )
% 5.48/5.73 | ( X2 = Ma )
% 5.48/5.73 | ( ( ord_less_nat @ X2 @ Ma )
% 5.48/5.73 & ( ord_less_nat @ Mi @ X2 )
% 5.48/5.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % member_inv
% 5.48/5.73 thf(fact_1110__C1_C,axiom,
% 5.48/5.73 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.48/5.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.48/5.73 @ ( if_nat
% 5.48/5.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_s_u_c_c @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( if_nat
% 5.48/5.73 @ ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 = none_nat )
% 5.48/5.73 @ one_one_nat
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % "1"
% 5.48/5.73 thf(fact_1111_both__member__options__from__complete__tree__to__child,axiom,
% 5.48/5.73 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.48/5.73 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 | ( X2 = Mi )
% 5.48/5.73 | ( X2 = Ma ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % both_member_options_from_complete_tree_to_child
% 5.48/5.73 thf(fact_1112_even__odd__cases,axiom,
% 5.48/5.73 ! [X2: nat] :
% 5.48/5.73 ( ! [N2: nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( plus_plus_nat @ N2 @ N2 ) )
% 5.48/5.73 => ~ ! [N2: nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % even_odd_cases
% 5.48/5.73 thf(fact_1113_deg__SUcn__Node,axiom,
% 5.48/5.73 ! [Tree: vEBT_VEBT,N: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 5.48/5.73 => ? [Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.48/5.73 ( Tree
% 5.48/5.73 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList2 @ S2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % deg_SUcn_Node
% 5.48/5.73 thf(fact_1114_less__shift,axiom,
% 5.48/5.73 ( ord_less_nat
% 5.48/5.73 = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_less @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_shift
% 5.48/5.73 thf(fact_1115_set__vebt__set__vebt_H__valid,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( vEBT_set_vebt @ T )
% 5.48/5.73 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % set_vebt_set_vebt'_valid
% 5.48/5.73 thf(fact_1116_bit__split__inv,axiom,
% 5.48/5.73 ! [X2: nat,D2: nat] :
% 5.48/5.73 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X2 @ D2 ) @ ( vEBT_VEBT_low @ X2 @ D2 ) @ D2 )
% 5.48/5.73 = X2 ) ).
% 5.48/5.73
% 5.48/5.73 % bit_split_inv
% 5.48/5.73 thf(fact_1117_old_Onat_Oinject,axiom,
% 5.48/5.73 ! [Nat: nat,Nat2: nat] :
% 5.48/5.73 ( ( ( suc @ Nat )
% 5.48/5.73 = ( suc @ Nat2 ) )
% 5.48/5.73 = ( Nat = Nat2 ) ) ).
% 5.48/5.73
% 5.48/5.73 % old.nat.inject
% 5.48/5.73 thf(fact_1118_nat_Oinject,axiom,
% 5.48/5.73 ! [X23: nat,Y22: nat] :
% 5.48/5.73 ( ( ( suc @ X23 )
% 5.48/5.73 = ( suc @ Y22 ) )
% 5.48/5.73 = ( X23 = Y22 ) ) ).
% 5.48/5.73
% 5.48/5.73 % nat.inject
% 5.48/5.73 thf(fact_1119_VEBT_Oinject_I1_J,axiom,
% 5.48/5.73 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.48/5.73 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.48/5.73 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.48/5.73 = ( ( X11 = Y11 )
% 5.48/5.73 & ( X12 = Y12 )
% 5.48/5.73 & ( X13 = Y13 )
% 5.48/5.73 & ( X14 = Y14 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT.inject(1)
% 5.48/5.73 thf(fact_1120_low__inv,axiom,
% 5.48/5.73 ! [X2: nat,N: nat,Y2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.48/5.73 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X2 ) @ N )
% 5.48/5.73 = X2 ) ) ).
% 5.48/5.73
% 5.48/5.73 % low_inv
% 5.48/5.73 thf(fact_1121_lessI,axiom,
% 5.48/5.73 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % lessI
% 5.48/5.73 thf(fact_1122_Suc__mono,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ M @ N )
% 5.48/5.73 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_mono
% 5.48/5.73 thf(fact_1123_Suc__less__eq,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.48/5.73 = ( ord_less_nat @ M @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_less_eq
% 5.48/5.73 thf(fact_1124_Suc__le__mono,axiom,
% 5.48/5.73 ! [N: nat,M: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 5.48/5.73 = ( ord_less_eq_nat @ N @ M ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_le_mono
% 5.48/5.73 thf(fact_1125_add__Suc__right,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 5.48/5.73 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_Suc_right
% 5.48/5.73 thf(fact_1126_Suc__diff__diff,axiom,
% 5.48/5.73 ! [M: nat,N: nat,K: nat] :
% 5.48/5.73 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 5.48/5.73 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_diff_diff
% 5.48/5.73 thf(fact_1127_diff__Suc__Suc,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.48/5.73 = ( minus_minus_nat @ M @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % diff_Suc_Suc
% 5.48/5.73 thf(fact_1128_False,axiom,
% 5.48/5.73 ~ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % False
% 5.48/5.73 thf(fact_1129_mult__Suc__right,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( times_times_nat @ M @ ( suc @ N ) )
% 5.48/5.73 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_Suc_right
% 5.48/5.73 thf(fact_1130_diff__Suc__1,axiom,
% 5.48/5.73 ! [N: nat] :
% 5.48/5.73 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.48/5.73 = N ) ).
% 5.48/5.73
% 5.48/5.73 % diff_Suc_1
% 5.48/5.73 thf(fact_1131_both__member__options__ding,axiom,
% 5.48/5.73 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.48/5.73 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.48/5.73 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % both_member_options_ding
% 5.48/5.73 thf(fact_1132_diff__Suc__diff__eq2,axiom,
% 5.48/5.73 ! [K: nat,J: nat,I: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ K @ J )
% 5.48/5.73 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 5.48/5.73 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % diff_Suc_diff_eq2
% 5.48/5.73 thf(fact_1133_diff__Suc__diff__eq1,axiom,
% 5.48/5.73 ! [K: nat,J: nat,I: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ K @ J )
% 5.48/5.73 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.48/5.73 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % diff_Suc_diff_eq1
% 5.48/5.73 thf(fact_1134_Suc__numeral,axiom,
% 5.48/5.73 ! [N: num] :
% 5.48/5.73 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 5.48/5.73 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_numeral
% 5.48/5.73 thf(fact_1135_add__2__eq__Suc_H,axiom,
% 5.48/5.73 ! [N: nat] :
% 5.48/5.73 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.73 = ( suc @ ( suc @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_2_eq_Suc'
% 5.48/5.73 thf(fact_1136_add__2__eq__Suc,axiom,
% 5.48/5.73 ! [N: nat] :
% 5.48/5.73 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.48/5.73 = ( suc @ ( suc @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_2_eq_Suc
% 5.48/5.73 thf(fact_1137_Suc__1,axiom,
% 5.48/5.73 ( ( suc @ one_one_nat )
% 5.48/5.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_1
% 5.48/5.73 thf(fact_1138_div2__Suc__Suc,axiom,
% 5.48/5.73 ! [M: nat] :
% 5.48/5.73 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.48/5.73 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % div2_Suc_Suc
% 5.48/5.73 thf(fact_1139_succ__member,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,X2: nat,Y2: nat] :
% 5.48/5.73 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Y2 )
% 5.48/5.73 = ( ( vEBT_vebt_member @ T @ Y2 )
% 5.48/5.73 & ( ord_less_nat @ X2 @ Y2 )
% 5.48/5.73 & ! [Z2: nat] :
% 5.48/5.73 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 5.48/5.73 & ( ord_less_nat @ X2 @ Z2 ) )
% 5.48/5.73 => ( ord_less_eq_nat @ Y2 @ Z2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % succ_member
% 5.48/5.73 thf(fact_1140_pred__member,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,X2: nat,Y2: nat] :
% 5.48/5.73 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Y2 )
% 5.48/5.73 = ( ( vEBT_vebt_member @ T @ Y2 )
% 5.48/5.73 & ( ord_less_nat @ Y2 @ X2 )
% 5.48/5.73 & ! [Z2: nat] :
% 5.48/5.73 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 5.48/5.73 & ( ord_less_nat @ Z2 @ X2 ) )
% 5.48/5.73 => ( ord_less_eq_nat @ Z2 @ Y2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % pred_member
% 5.48/5.73 thf(fact_1141_succ__corr,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.48/5.73 = ( some_nat @ Sx ) )
% 5.48/5.73 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % succ_corr
% 5.48/5.73 thf(fact_1142_pred__corr,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat,X2: nat,Px: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.48/5.73 = ( some_nat @ Px ) )
% 5.48/5.73 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Px ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % pred_corr
% 5.48/5.73 thf(fact_1143_succ__correct,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.48/5.73 = ( some_nat @ Sx ) )
% 5.48/5.73 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % succ_correct
% 5.48/5.73 thf(fact_1144_Suc__div__eq__add3__div__numeral,axiom,
% 5.48/5.73 ! [M: nat,V: num] :
% 5.48/5.73 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.48/5.73 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_div_eq_add3_div_numeral
% 5.48/5.73 thf(fact_1145_div__Suc__eq__div__add3,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.48/5.73 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % div_Suc_eq_div_add3
% 5.48/5.73 thf(fact_1146_pred__correct,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.48/5.73 = ( some_nat @ Sx ) )
% 5.48/5.73 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % pred_correct
% 5.48/5.73 thf(fact_1147_n__not__Suc__n,axiom,
% 5.48/5.73 ! [N: nat] :
% 5.48/5.73 ( N
% 5.48/5.73 != ( suc @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % n_not_Suc_n
% 5.48/5.73 thf(fact_1148_Suc__inject,axiom,
% 5.48/5.73 ! [X2: nat,Y2: nat] :
% 5.48/5.73 ( ( ( suc @ X2 )
% 5.48/5.73 = ( suc @ Y2 ) )
% 5.48/5.73 => ( X2 = Y2 ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_inject
% 5.48/5.73 thf(fact_1149_Nat_OlessE,axiom,
% 5.48/5.73 ! [I: nat,K: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I @ K )
% 5.48/5.73 => ( ( K
% 5.48/5.73 != ( suc @ I ) )
% 5.48/5.73 => ~ ! [J2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I @ J2 )
% 5.48/5.73 => ( K
% 5.48/5.73 != ( suc @ J2 ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Nat.lessE
% 5.48/5.73 thf(fact_1150_Suc__lessD,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 5.48/5.73 => ( ord_less_nat @ M @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_lessD
% 5.48/5.73 thf(fact_1151_Suc__lessE,axiom,
% 5.48/5.73 ! [I: nat,K: nat] :
% 5.48/5.73 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 5.48/5.73 => ~ ! [J2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I @ J2 )
% 5.48/5.73 => ( K
% 5.48/5.73 != ( suc @ J2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_lessE
% 5.48/5.73 thf(fact_1152_Suc__lessI,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ M @ N )
% 5.48/5.73 => ( ( ( suc @ M )
% 5.48/5.73 != N )
% 5.48/5.73 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_lessI
% 5.48/5.73 thf(fact_1153_less__SucE,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.48/5.73 => ( ~ ( ord_less_nat @ M @ N )
% 5.48/5.73 => ( M = N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_SucE
% 5.48/5.73 thf(fact_1154_less__SucI,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ M @ N )
% 5.48/5.73 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_SucI
% 5.48/5.73 thf(fact_1155_Ex__less__Suc,axiom,
% 5.48/5.73 ! [N: nat,P: nat > $o] :
% 5.48/5.73 ( ( ? [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.48/5.73 & ( P @ I4 ) ) )
% 5.48/5.73 = ( ( P @ N )
% 5.48/5.73 | ? [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ N )
% 5.48/5.73 & ( P @ I4 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Ex_less_Suc
% 5.48/5.73 thf(fact_1156_less__Suc__eq,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.48/5.73 = ( ( ord_less_nat @ M @ N )
% 5.48/5.73 | ( M = N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_Suc_eq
% 5.48/5.73 thf(fact_1157_not__less__eq,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ~ ( ord_less_nat @ M @ N ) )
% 5.48/5.73 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % not_less_eq
% 5.48/5.73 thf(fact_1158_All__less__Suc,axiom,
% 5.48/5.73 ! [N: nat,P: nat > $o] :
% 5.48/5.73 ( ( ! [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.48/5.73 => ( P @ I4 ) ) )
% 5.48/5.73 = ( ( P @ N )
% 5.48/5.73 & ! [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ N )
% 5.48/5.73 => ( P @ I4 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % All_less_Suc
% 5.48/5.73 thf(fact_1159_Suc__less__eq2,axiom,
% 5.48/5.73 ! [N: nat,M: nat] :
% 5.48/5.73 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.48/5.73 = ( ? [M5: nat] :
% 5.48/5.73 ( ( M
% 5.48/5.73 = ( suc @ M5 ) )
% 5.48/5.73 & ( ord_less_nat @ N @ M5 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_less_eq2
% 5.48/5.73 thf(fact_1160_less__antisym,axiom,
% 5.48/5.73 ! [N: nat,M: nat] :
% 5.48/5.73 ( ~ ( ord_less_nat @ N @ M )
% 5.48/5.73 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.48/5.73 => ( M = N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_antisym
% 5.48/5.73 thf(fact_1161_Suc__less__SucD,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.48/5.73 => ( ord_less_nat @ M @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_less_SucD
% 5.48/5.73 thf(fact_1162_less__trans__Suc,axiom,
% 5.48/5.73 ! [I: nat,J: nat,K: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I @ J )
% 5.48/5.73 => ( ( ord_less_nat @ J @ K )
% 5.48/5.73 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_trans_Suc
% 5.48/5.73 thf(fact_1163_less__Suc__induct,axiom,
% 5.48/5.73 ! [I: nat,J: nat,P: nat > nat > $o] :
% 5.48/5.73 ( ( ord_less_nat @ I @ J )
% 5.48/5.73 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 5.48/5.73 => ( ! [I2: nat,J2: nat,K3: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ J2 )
% 5.48/5.73 => ( ( ord_less_nat @ J2 @ K3 )
% 5.48/5.73 => ( ( P @ I2 @ J2 )
% 5.48/5.73 => ( ( P @ J2 @ K3 )
% 5.48/5.73 => ( P @ I2 @ K3 ) ) ) ) )
% 5.48/5.73 => ( P @ I @ J ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_Suc_induct
% 5.48/5.73 thf(fact_1164_strict__inc__induct,axiom,
% 5.48/5.73 ! [I: nat,J: nat,P: nat > $o] :
% 5.48/5.73 ( ( ord_less_nat @ I @ J )
% 5.48/5.73 => ( ! [I2: nat] :
% 5.48/5.73 ( ( J
% 5.48/5.73 = ( suc @ I2 ) )
% 5.48/5.73 => ( P @ I2 ) )
% 5.48/5.73 => ( ! [I2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ J )
% 5.48/5.73 => ( ( P @ ( suc @ I2 ) )
% 5.48/5.73 => ( P @ I2 ) ) )
% 5.48/5.73 => ( P @ I ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % strict_inc_induct
% 5.48/5.73 thf(fact_1165_not__less__less__Suc__eq,axiom,
% 5.48/5.73 ! [N: nat,M: nat] :
% 5.48/5.73 ( ~ ( ord_less_nat @ N @ M )
% 5.48/5.73 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.48/5.73 = ( N = M ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % not_less_less_Suc_eq
% 5.48/5.73 thf(fact_1166_transitive__stepwise__le,axiom,
% 5.48/5.73 ! [M: nat,N: nat,R2: nat > nat > $o] :
% 5.48/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.73 => ( ! [X4: nat] : ( R2 @ X4 @ X4 )
% 5.48/5.73 => ( ! [X4: nat,Y3: nat,Z3: nat] :
% 5.48/5.73 ( ( R2 @ X4 @ Y3 )
% 5.48/5.73 => ( ( R2 @ Y3 @ Z3 )
% 5.48/5.73 => ( R2 @ X4 @ Z3 ) ) )
% 5.48/5.73 => ( ! [N2: nat] : ( R2 @ N2 @ ( suc @ N2 ) )
% 5.48/5.73 => ( R2 @ M @ N ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % transitive_stepwise_le
% 5.48/5.73 thf(fact_1167_nat__induct__at__least,axiom,
% 5.48/5.73 ! [M: nat,N: nat,P: nat > $o] :
% 5.48/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.73 => ( ( P @ M )
% 5.48/5.73 => ( ! [N2: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ M @ N2 )
% 5.48/5.73 => ( ( P @ N2 )
% 5.48/5.73 => ( P @ ( suc @ N2 ) ) ) )
% 5.48/5.73 => ( P @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nat_induct_at_least
% 5.48/5.73 thf(fact_1168_full__nat__induct,axiom,
% 5.48/5.73 ! [P: nat > $o,N: nat] :
% 5.48/5.73 ( ! [N2: nat] :
% 5.48/5.73 ( ! [M2: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 )
% 5.48/5.73 => ( P @ M2 ) )
% 5.48/5.73 => ( P @ N2 ) )
% 5.48/5.73 => ( P @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % full_nat_induct
% 5.48/5.73 thf(fact_1169_not__less__eq__eq,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 5.48/5.73 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 5.48/5.73
% 5.48/5.73 % not_less_eq_eq
% 5.48/5.73 thf(fact_1170_Suc__n__not__le__n,axiom,
% 5.48/5.73 ! [N: nat] :
% 5.48/5.73 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_n_not_le_n
% 5.48/5.73 thf(fact_1171_le__Suc__eq,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.48/5.73 = ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.73 | ( M
% 5.48/5.73 = ( suc @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % le_Suc_eq
% 5.48/5.73 thf(fact_1172_Suc__le__D,axiom,
% 5.48/5.73 ! [N: nat,M6: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
% 5.48/5.73 => ? [M4: nat] :
% 5.48/5.73 ( M6
% 5.48/5.73 = ( suc @ M4 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_le_D
% 5.48/5.73 thf(fact_1173_le__SucI,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.73 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % le_SucI
% 5.48/5.73 thf(fact_1174_le__SucE,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.48/5.73 => ( ~ ( ord_less_eq_nat @ M @ N )
% 5.48/5.73 => ( M
% 5.48/5.73 = ( suc @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % le_SucE
% 5.48/5.73 thf(fact_1175_Suc__leD,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.48/5.73 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_leD
% 5.48/5.73 thf(fact_1176_add__Suc__shift,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.48/5.73 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_Suc_shift
% 5.48/5.73 thf(fact_1177_add__Suc,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.48/5.73 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_Suc
% 5.48/5.73 thf(fact_1178_nat__arith_Osuc1,axiom,
% 5.48/5.73 ! [A2: nat,K: nat,A: nat] :
% 5.48/5.73 ( ( A2
% 5.48/5.73 = ( plus_plus_nat @ K @ A ) )
% 5.48/5.73 => ( ( suc @ A2 )
% 5.48/5.73 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nat_arith.suc1
% 5.48/5.73 thf(fact_1179_zero__induct__lemma,axiom,
% 5.48/5.73 ! [P: nat > $o,K: nat,I: nat] :
% 5.48/5.73 ( ( P @ K )
% 5.48/5.73 => ( ! [N2: nat] :
% 5.48/5.73 ( ( P @ ( suc @ N2 ) )
% 5.48/5.73 => ( P @ N2 ) )
% 5.48/5.73 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % zero_induct_lemma
% 5.48/5.73 thf(fact_1180_Suc__mult__cancel1,axiom,
% 5.48/5.73 ! [K: nat,M: nat,N: nat] :
% 5.48/5.73 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.48/5.73 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.48/5.73 = ( M = N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_mult_cancel1
% 5.48/5.73 thf(fact_1181_add__diff__assoc__enat,axiom,
% 5.48/5.73 ! [Z: extended_enat,Y2: extended_enat,X2: extended_enat] :
% 5.48/5.73 ( ( ord_le2932123472753598470d_enat @ Z @ Y2 )
% 5.48/5.73 => ( ( plus_p3455044024723400733d_enat @ X2 @ ( minus_3235023915231533773d_enat @ Y2 @ Z ) )
% 5.48/5.73 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_diff_assoc_enat
% 5.48/5.73 thf(fact_1182_lift__Suc__mono__less,axiom,
% 5.48/5.73 ! [F: nat > real,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_less
% 5.48/5.73 thf(fact_1183_lift__Suc__mono__less,axiom,
% 5.48/5.73 ! [F: nat > rat,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_less
% 5.48/5.73 thf(fact_1184_lift__Suc__mono__less,axiom,
% 5.48/5.73 ! [F: nat > num,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_less
% 5.48/5.73 thf(fact_1185_lift__Suc__mono__less,axiom,
% 5.48/5.73 ! [F: nat > nat,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_less
% 5.48/5.73 thf(fact_1186_lift__Suc__mono__less,axiom,
% 5.48/5.73 ! [F: nat > int,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_less
% 5.48/5.73 thf(fact_1187_lift__Suc__mono__less__iff,axiom,
% 5.48/5.73 ! [F: nat > real,N: nat,M: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 5.48/5.73 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_less_iff
% 5.48/5.73 thf(fact_1188_lift__Suc__mono__less__iff,axiom,
% 5.48/5.73 ! [F: nat > rat,N: nat,M: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 5.48/5.73 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_less_iff
% 5.48/5.73 thf(fact_1189_lift__Suc__mono__less__iff,axiom,
% 5.48/5.73 ! [F: nat > num,N: nat,M: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 5.48/5.73 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_less_iff
% 5.48/5.73 thf(fact_1190_lift__Suc__mono__less__iff,axiom,
% 5.48/5.73 ! [F: nat > nat,N: nat,M: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 5.48/5.73 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_less_iff
% 5.48/5.73 thf(fact_1191_lift__Suc__mono__less__iff,axiom,
% 5.48/5.73 ! [F: nat > int,N: nat,M: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 5.48/5.73 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_less_iff
% 5.48/5.73 thf(fact_1192_power__Suc2,axiom,
% 5.48/5.73 ! [A: complex,N: nat] :
% 5.48/5.73 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.48/5.73 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_Suc2
% 5.48/5.73 thf(fact_1193_power__Suc2,axiom,
% 5.48/5.73 ! [A: real,N: nat] :
% 5.48/5.73 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.48/5.73 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_Suc2
% 5.48/5.73 thf(fact_1194_power__Suc2,axiom,
% 5.48/5.73 ! [A: rat,N: nat] :
% 5.48/5.73 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.48/5.73 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_Suc2
% 5.48/5.73 thf(fact_1195_power__Suc2,axiom,
% 5.48/5.73 ! [A: nat,N: nat] :
% 5.48/5.73 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.48/5.73 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_Suc2
% 5.48/5.73 thf(fact_1196_power__Suc2,axiom,
% 5.48/5.73 ! [A: int,N: nat] :
% 5.48/5.73 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.48/5.73 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_Suc2
% 5.48/5.73 thf(fact_1197_power__Suc,axiom,
% 5.48/5.73 ! [A: complex,N: nat] :
% 5.48/5.73 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.48/5.73 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_Suc
% 5.48/5.73 thf(fact_1198_power__Suc,axiom,
% 5.48/5.73 ! [A: real,N: nat] :
% 5.48/5.73 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.48/5.73 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_Suc
% 5.48/5.73 thf(fact_1199_power__Suc,axiom,
% 5.48/5.73 ! [A: rat,N: nat] :
% 5.48/5.73 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.48/5.73 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_Suc
% 5.48/5.73 thf(fact_1200_power__Suc,axiom,
% 5.48/5.73 ! [A: nat,N: nat] :
% 5.48/5.73 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.48/5.73 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_Suc
% 5.48/5.73 thf(fact_1201_power__Suc,axiom,
% 5.48/5.73 ! [A: int,N: nat] :
% 5.48/5.73 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.48/5.73 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_Suc
% 5.48/5.73 thf(fact_1202_lift__Suc__antimono__le,axiom,
% 5.48/5.73 ! [F: nat > set_nat,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_eq_set_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_antimono_le
% 5.48/5.73 thf(fact_1203_lift__Suc__antimono__le,axiom,
% 5.48/5.73 ! [F: nat > rat,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_antimono_le
% 5.48/5.73 thf(fact_1204_lift__Suc__antimono__le,axiom,
% 5.48/5.73 ! [F: nat > num,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_antimono_le
% 5.48/5.73 thf(fact_1205_lift__Suc__antimono__le,axiom,
% 5.48/5.73 ! [F: nat > nat,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_antimono_le
% 5.48/5.73 thf(fact_1206_lift__Suc__antimono__le,axiom,
% 5.48/5.73 ! [F: nat > int,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_antimono_le
% 5.48/5.73 thf(fact_1207_lift__Suc__mono__le,axiom,
% 5.48/5.73 ! [F: nat > set_nat,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_le
% 5.48/5.73 thf(fact_1208_lift__Suc__mono__le,axiom,
% 5.48/5.73 ! [F: nat > rat,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_le
% 5.48/5.73 thf(fact_1209_lift__Suc__mono__le,axiom,
% 5.48/5.73 ! [F: nat > num,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_le
% 5.48/5.73 thf(fact_1210_lift__Suc__mono__le,axiom,
% 5.48/5.73 ! [F: nat > nat,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_le
% 5.48/5.73 thf(fact_1211_lift__Suc__mono__le,axiom,
% 5.48/5.73 ! [F: nat > int,N: nat,N5: nat] :
% 5.48/5.73 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.48/5.73 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % lift_Suc_mono_le
% 5.48/5.73 thf(fact_1212_le__imp__less__Suc,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.73 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % le_imp_less_Suc
% 5.48/5.73 thf(fact_1213_less__eq__Suc__le,axiom,
% 5.48/5.73 ( ord_less_nat
% 5.48/5.73 = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_eq_Suc_le
% 5.48/5.73 thf(fact_1214_less__Suc__eq__le,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.48/5.73 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_Suc_eq_le
% 5.48/5.73 thf(fact_1215_le__less__Suc__eq,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.48/5.73 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.48/5.73 = ( N = M ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % le_less_Suc_eq
% 5.48/5.73 thf(fact_1216_Suc__le__lessD,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.48/5.73 => ( ord_less_nat @ M @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_le_lessD
% 5.48/5.73 thf(fact_1217_inc__induct,axiom,
% 5.48/5.73 ! [I: nat,J: nat,P: nat > $o] :
% 5.48/5.73 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.73 => ( ( P @ J )
% 5.48/5.73 => ( ! [N2: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ I @ N2 )
% 5.48/5.73 => ( ( ord_less_nat @ N2 @ J )
% 5.48/5.73 => ( ( P @ ( suc @ N2 ) )
% 5.48/5.73 => ( P @ N2 ) ) ) )
% 5.48/5.73 => ( P @ I ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % inc_induct
% 5.48/5.73 thf(fact_1218_dec__induct,axiom,
% 5.48/5.73 ! [I: nat,J: nat,P: nat > $o] :
% 5.48/5.73 ( ( ord_less_eq_nat @ I @ J )
% 5.48/5.73 => ( ( P @ I )
% 5.48/5.73 => ( ! [N2: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ I @ N2 )
% 5.48/5.73 => ( ( ord_less_nat @ N2 @ J )
% 5.48/5.73 => ( ( P @ N2 )
% 5.48/5.73 => ( P @ ( suc @ N2 ) ) ) ) )
% 5.48/5.73 => ( P @ J ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % dec_induct
% 5.48/5.73 thf(fact_1219_Suc__le__eq,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.48/5.73 = ( ord_less_nat @ M @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_le_eq
% 5.48/5.73 thf(fact_1220_Suc__leI,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ M @ N )
% 5.48/5.73 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_leI
% 5.48/5.73 thf(fact_1221_less__imp__Suc__add,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ M @ N )
% 5.48/5.73 => ? [K3: nat] :
% 5.48/5.73 ( N
% 5.48/5.73 = ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_imp_Suc_add
% 5.48/5.73 thf(fact_1222_less__iff__Suc__add,axiom,
% 5.48/5.73 ( ord_less_nat
% 5.48/5.73 = ( ^ [M3: nat,N3: nat] :
% 5.48/5.73 ? [K2: nat] :
% 5.48/5.73 ( N3
% 5.48/5.73 = ( suc @ ( plus_plus_nat @ M3 @ K2 ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_iff_Suc_add
% 5.48/5.73 thf(fact_1223_less__add__Suc2,axiom,
% 5.48/5.73 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_add_Suc2
% 5.48/5.73 thf(fact_1224_less__add__Suc1,axiom,
% 5.48/5.73 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_add_Suc1
% 5.48/5.73 thf(fact_1225_less__natE,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ M @ N )
% 5.48/5.73 => ~ ! [Q3: nat] :
% 5.48/5.73 ( N
% 5.48/5.73 != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % less_natE
% 5.48/5.73 thf(fact_1226_Suc__diff__Suc,axiom,
% 5.48/5.73 ! [N: nat,M: nat] :
% 5.48/5.73 ( ( ord_less_nat @ N @ M )
% 5.48/5.73 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 5.48/5.73 = ( minus_minus_nat @ M @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_diff_Suc
% 5.48/5.73 thf(fact_1227_diff__less__Suc,axiom,
% 5.48/5.73 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 5.48/5.73
% 5.48/5.73 % diff_less_Suc
% 5.48/5.73 thf(fact_1228_Suc__mult__less__cancel1,axiom,
% 5.48/5.73 ! [K: nat,M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.48/5.73 = ( ord_less_nat @ M @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_mult_less_cancel1
% 5.48/5.73 thf(fact_1229_Suc__eq__plus1__left,axiom,
% 5.48/5.73 ( suc
% 5.48/5.73 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_eq_plus1_left
% 5.48/5.73 thf(fact_1230_plus__1__eq__Suc,axiom,
% 5.48/5.73 ( ( plus_plus_nat @ one_one_nat )
% 5.48/5.73 = suc ) ).
% 5.48/5.73
% 5.48/5.73 % plus_1_eq_Suc
% 5.48/5.73 thf(fact_1231_Suc__eq__plus1,axiom,
% 5.48/5.73 ( suc
% 5.48/5.73 = ( ^ [N3: nat] : ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_eq_plus1
% 5.48/5.73 thf(fact_1232_Suc__diff__le,axiom,
% 5.48/5.73 ! [N: nat,M: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ N @ M )
% 5.48/5.73 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.48/5.73 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_diff_le
% 5.48/5.73 thf(fact_1233_Suc__mult__le__cancel1,axiom,
% 5.48/5.73 ! [K: nat,M: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.48/5.73 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_mult_le_cancel1
% 5.48/5.73 thf(fact_1234_Suc__div__le__mono,axiom,
% 5.48/5.73 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_div_le_mono
% 5.48/5.73 thf(fact_1235_mult__Suc,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( times_times_nat @ ( suc @ M ) @ N )
% 5.48/5.73 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_Suc
% 5.48/5.73 thf(fact_1236_diff__Suc__eq__diff__pred,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.48/5.73 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % diff_Suc_eq_diff_pred
% 5.48/5.73 thf(fact_1237_xor__num_Ocases,axiom,
% 5.48/5.73 ! [X2: product_prod_num_num] :
% 5.48/5.73 ( ( X2
% 5.48/5.73 != ( product_Pair_num_num @ one @ one ) )
% 5.48/5.73 => ( ! [N2: num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) )
% 5.48/5.73 => ( ! [N2: num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) )
% 5.48/5.73 => ( ! [M4: num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 5.48/5.73 => ( ! [M4: num,N2: num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) )
% 5.48/5.73 => ( ! [M4: num,N2: num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) )
% 5.48/5.73 => ( ! [M4: num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 5.48/5.73 => ( ! [M4: num,N2: num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) )
% 5.48/5.73 => ~ ! [M4: num,N2: num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % xor_num.cases
% 5.48/5.73 thf(fact_1238_power__gt1,axiom,
% 5.48/5.73 ! [A: real,N: nat] :
% 5.48/5.73 ( ( ord_less_real @ one_one_real @ A )
% 5.48/5.73 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_gt1
% 5.48/5.73 thf(fact_1239_power__gt1,axiom,
% 5.48/5.73 ! [A: rat,N: nat] :
% 5.48/5.73 ( ( ord_less_rat @ one_one_rat @ A )
% 5.48/5.73 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_gt1
% 5.48/5.73 thf(fact_1240_power__gt1,axiom,
% 5.48/5.73 ! [A: nat,N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ one_one_nat @ A )
% 5.48/5.73 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_gt1
% 5.48/5.73 thf(fact_1241_power__gt1,axiom,
% 5.48/5.73 ! [A: int,N: nat] :
% 5.48/5.73 ( ( ord_less_int @ one_one_int @ A )
% 5.48/5.73 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_gt1
% 5.48/5.73 thf(fact_1242_eval__nat__numeral_I3_J,axiom,
% 5.48/5.73 ! [N: num] :
% 5.48/5.73 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.48/5.73 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % eval_nat_numeral(3)
% 5.48/5.73 thf(fact_1243_Suc3__eq__add__3,axiom,
% 5.48/5.73 ! [N: nat] :
% 5.48/5.73 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 5.48/5.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc3_eq_add_3
% 5.48/5.73 thf(fact_1244_div__nat__eqI,axiom,
% 5.48/5.73 ! [N: nat,Q2: nat,M: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 5.48/5.73 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 5.48/5.73 => ( ( divide_divide_nat @ M @ N )
% 5.48/5.73 = Q2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % div_nat_eqI
% 5.48/5.73 thf(fact_1245_Suc__nat__number__of__add,axiom,
% 5.48/5.73 ! [V: num,N: nat] :
% 5.48/5.73 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.48/5.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_nat_number_of_add
% 5.48/5.73 thf(fact_1246_Suc__div__eq__add3__div,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.48/5.73 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_div_eq_add3_div
% 5.48/5.73 thf(fact_1247_power__odd__eq,axiom,
% 5.48/5.73 ! [A: complex,N: nat] :
% 5.48/5.73 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.48/5.73 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_odd_eq
% 5.48/5.73 thf(fact_1248_power__odd__eq,axiom,
% 5.48/5.73 ! [A: real,N: nat] :
% 5.48/5.73 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.48/5.73 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_odd_eq
% 5.48/5.73 thf(fact_1249_power__odd__eq,axiom,
% 5.48/5.73 ! [A: rat,N: nat] :
% 5.48/5.73 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.48/5.73 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_odd_eq
% 5.48/5.73 thf(fact_1250_power__odd__eq,axiom,
% 5.48/5.73 ! [A: nat,N: nat] :
% 5.48/5.73 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.48/5.73 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_odd_eq
% 5.48/5.73 thf(fact_1251_power__odd__eq,axiom,
% 5.48/5.73 ! [A: int,N: nat] :
% 5.48/5.73 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.48/5.73 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_odd_eq
% 5.48/5.73 thf(fact_1252_invar__vebt_Ointros_I5_J,axiom,
% 5.48/5.73 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.48/5.73 ( ! [X4: vEBT_VEBT] :
% 5.48/5.73 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.48/5.73 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.48/5.73 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.48/5.73 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.48/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.48/5.73 => ( ( M
% 5.48/5.73 = ( suc @ N ) )
% 5.48/5.73 => ( ( Deg
% 5.48/5.73 = ( plus_plus_nat @ N @ M ) )
% 5.48/5.73 => ( ! [I2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.48/5.73 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X7 ) )
% 5.48/5.73 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.48/5.73 => ( ( ( Mi = Ma )
% 5.48/5.73 => ! [X4: vEBT_VEBT] :
% 5.48/5.73 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.48/5.73 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.48/5.73 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.48/5.73 => ( ( ( Mi != Ma )
% 5.48/5.73 => ! [I2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.48/5.73 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.48/5.73 = I2 )
% 5.48/5.73 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.48/5.73 & ! [X4: nat] :
% 5.48/5.73 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 5.48/5.73 = I2 )
% 5.48/5.73 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 5.48/5.73 => ( ( ord_less_nat @ Mi @ X4 )
% 5.48/5.73 & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 5.48/5.73 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % invar_vebt.intros(5)
% 5.48/5.73 thf(fact_1253_invar__vebt_Ointros_I3_J,axiom,
% 5.48/5.73 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.48/5.73 ( ! [X4: vEBT_VEBT] :
% 5.48/5.73 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.48/5.73 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.48/5.73 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.48/5.73 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.48/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.48/5.73 => ( ( M
% 5.48/5.73 = ( suc @ N ) )
% 5.48/5.73 => ( ( Deg
% 5.48/5.73 = ( plus_plus_nat @ N @ M ) )
% 5.48/5.73 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.48/5.73 => ( ! [X4: vEBT_VEBT] :
% 5.48/5.73 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.48/5.73 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 5.48/5.73 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % invar_vebt.intros(3)
% 5.48/5.73 thf(fact_1254_invar__vebt_Ointros_I4_J,axiom,
% 5.48/5.73 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.48/5.73 ( ! [X4: vEBT_VEBT] :
% 5.48/5.73 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.48/5.73 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.48/5.73 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.48/5.73 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.48/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.48/5.73 => ( ( M = N )
% 5.48/5.73 => ( ( Deg
% 5.48/5.73 = ( plus_plus_nat @ N @ M ) )
% 5.48/5.73 => ( ! [I2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.48/5.73 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X7 ) )
% 5.48/5.73 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.48/5.73 => ( ( ( Mi = Ma )
% 5.48/5.73 => ! [X4: vEBT_VEBT] :
% 5.48/5.73 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.48/5.73 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 5.48/5.73 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.48/5.73 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.48/5.73 => ( ( ( Mi != Ma )
% 5.48/5.73 => ! [I2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.48/5.73 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.48/5.73 = I2 )
% 5.48/5.73 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.48/5.73 & ! [X4: nat] :
% 5.48/5.73 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 5.48/5.73 = I2 )
% 5.48/5.73 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 5.48/5.73 => ( ( ord_less_nat @ Mi @ X4 )
% 5.48/5.73 & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 5.48/5.73 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % invar_vebt.intros(4)
% 5.48/5.73 thf(fact_1255_in__children__def,axiom,
% 5.48/5.73 ( vEBT_V5917875025757280293ildren
% 5.48/5.73 = ( ^ [N3: nat,TreeList3: list_VEBT_VEBT,X: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ X @ N3 ) ) @ ( vEBT_VEBT_low @ X @ N3 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % in_children_def
% 5.48/5.73 thf(fact_1256_real__average__minus__first,axiom,
% 5.48/5.73 ! [A: real,B: real] :
% 5.48/5.73 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.48/5.73 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % real_average_minus_first
% 5.48/5.73 thf(fact_1257_real__average__minus__second,axiom,
% 5.48/5.73 ! [B: real,A: real] :
% 5.48/5.73 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.48/5.73 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % real_average_minus_second
% 5.48/5.73 thf(fact_1258_vebt__insert_Osimps_I4_J,axiom,
% 5.48/5.73 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.48/5.73 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) ) ).
% 5.48/5.73
% 5.48/5.73 % vebt_insert.simps(4)
% 5.48/5.73 thf(fact_1259__C0_C,axiom,
% 5.48/5.73 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.48/5.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.48/5.73 @ ( if_nat
% 5.48/5.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 5.48/5.73 @ ( if_nat
% 5.48/5.73 @ ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 = none_nat )
% 5.48/5.73 @ one_one_nat
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % "0"
% 5.48/5.73 thf(fact_1260_vebt__mint_Osimps_I3_J,axiom,
% 5.48/5.73 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.48/5.73 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.48/5.73 = ( some_nat @ Mi ) ) ).
% 5.48/5.73
% 5.48/5.73 % vebt_mint.simps(3)
% 5.48/5.73 thf(fact_1261_vebt__maxt_Osimps_I3_J,axiom,
% 5.48/5.73 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.48/5.73 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.48/5.73 = ( some_nat @ Ma ) ) ).
% 5.48/5.73
% 5.48/5.73 % vebt_maxt.simps(3)
% 5.48/5.73 thf(fact_1262_double__not__eq__Suc__double,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.48/5.73 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % double_not_eq_Suc_double
% 5.48/5.73 thf(fact_1263_Suc__double__not__eq__double,axiom,
% 5.48/5.73 ! [M: nat,N: nat] :
% 5.48/5.73 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.48/5.73 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % Suc_double_not_eq_double
% 5.48/5.73 thf(fact_1264_pred__lesseq__max,axiom,
% 5.48/5.73 ! [Deg: nat,X2: nat,Ma: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.48/5.73 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.48/5.73 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 @ ( if_option_nat
% 5.48/5.73 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( if_option_nat
% 5.48/5.73 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 = none_nat )
% 5.48/5.73 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.48/5.73 @ none_nat ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % pred_lesseq_max
% 5.48/5.73 thf(fact_1265_pred__less__length__list,axiom,
% 5.48/5.73 ! [Deg: nat,X2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.48/5.73 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.48/5.73 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( if_option_nat
% 5.48/5.73 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( if_option_nat
% 5.48/5.73 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 = none_nat )
% 5.48/5.73 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % pred_less_length_list
% 5.48/5.73 thf(fact_1266_set__vebt_H__def,axiom,
% 5.48/5.73 ( vEBT_VEBT_set_vebt
% 5.48/5.73 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % set_vebt'_def
% 5.48/5.73 thf(fact_1267_succ__greatereq__min,axiom,
% 5.48/5.73 ! [Deg: nat,Mi: nat,X2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.48/5.73 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.48/5.73 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 @ ( if_option_nat
% 5.48/5.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( if_option_nat
% 5.48/5.73 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 = none_nat )
% 5.48/5.73 @ none_nat
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.48/5.73 @ none_nat ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % succ_greatereq_min
% 5.48/5.73 thf(fact_1268_succ__less__length__list,axiom,
% 5.48/5.73 ! [Deg: nat,Mi: nat,X2: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.48/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.48/5.73 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.48/5.73 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( if_option_nat
% 5.48/5.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( if_option_nat
% 5.48/5.73 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 = none_nat )
% 5.48/5.73 @ none_nat
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % succ_less_length_list
% 5.48/5.73 thf(fact_1269_mult__commute__abs,axiom,
% 5.48/5.73 ! [C: real] :
% 5.48/5.73 ( ( ^ [X: real] : ( times_times_real @ X @ C ) )
% 5.48/5.73 = ( times_times_real @ C ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_commute_abs
% 5.48/5.73 thf(fact_1270_mult__commute__abs,axiom,
% 5.48/5.73 ! [C: rat] :
% 5.48/5.73 ( ( ^ [X: rat] : ( times_times_rat @ X @ C ) )
% 5.48/5.73 = ( times_times_rat @ C ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_commute_abs
% 5.48/5.73 thf(fact_1271_mult__commute__abs,axiom,
% 5.48/5.73 ! [C: nat] :
% 5.48/5.73 ( ( ^ [X: nat] : ( times_times_nat @ X @ C ) )
% 5.48/5.73 = ( times_times_nat @ C ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_commute_abs
% 5.48/5.73 thf(fact_1272_mult__commute__abs,axiom,
% 5.48/5.73 ! [C: int] :
% 5.48/5.73 ( ( ^ [X: int] : ( times_times_int @ X @ C ) )
% 5.48/5.73 = ( times_times_int @ C ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_commute_abs
% 5.48/5.73 thf(fact_1273_lambda__one,axiom,
% 5.48/5.73 ( ( ^ [X: complex] : X )
% 5.48/5.73 = ( times_times_complex @ one_one_complex ) ) ).
% 5.48/5.73
% 5.48/5.73 % lambda_one
% 5.48/5.73 thf(fact_1274_lambda__one,axiom,
% 5.48/5.73 ( ( ^ [X: real] : X )
% 5.48/5.73 = ( times_times_real @ one_one_real ) ) ).
% 5.48/5.73
% 5.48/5.73 % lambda_one
% 5.48/5.73 thf(fact_1275_lambda__one,axiom,
% 5.48/5.73 ( ( ^ [X: rat] : X )
% 5.48/5.73 = ( times_times_rat @ one_one_rat ) ) ).
% 5.48/5.73
% 5.48/5.73 % lambda_one
% 5.48/5.73 thf(fact_1276_lambda__one,axiom,
% 5.48/5.73 ( ( ^ [X: nat] : X )
% 5.48/5.73 = ( times_times_nat @ one_one_nat ) ) ).
% 5.48/5.73
% 5.48/5.73 % lambda_one
% 5.48/5.73 thf(fact_1277_lambda__one,axiom,
% 5.48/5.73 ( ( ^ [X: int] : X )
% 5.48/5.73 = ( times_times_int @ one_one_int ) ) ).
% 5.48/5.73
% 5.48/5.73 % lambda_one
% 5.48/5.73 thf(fact_1278_numeral__code_I2_J,axiom,
% 5.48/5.73 ! [N: num] :
% 5.48/5.73 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.48/5.73 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % numeral_code(2)
% 5.48/5.73 thf(fact_1279_numeral__code_I2_J,axiom,
% 5.48/5.73 ! [N: num] :
% 5.48/5.73 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.48/5.73 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % numeral_code(2)
% 5.48/5.73 thf(fact_1280_numeral__code_I2_J,axiom,
% 5.48/5.73 ! [N: num] :
% 5.48/5.73 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.48/5.73 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % numeral_code(2)
% 5.48/5.73 thf(fact_1281_numeral__code_I2_J,axiom,
% 5.48/5.73 ! [N: num] :
% 5.48/5.73 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.48/5.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % numeral_code(2)
% 5.48/5.73 thf(fact_1282_numeral__code_I2_J,axiom,
% 5.48/5.73 ! [N: num] :
% 5.48/5.73 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.48/5.73 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % numeral_code(2)
% 5.48/5.73 thf(fact_1283_numeral__code_I3_J,axiom,
% 5.48/5.73 ! [N: num] :
% 5.48/5.73 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.48/5.73 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.48/5.73
% 5.48/5.73 % numeral_code(3)
% 5.48/5.73 thf(fact_1284_numeral__code_I3_J,axiom,
% 5.48/5.73 ! [N: num] :
% 5.48/5.73 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.48/5.73 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.48/5.73
% 5.48/5.73 % numeral_code(3)
% 5.48/5.73 thf(fact_1285_numeral__code_I3_J,axiom,
% 5.48/5.73 ! [N: num] :
% 5.48/5.73 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.48/5.73 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.48/5.73
% 5.48/5.73 % numeral_code(3)
% 5.48/5.73 thf(fact_1286_numeral__code_I3_J,axiom,
% 5.48/5.73 ! [N: num] :
% 5.48/5.73 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.48/5.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.48/5.73
% 5.48/5.73 % numeral_code(3)
% 5.48/5.73 thf(fact_1287_numeral__code_I3_J,axiom,
% 5.48/5.73 ! [N: num] :
% 5.48/5.73 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.48/5.73 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.48/5.73
% 5.48/5.73 % numeral_code(3)
% 5.48/5.73 thf(fact_1288_power__numeral__even,axiom,
% 5.48/5.73 ! [Z: complex,W: num] :
% 5.48/5.73 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.48/5.73 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_numeral_even
% 5.48/5.73 thf(fact_1289_power__numeral__even,axiom,
% 5.48/5.73 ! [Z: real,W: num] :
% 5.48/5.73 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.48/5.73 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_numeral_even
% 5.48/5.73 thf(fact_1290_power__numeral__even,axiom,
% 5.48/5.73 ! [Z: rat,W: num] :
% 5.48/5.73 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.48/5.73 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_numeral_even
% 5.48/5.73 thf(fact_1291_power__numeral__even,axiom,
% 5.48/5.73 ! [Z: nat,W: num] :
% 5.48/5.73 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.48/5.73 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_numeral_even
% 5.48/5.73 thf(fact_1292_power__numeral__even,axiom,
% 5.48/5.73 ! [Z: int,W: num] :
% 5.48/5.73 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.48/5.73 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_numeral_even
% 5.48/5.73 thf(fact_1293_power__numeral__odd,axiom,
% 5.48/5.73 ! [Z: complex,W: num] :
% 5.48/5.73 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.48/5.73 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_numeral_odd
% 5.48/5.73 thf(fact_1294_power__numeral__odd,axiom,
% 5.48/5.73 ! [Z: real,W: num] :
% 5.48/5.73 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.48/5.73 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_numeral_odd
% 5.48/5.73 thf(fact_1295_power__numeral__odd,axiom,
% 5.48/5.73 ! [Z: rat,W: num] :
% 5.48/5.73 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.48/5.73 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_numeral_odd
% 5.48/5.73 thf(fact_1296_power__numeral__odd,axiom,
% 5.48/5.73 ! [Z: nat,W: num] :
% 5.48/5.73 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.48/5.73 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_numeral_odd
% 5.48/5.73 thf(fact_1297_power__numeral__odd,axiom,
% 5.48/5.73 ! [Z: int,W: num] :
% 5.48/5.73 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.48/5.73 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % power_numeral_odd
% 5.48/5.73 thf(fact_1298_is__pred__in__set__def,axiom,
% 5.48/5.73 ( vEBT_is_pred_in_set
% 5.48/5.73 = ( ^ [Xs: set_nat,X: nat,Y: nat] :
% 5.48/5.73 ( ( member_nat @ Y @ Xs )
% 5.48/5.73 & ( ord_less_nat @ Y @ X )
% 5.48/5.73 & ! [Z2: nat] :
% 5.48/5.73 ( ( member_nat @ Z2 @ Xs )
% 5.48/5.73 => ( ( ord_less_nat @ Z2 @ X )
% 5.48/5.73 => ( ord_less_eq_nat @ Z2 @ Y ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % is_pred_in_set_def
% 5.48/5.73 thf(fact_1299_is__succ__in__set__def,axiom,
% 5.48/5.73 ( vEBT_is_succ_in_set
% 5.48/5.73 = ( ^ [Xs: set_nat,X: nat,Y: nat] :
% 5.48/5.73 ( ( member_nat @ Y @ Xs )
% 5.48/5.73 & ( ord_less_nat @ X @ Y )
% 5.48/5.73 & ! [Z2: nat] :
% 5.48/5.73 ( ( member_nat @ Z2 @ Xs )
% 5.48/5.73 => ( ( ord_less_nat @ X @ Z2 )
% 5.48/5.73 => ( ord_less_eq_nat @ Y @ Z2 ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % is_succ_in_set_def
% 5.48/5.73 thf(fact_1300_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.48/5.73 ! [X2: produc5491161045314408544at_nat] :
% 5.48/5.73 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.48/5.73 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.48/5.73 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X4 ) @ ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_comp_shift.cases
% 5.48/5.73 thf(fact_1301_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.48/5.73 ! [X2: produc2233624965454879586on_nat] :
% 5.48/5.73 ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.48/5.73 => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.48/5.73 => ~ ! [F2: nat > nat > $o,X4: nat,Y3: nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X4 ) @ ( some_nat @ Y3 ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_comp_shift.cases
% 5.48/5.73 thf(fact_1302_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.48/5.73 ! [X2: produc7036089656553540234on_num] :
% 5.48/5.73 ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.48/5.73 => ( ! [Uw2: num > num > $o,V2: num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.48/5.73 => ~ ! [F2: num > num > $o,X4: num,Y3: num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X4 ) @ ( some_num @ Y3 ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_comp_shift.cases
% 5.48/5.73 thf(fact_1303_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.48/5.73 ! [X2: produc5542196010084753463at_nat] :
% 5.48/5.73 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.48/5.73 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.48/5.73 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A3: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A3 ) @ ( some_P7363390416028606310at_nat @ B2 ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.cases
% 5.48/5.73 thf(fact_1304_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.48/5.73 ! [X2: produc8306885398267862888on_nat] :
% 5.48/5.73 ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.48/5.73 => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.48/5.73 => ~ ! [F2: nat > nat > nat,A3: nat,B2: nat] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A3 ) @ ( some_nat @ B2 ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.cases
% 5.48/5.73 thf(fact_1305_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.48/5.73 ! [X2: produc1193250871479095198on_num] :
% 5.48/5.73 ( ! [Uu2: num > num > num,Uv2: option_num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.48/5.73 => ( ! [Uw2: num > num > num,V2: num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.48/5.73 => ~ ! [F2: num > num > num,A3: num,B2: num] :
% 5.48/5.73 ( X2
% 5.48/5.73 != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A3 ) @ ( some_num @ B2 ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.cases
% 5.48/5.73 thf(fact_1306_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.48/5.73 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.48/5.73 ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 5.48/5.73 = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.simps(3)
% 5.48/5.73 thf(fact_1307_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.48/5.73 ! [F: num > num > num,A: num,B: num] :
% 5.48/5.73 ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 5.48/5.73 = ( some_num @ ( F @ A @ B ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.simps(3)
% 5.48/5.73 thf(fact_1308_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.48/5.73 ! [F: nat > nat > nat,A: nat,B: nat] :
% 5.48/5.73 ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 5.48/5.73 = ( some_nat @ ( F @ A @ B ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.simps(3)
% 5.48/5.73 thf(fact_1309_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.48/5.73 ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 5.48/5.73 ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 5.48/5.73 = none_P5556105721700978146at_nat ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.simps(1)
% 5.48/5.73 thf(fact_1310_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.48/5.73 ! [Uu: num > num > num,Uv: option_num] :
% 5.48/5.73 ( ( vEBT_V819420779217536731ft_num @ Uu @ none_num @ Uv )
% 5.48/5.73 = none_num ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.simps(1)
% 5.48/5.73 thf(fact_1311_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.48/5.73 ! [Uu: nat > nat > nat,Uv: option_nat] :
% 5.48/5.73 ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 5.48/5.73 = none_nat ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.simps(1)
% 5.48/5.73 thf(fact_1312_vebt__succ_Osimps_I6_J,axiom,
% 5.48/5.73 ! [X2: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.48/5.73 ( ( ( ord_less_nat @ X2 @ Mi )
% 5.48/5.73 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( some_nat @ Mi ) ) )
% 5.48/5.73 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.48/5.73 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 @ ( if_option_nat
% 5.48/5.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( if_option_nat
% 5.48/5.73 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 = none_nat )
% 5.48/5.73 @ none_nat
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.48/5.73 @ none_nat ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % vebt_succ.simps(6)
% 5.48/5.73 thf(fact_1313_vebt__pred_Osimps_I7_J,axiom,
% 5.48/5.73 ! [Ma: nat,X2: nat,Mi: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.48/5.73 ( ( ( ord_less_nat @ Ma @ X2 )
% 5.48/5.73 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( some_nat @ Ma ) ) )
% 5.48/5.73 & ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.48/5.73 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 @ ( if_option_nat
% 5.48/5.73 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( if_option_nat
% 5.48/5.73 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 = none_nat )
% 5.48/5.73 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.48/5.73 @ none_nat ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % vebt_pred.simps(7)
% 5.48/5.73 thf(fact_1314_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I6_J,axiom,
% 5.48/5.73 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.48/5.73 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( plus_plus_nat @ one_one_nat
% 5.48/5.73 @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ one_one_nat
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 5.48/5.73 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.48/5.73 @ ( if_nat
% 5.48/5.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 5.48/5.73 @ ( if_nat
% 5.48/5.73 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 = none_nat )
% 5.48/5.73 @ one_one_nat
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.48/5.73 @ one_one_nat ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(6)
% 5.48/5.73 thf(fact_1315_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.48/5.73 ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 5.48/5.73 ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 5.48/5.73 = none_P5556105721700978146at_nat ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.simps(2)
% 5.48/5.73 thf(fact_1316_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.48/5.73 ! [Uw: num > num > num,V: num] :
% 5.48/5.73 ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 5.48/5.73 = none_num ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.simps(2)
% 5.48/5.73 thf(fact_1317_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.48/5.73 ! [Uw: nat > nat > nat,V: nat] :
% 5.48/5.73 ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 5.48/5.73 = none_nat ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.simps(2)
% 5.48/5.73 thf(fact_1318_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.48/5.73 ! [X2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y2: option4927543243414619207at_nat] :
% 5.48/5.73 ( ( ( vEBT_V1502963449132264192at_nat @ X2 @ Xa2 @ Xb )
% 5.48/5.73 = Y2 )
% 5.48/5.73 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.48/5.73 => ( Y2 != none_P5556105721700978146at_nat ) )
% 5.48/5.73 => ( ( ? [V2: product_prod_nat_nat] :
% 5.48/5.73 ( Xa2
% 5.48/5.73 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.48/5.73 => ( ( Xb = none_P5556105721700978146at_nat )
% 5.48/5.73 => ( Y2 != none_P5556105721700978146at_nat ) ) )
% 5.48/5.73 => ~ ! [A3: product_prod_nat_nat] :
% 5.48/5.73 ( ( Xa2
% 5.48/5.73 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.48/5.73 => ! [B2: product_prod_nat_nat] :
% 5.48/5.73 ( ( Xb
% 5.48/5.73 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.48/5.73 => ( Y2
% 5.48/5.73 != ( some_P7363390416028606310at_nat @ ( X2 @ A3 @ B2 ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.elims
% 5.48/5.73 thf(fact_1319_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.48/5.73 ! [X2: num > num > num,Xa2: option_num,Xb: option_num,Y2: option_num] :
% 5.48/5.73 ( ( ( vEBT_V819420779217536731ft_num @ X2 @ Xa2 @ Xb )
% 5.48/5.73 = Y2 )
% 5.48/5.73 => ( ( ( Xa2 = none_num )
% 5.48/5.73 => ( Y2 != none_num ) )
% 5.48/5.73 => ( ( ? [V2: num] :
% 5.48/5.73 ( Xa2
% 5.48/5.73 = ( some_num @ V2 ) )
% 5.48/5.73 => ( ( Xb = none_num )
% 5.48/5.73 => ( Y2 != none_num ) ) )
% 5.48/5.73 => ~ ! [A3: num] :
% 5.48/5.73 ( ( Xa2
% 5.48/5.73 = ( some_num @ A3 ) )
% 5.48/5.73 => ! [B2: num] :
% 5.48/5.73 ( ( Xb
% 5.48/5.73 = ( some_num @ B2 ) )
% 5.48/5.73 => ( Y2
% 5.48/5.73 != ( some_num @ ( X2 @ A3 @ B2 ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.elims
% 5.48/5.73 thf(fact_1320_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.48/5.73 ! [X2: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y2: option_nat] :
% 5.48/5.73 ( ( ( vEBT_V4262088993061758097ft_nat @ X2 @ Xa2 @ Xb )
% 5.48/5.73 = Y2 )
% 5.48/5.73 => ( ( ( Xa2 = none_nat )
% 5.48/5.73 => ( Y2 != none_nat ) )
% 5.48/5.73 => ( ( ? [V2: nat] :
% 5.48/5.73 ( Xa2
% 5.48/5.73 = ( some_nat @ V2 ) )
% 5.48/5.73 => ( ( Xb = none_nat )
% 5.48/5.73 => ( Y2 != none_nat ) ) )
% 5.48/5.73 => ~ ! [A3: nat] :
% 5.48/5.73 ( ( Xa2
% 5.48/5.73 = ( some_nat @ A3 ) )
% 5.48/5.73 => ! [B2: nat] :
% 5.48/5.73 ( ( Xb
% 5.48/5.73 = ( some_nat @ B2 ) )
% 5.48/5.73 => ( Y2
% 5.48/5.73 != ( some_nat @ ( X2 @ A3 @ B2 ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.option_shift.elims
% 5.48/5.73 thf(fact_1321_vebt__maxt_Osimps_I2_J,axiom,
% 5.48/5.73 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.48/5.73 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.48/5.73 = none_nat ) ).
% 5.48/5.73
% 5.48/5.73 % vebt_maxt.simps(2)
% 5.48/5.73 thf(fact_1322_vebt__mint_Osimps_I2_J,axiom,
% 5.48/5.73 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.48/5.73 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.48/5.73 = none_nat ) ).
% 5.48/5.73
% 5.48/5.73 % vebt_mint.simps(2)
% 5.48/5.73 thf(fact_1323_vebt__member_Osimps_I5_J,axiom,
% 5.48/5.73 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.48/5.73 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( ( X2 != Mi )
% 5.48/5.73 => ( ( X2 != Ma )
% 5.48/5.73 => ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.48/5.73 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.48/5.73 => ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.48/5.73 & ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.48/5.73 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % vebt_member.simps(5)
% 5.48/5.73 thf(fact_1324_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I6_J,axiom,
% 5.48/5.73 ! [X2: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.48/5.73 ( ( ( ord_less_nat @ X2 @ Mi )
% 5.48/5.73 => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = one_one_nat ) )
% 5.48/5.73 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.48/5.73 => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 @ ( if_nat
% 5.48/5.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.48/5.73 @ one_one_nat ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(6)
% 5.48/5.73 thf(fact_1325_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I5_J,axiom,
% 5.48/5.73 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.48/5.73 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.48/5.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X2 = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X2 = Ma ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma @ X2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(5)
% 5.48/5.73 thf(fact_1326_pred__empty,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.48/5.73 = none_nat )
% 5.48/5.73 = ( ( collect_nat
% 5.48/5.73 @ ^ [Y: nat] :
% 5.48/5.73 ( ( vEBT_vebt_member @ T @ Y )
% 5.48/5.73 & ( ord_less_nat @ Y @ X2 ) ) )
% 5.48/5.73 = bot_bot_set_nat ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % pred_empty
% 5.48/5.73 thf(fact_1327_succ__empty,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.48/5.73 = none_nat )
% 5.48/5.73 = ( ( collect_nat
% 5.48/5.73 @ ^ [Y: nat] :
% 5.48/5.73 ( ( vEBT_vebt_member @ T @ Y )
% 5.48/5.73 & ( ord_less_nat @ X2 @ Y ) ) )
% 5.48/5.73 = bot_bot_set_nat ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % succ_empty
% 5.48/5.73 thf(fact_1328_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.48/5.73 ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.48/5.73 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc ) @ X2 )
% 5.48/5.73 = ( ( X2 = Mi )
% 5.48/5.73 | ( X2 = Ma )
% 5.48/5.73 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.membermima.simps(4)
% 5.48/5.73 thf(fact_1329_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.48/5.73 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.48/5.73 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ X2 )
% 5.48/5.73 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.naive_member.simps(3)
% 5.48/5.73 thf(fact_1330_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.48/5.73 ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT,X2: nat] :
% 5.48/5.73 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ X2 )
% 5.48/5.73 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.48/5.73 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.membermima.simps(5)
% 5.48/5.73 thf(fact_1331_member__bound__height,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r @ T @ X2 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % member_bound_height
% 5.48/5.73 thf(fact_1332_mint__corr__help__empty,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( ( vEBT_vebt_mint @ T )
% 5.48/5.73 = none_nat )
% 5.48/5.73 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.48/5.73 = bot_bot_set_nat ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mint_corr_help_empty
% 5.48/5.73 thf(fact_1333_both__member__options__def,axiom,
% 5.48/5.73 ( vEBT_V8194947554948674370ptions
% 5.48/5.73 = ( ^ [T2: vEBT_VEBT,X: nat] :
% 5.48/5.73 ( ( vEBT_V5719532721284313246member @ T2 @ X )
% 5.48/5.73 | ( vEBT_VEBT_membermima @ T2 @ X ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % both_member_options_def
% 5.48/5.73 thf(fact_1334_member__valid__both__member__options,axiom,
% 5.48/5.73 ! [Tree: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ Tree @ N )
% 5.48/5.73 => ( ( vEBT_vebt_member @ Tree @ X2 )
% 5.48/5.73 => ( ( vEBT_V5719532721284313246member @ Tree @ X2 )
% 5.48/5.73 | ( vEBT_VEBT_membermima @ Tree @ X2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % member_valid_both_member_options
% 5.48/5.73 thf(fact_1335_maxt__corr__help__empty,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( ( vEBT_vebt_maxt @ T )
% 5.48/5.73 = none_nat )
% 5.48/5.73 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.48/5.73 = bot_bot_set_nat ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % maxt_corr_help_empty
% 5.48/5.73 thf(fact_1336_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I3_J,axiom,
% 5.48/5.73 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.48/5.73 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.48/5.73 = one_one_nat ) ).
% 5.48/5.73
% 5.48/5.73 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(3)
% 5.48/5.73 thf(fact_1337_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I2_J,axiom,
% 5.48/5.73 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X2: nat] :
% 5.48/5.73 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X2 )
% 5.48/5.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(2)
% 5.48/5.73 thf(fact_1338_vebt__member_Osimps_I2_J,axiom,
% 5.48/5.73 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X2: nat] :
% 5.48/5.73 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X2 ) ).
% 5.48/5.73
% 5.48/5.73 % vebt_member.simps(2)
% 5.48/5.73 thf(fact_1339_buildup__gives__empty,axiom,
% 5.48/5.73 ! [N: nat] :
% 5.48/5.73 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 5.48/5.73 = bot_bot_set_nat ) ).
% 5.48/5.73
% 5.48/5.73 % buildup_gives_empty
% 5.48/5.73 thf(fact_1340_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.48/5.73 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.48/5.73 ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.48/5.73 => ( ! [Mi2: nat,Ma2: nat] :
% 5.48/5.73 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.48/5.73 => ~ ( ( Xa2 = Mi2 )
% 5.48/5.73 | ( Xa2 = Ma2 ) ) )
% 5.48/5.73 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.48/5.73 ( ? [Vc2: vEBT_VEBT] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.48/5.73 => ~ ( ( Xa2 = Mi2 )
% 5.48/5.73 | ( Xa2 = Ma2 )
% 5.48/5.73 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.48/5.73 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.48/5.73 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.48/5.73 ( ? [Vd2: vEBT_VEBT] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.48/5.73 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.48/5.73 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % VEBT_internal.membermima.elims(2)
% 5.48/5.73 thf(fact_1341_insert__bound__height,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ X2 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % insert_bound_height
% 5.48/5.73 thf(fact_1342_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Oelims,axiom,
% 5.48/5.73 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.48/5.73 ( ( ( vEBT_T_s_u_c_c @ X2 @ Xa2 )
% 5.48/5.73 = Y2 )
% 5.48/5.73 => ( ( ? [Uu2: $o,B2: $o] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 5.48/5.73 => ( ( Xa2 = zero_zero_nat )
% 5.48/5.73 => ( Y2
% 5.48/5.73 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.48/5.73 => ( ( ? [Uv2: $o,Uw2: $o] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.48/5.73 => ( ? [N2: nat] :
% 5.48/5.73 ( Xa2
% 5.48/5.73 = ( suc @ N2 ) )
% 5.48/5.73 => ( Y2 != one_one_nat ) ) )
% 5.48/5.73 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.48/5.73 => ( Y2 != one_one_nat ) )
% 5.48/5.73 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.48/5.73 => ( Y2 != one_one_nat ) )
% 5.48/5.73 => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.48/5.73 => ( Y2 != one_one_nat ) )
% 5.48/5.73 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.48/5.73 ( ( X2
% 5.48/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.48/5.73 => ( Y2
% 5.48/5.73 != ( plus_plus_nat @ one_one_nat
% 5.48/5.73 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 5.48/5.73 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.48/5.73 @ ( if_nat
% 5.48/5.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 5.48/5.73 @ ( if_nat
% 5.48/5.73 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 = none_nat )
% 5.48/5.73 @ one_one_nat
% 5.48/5.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.48/5.73 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.elims
% 5.48/5.73 thf(fact_1343_all__set__conv__all__nth,axiom,
% 5.48/5.73 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.48/5.73 ( ( ! [X: vEBT_VEBT] :
% 5.48/5.73 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X ) ) )
% 5.48/5.73 = ( ! [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.48/5.73 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % all_set_conv_all_nth
% 5.48/5.73 thf(fact_1344_all__set__conv__all__nth,axiom,
% 5.48/5.73 ! [Xs2: list_o,P: $o > $o] :
% 5.48/5.73 ( ( ! [X: $o] :
% 5.48/5.73 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X ) ) )
% 5.48/5.73 = ( ! [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.48/5.73 => ( P @ ( nth_o @ Xs2 @ I4 ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % all_set_conv_all_nth
% 5.48/5.73 thf(fact_1345_all__set__conv__all__nth,axiom,
% 5.48/5.73 ! [Xs2: list_nat,P: nat > $o] :
% 5.48/5.73 ( ( ! [X: nat] :
% 5.48/5.73 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X ) ) )
% 5.48/5.73 = ( ! [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.48/5.73 => ( P @ ( nth_nat @ Xs2 @ I4 ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % all_set_conv_all_nth
% 5.48/5.73 thf(fact_1346_all__nth__imp__all__set,axiom,
% 5.48/5.73 ! [Xs2: list_option_nat,P: option_nat > $o,X2: option_nat] :
% 5.48/5.73 ( ! [I2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 5.48/5.73 => ( P @ ( nth_option_nat @ Xs2 @ I2 ) ) )
% 5.48/5.73 => ( ( member_option_nat @ X2 @ ( set_option_nat2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % all_nth_imp_all_set
% 5.48/5.73 thf(fact_1347_all__nth__imp__all__set,axiom,
% 5.48/5.73 ! [Xs2: list_real,P: real > $o,X2: real] :
% 5.48/5.73 ( ! [I2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs2 ) )
% 5.48/5.73 => ( P @ ( nth_real @ Xs2 @ I2 ) ) )
% 5.48/5.73 => ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % all_nth_imp_all_set
% 5.48/5.73 thf(fact_1348_all__nth__imp__all__set,axiom,
% 5.48/5.73 ! [Xs2: list_set_nat_rat,P: set_nat_rat > $o,X2: set_nat_rat] :
% 5.48/5.73 ( ! [I2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ ( size_s3959913991096427681at_rat @ Xs2 ) )
% 5.48/5.73 => ( P @ ( nth_set_nat_rat @ Xs2 @ I2 ) ) )
% 5.48/5.73 => ( ( member_set_nat_rat @ X2 @ ( set_set_nat_rat2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % all_nth_imp_all_set
% 5.48/5.73 thf(fact_1349_all__nth__imp__all__set,axiom,
% 5.48/5.73 ! [Xs2: list_int,P: int > $o,X2: int] :
% 5.48/5.73 ( ! [I2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.48/5.73 => ( P @ ( nth_int @ Xs2 @ I2 ) ) )
% 5.48/5.73 => ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % all_nth_imp_all_set
% 5.48/5.73 thf(fact_1350_all__nth__imp__all__set,axiom,
% 5.48/5.73 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 5.48/5.73 ( ! [I2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.48/5.73 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 5.48/5.73 => ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % all_nth_imp_all_set
% 5.48/5.73 thf(fact_1351_all__nth__imp__all__set,axiom,
% 5.48/5.73 ! [Xs2: list_o,P: $o > $o,X2: $o] :
% 5.48/5.73 ( ! [I2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.48/5.73 => ( P @ ( nth_o @ Xs2 @ I2 ) ) )
% 5.48/5.73 => ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % all_nth_imp_all_set
% 5.48/5.73 thf(fact_1352_all__nth__imp__all__set,axiom,
% 5.48/5.73 ! [Xs2: list_nat,P: nat > $o,X2: nat] :
% 5.48/5.73 ( ! [I2: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.48/5.73 => ( P @ ( nth_nat @ Xs2 @ I2 ) ) )
% 5.48/5.73 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % all_nth_imp_all_set
% 5.48/5.73 thf(fact_1353_in__set__conv__nth,axiom,
% 5.48/5.73 ! [X2: option_nat,Xs2: list_option_nat] :
% 5.48/5.73 ( ( member_option_nat @ X2 @ ( set_option_nat2 @ Xs2 ) )
% 5.48/5.73 = ( ? [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 5.48/5.73 & ( ( nth_option_nat @ Xs2 @ I4 )
% 5.48/5.73 = X2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % in_set_conv_nth
% 5.48/5.73 thf(fact_1354_in__set__conv__nth,axiom,
% 5.48/5.73 ! [X2: real,Xs2: list_real] :
% 5.48/5.73 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.48/5.73 = ( ? [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs2 ) )
% 5.48/5.73 & ( ( nth_real @ Xs2 @ I4 )
% 5.48/5.73 = X2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % in_set_conv_nth
% 5.48/5.73 thf(fact_1355_in__set__conv__nth,axiom,
% 5.48/5.73 ! [X2: set_nat_rat,Xs2: list_set_nat_rat] :
% 5.48/5.73 ( ( member_set_nat_rat @ X2 @ ( set_set_nat_rat2 @ Xs2 ) )
% 5.48/5.73 = ( ? [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ ( size_s3959913991096427681at_rat @ Xs2 ) )
% 5.48/5.73 & ( ( nth_set_nat_rat @ Xs2 @ I4 )
% 5.48/5.73 = X2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % in_set_conv_nth
% 5.48/5.73 thf(fact_1356_in__set__conv__nth,axiom,
% 5.48/5.73 ! [X2: int,Xs2: list_int] :
% 5.48/5.73 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.48/5.73 = ( ? [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 5.48/5.73 & ( ( nth_int @ Xs2 @ I4 )
% 5.48/5.73 = X2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % in_set_conv_nth
% 5.48/5.73 thf(fact_1357_in__set__conv__nth,axiom,
% 5.48/5.73 ! [X2: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.48/5.73 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.48/5.73 = ( ? [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.48/5.73 & ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 5.48/5.73 = X2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % in_set_conv_nth
% 5.48/5.73 thf(fact_1358_in__set__conv__nth,axiom,
% 5.48/5.73 ! [X2: $o,Xs2: list_o] :
% 5.48/5.73 ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.48/5.73 = ( ? [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.48/5.73 & ( ( nth_o @ Xs2 @ I4 )
% 5.48/5.73 = X2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % in_set_conv_nth
% 5.48/5.73 thf(fact_1359_in__set__conv__nth,axiom,
% 5.48/5.73 ! [X2: nat,Xs2: list_nat] :
% 5.48/5.73 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.48/5.73 = ( ? [I4: nat] :
% 5.48/5.73 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.48/5.73 & ( ( nth_nat @ Xs2 @ I4 )
% 5.48/5.73 = X2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % in_set_conv_nth
% 5.48/5.73 thf(fact_1360_list__ball__nth,axiom,
% 5.48/5.73 ! [N: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.48/5.73 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.48/5.73 => ( ! [X4: vEBT_VEBT] :
% 5.48/5.73 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X4 ) )
% 5.48/5.73 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % list_ball_nth
% 5.48/5.73 thf(fact_1361_list__ball__nth,axiom,
% 5.48/5.73 ! [N: nat,Xs2: list_o,P: $o > $o] :
% 5.48/5.73 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.48/5.73 => ( ! [X4: $o] :
% 5.48/5.73 ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X4 ) )
% 5.48/5.73 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % list_ball_nth
% 5.48/5.73 thf(fact_1362_list__ball__nth,axiom,
% 5.48/5.73 ! [N: nat,Xs2: list_nat,P: nat > $o] :
% 5.48/5.73 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.48/5.73 => ( ! [X4: nat] :
% 5.48/5.73 ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 5.48/5.73 => ( P @ X4 ) )
% 5.48/5.73 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % list_ball_nth
% 5.48/5.73 thf(fact_1363_nth__mem,axiom,
% 5.48/5.73 ! [N: nat,Xs2: list_option_nat] :
% 5.48/5.73 ( ( ord_less_nat @ N @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 5.48/5.73 => ( member_option_nat @ ( nth_option_nat @ Xs2 @ N ) @ ( set_option_nat2 @ Xs2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nth_mem
% 5.48/5.73 thf(fact_1364_nth__mem,axiom,
% 5.48/5.73 ! [N: nat,Xs2: list_real] :
% 5.48/5.73 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.48/5.73 => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nth_mem
% 5.48/5.73 thf(fact_1365_nth__mem,axiom,
% 5.48/5.73 ! [N: nat,Xs2: list_set_nat_rat] :
% 5.48/5.73 ( ( ord_less_nat @ N @ ( size_s3959913991096427681at_rat @ Xs2 ) )
% 5.48/5.73 => ( member_set_nat_rat @ ( nth_set_nat_rat @ Xs2 @ N ) @ ( set_set_nat_rat2 @ Xs2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nth_mem
% 5.48/5.73 thf(fact_1366_nth__mem,axiom,
% 5.48/5.73 ! [N: nat,Xs2: list_int] :
% 5.48/5.73 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.48/5.73 => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nth_mem
% 5.48/5.73 thf(fact_1367_nth__mem,axiom,
% 5.48/5.73 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 5.48/5.73 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.48/5.73 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nth_mem
% 5.48/5.73 thf(fact_1368_nth__mem,axiom,
% 5.48/5.73 ! [N: nat,Xs2: list_o] :
% 5.48/5.73 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.48/5.73 => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nth_mem
% 5.48/5.73 thf(fact_1369_nth__mem,axiom,
% 5.48/5.73 ! [N: nat,Xs2: list_nat] :
% 5.48/5.73 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.48/5.73 => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % nth_mem
% 5.48/5.73 thf(fact_1370_vebt__pred_Oelims,axiom,
% 5.48/5.73 ! [X2: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 5.48/5.73 ( ( ( vEBT_vebt_pred @ X2 @ Xa2 )
% 5.48/5.73 = Y2 )
% 5.48/5.73 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.48/5.73 => ( ( Xa2 = zero_zero_nat )
% 5.48/5.73 => ( Y2 != none_nat ) ) )
% 5.48/5.73 => ( ! [A3: $o] :
% 5.48/5.73 ( ? [Uw2: $o] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.48/5.73 => ( ( Xa2
% 5.48/5.73 = ( suc @ zero_zero_nat ) )
% 5.48/5.73 => ~ ( ( A3
% 5.48/5.73 => ( Y2
% 5.48/5.73 = ( some_nat @ zero_zero_nat ) ) )
% 5.48/5.73 & ( ~ A3
% 5.48/5.73 => ( Y2 = none_nat ) ) ) ) )
% 5.48/5.73 => ( ! [A3: $o,B2: $o] :
% 5.48/5.73 ( ( X2
% 5.48/5.73 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.48/5.73 => ( ? [Va3: nat] :
% 5.48/5.73 ( Xa2
% 5.48/5.73 = ( suc @ ( suc @ Va3 ) ) )
% 5.48/5.73 => ~ ( ( B2
% 5.48/5.73 => ( Y2
% 5.48/5.73 = ( some_nat @ one_one_nat ) ) )
% 5.48/5.73 & ( ~ B2
% 5.48/5.73 => ( ( A3
% 5.48/5.73 => ( Y2
% 5.48/5.73 = ( some_nat @ zero_zero_nat ) ) )
% 5.48/5.73 & ( ~ A3
% 5.48/5.73 => ( Y2 = none_nat ) ) ) ) ) ) )
% 5.48/5.73 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.48/5.73 => ( Y2 != none_nat ) )
% 5.48/5.73 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) )
% 5.48/5.73 => ( Y2 != none_nat ) )
% 5.48/5.73 => ( ( ? [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.48/5.73 ( X2
% 5.48/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.48/5.73 => ( Y2 != none_nat ) )
% 5.48/5.73 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.48/5.73 ( ( X2
% 5.48/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.48/5.73 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.48/5.73 => ( Y2
% 5.48/5.73 = ( some_nat @ Ma2 ) ) )
% 5.48/5.73 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.48/5.73 => ( Y2
% 5.48/5.73 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.48/5.73 @ ( if_option_nat
% 5.48/5.73 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 != none_nat )
% 5.48/5.73 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.48/5.73 @ ( if_option_nat
% 5.48/5.73 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.48/5.73 = none_nat )
% 5.48/5.73 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.48/5.73 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.48/5.73 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % vebt_pred.elims
% 5.48/5.73 thf(fact_1371_valid__tree__deg__neq__0,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT] :
% 5.48/5.73 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.48/5.73
% 5.48/5.73 % valid_tree_deg_neq_0
% 5.48/5.73 thf(fact_1372_valid__0__not,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT] :
% 5.48/5.73 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.48/5.73
% 5.48/5.73 % valid_0_not
% 5.48/5.73 thf(fact_1373_buildup__nothing__in__min__max,axiom,
% 5.48/5.73 ! [N: nat,X2: nat] :
% 5.48/5.73 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X2 ) ).
% 5.48/5.73
% 5.48/5.73 % buildup_nothing_in_min_max
% 5.48/5.73 thf(fact_1374_buildup__nothing__in__leaf,axiom,
% 5.48/5.73 ! [N: nat,X2: nat] :
% 5.48/5.73 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X2 ) ).
% 5.48/5.73
% 5.48/5.73 % buildup_nothing_in_leaf
% 5.48/5.73 thf(fact_1375_deg__not__0,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % deg_not_0
% 5.48/5.73 thf(fact_1376_Leaf__0__not,axiom,
% 5.48/5.73 ! [A: $o,B: $o] :
% 5.48/5.73 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 5.48/5.73
% 5.48/5.73 % Leaf_0_not
% 5.48/5.73 thf(fact_1377_deg1Leaf,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.48/5.73 = ( ? [A4: $o,B3: $o] :
% 5.48/5.73 ( T
% 5.48/5.73 = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % deg1Leaf
% 5.48/5.73 thf(fact_1378_deg__1__Leaf,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.48/5.73 => ? [A3: $o,B2: $o] :
% 5.48/5.73 ( T
% 5.48/5.73 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % deg_1_Leaf
% 5.48/5.73 thf(fact_1379_deg__1__Leafy,axiom,
% 5.48/5.73 ! [T: vEBT_VEBT,N: nat] :
% 5.48/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 5.48/5.73 => ( ( N = one_one_nat )
% 5.48/5.73 => ? [A3: $o,B2: $o] :
% 5.48/5.73 ( T
% 5.48/5.73 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % deg_1_Leafy
% 5.48/5.73 thf(fact_1380_buildup__gives__valid,axiom,
% 5.48/5.73 ! [N: nat] :
% 5.48/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.48/5.73 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.48/5.73
% 5.48/5.73 % buildup_gives_valid
% 5.48/5.73 thf(fact_1381_le__zero__eq,axiom,
% 5.48/5.73 ! [N: nat] :
% 5.48/5.73 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.48/5.73 = ( N = zero_zero_nat ) ) ).
% 5.48/5.73
% 5.48/5.73 % le_zero_eq
% 5.48/5.73 thf(fact_1382_not__gr__zero,axiom,
% 5.48/5.73 ! [N: nat] :
% 5.48/5.73 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.48/5.73 = ( N = zero_zero_nat ) ) ).
% 5.48/5.73
% 5.48/5.73 % not_gr_zero
% 5.48/5.73 thf(fact_1383_mult__zero__left,axiom,
% 5.48/5.73 ! [A: real] :
% 5.48/5.73 ( ( times_times_real @ zero_zero_real @ A )
% 5.48/5.73 = zero_zero_real ) ).
% 5.48/5.73
% 5.48/5.73 % mult_zero_left
% 5.48/5.73 thf(fact_1384_mult__zero__left,axiom,
% 5.48/5.73 ! [A: rat] :
% 5.48/5.73 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.48/5.73 = zero_zero_rat ) ).
% 5.48/5.73
% 5.48/5.73 % mult_zero_left
% 5.48/5.73 thf(fact_1385_mult__zero__left,axiom,
% 5.48/5.73 ! [A: nat] :
% 5.48/5.73 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.48/5.73 = zero_zero_nat ) ).
% 5.48/5.73
% 5.48/5.73 % mult_zero_left
% 5.48/5.73 thf(fact_1386_mult__zero__left,axiom,
% 5.48/5.73 ! [A: int] :
% 5.48/5.73 ( ( times_times_int @ zero_zero_int @ A )
% 5.48/5.73 = zero_zero_int ) ).
% 5.48/5.73
% 5.48/5.73 % mult_zero_left
% 5.48/5.73 thf(fact_1387_mult__zero__right,axiom,
% 5.48/5.73 ! [A: real] :
% 5.48/5.73 ( ( times_times_real @ A @ zero_zero_real )
% 5.48/5.73 = zero_zero_real ) ).
% 5.48/5.73
% 5.48/5.73 % mult_zero_right
% 5.48/5.73 thf(fact_1388_mult__zero__right,axiom,
% 5.48/5.73 ! [A: rat] :
% 5.48/5.73 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.48/5.73 = zero_zero_rat ) ).
% 5.48/5.73
% 5.48/5.73 % mult_zero_right
% 5.48/5.73 thf(fact_1389_mult__zero__right,axiom,
% 5.48/5.73 ! [A: nat] :
% 5.48/5.73 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.48/5.73 = zero_zero_nat ) ).
% 5.48/5.73
% 5.48/5.73 % mult_zero_right
% 5.48/5.73 thf(fact_1390_mult__zero__right,axiom,
% 5.48/5.73 ! [A: int] :
% 5.48/5.73 ( ( times_times_int @ A @ zero_zero_int )
% 5.48/5.73 = zero_zero_int ) ).
% 5.48/5.73
% 5.48/5.73 % mult_zero_right
% 5.48/5.73 thf(fact_1391_mult__eq__0__iff,axiom,
% 5.48/5.73 ! [A: real,B: real] :
% 5.48/5.73 ( ( ( times_times_real @ A @ B )
% 5.48/5.73 = zero_zero_real )
% 5.48/5.73 = ( ( A = zero_zero_real )
% 5.48/5.73 | ( B = zero_zero_real ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_eq_0_iff
% 5.48/5.73 thf(fact_1392_mult__eq__0__iff,axiom,
% 5.48/5.73 ! [A: rat,B: rat] :
% 5.48/5.73 ( ( ( times_times_rat @ A @ B )
% 5.48/5.73 = zero_zero_rat )
% 5.48/5.73 = ( ( A = zero_zero_rat )
% 5.48/5.73 | ( B = zero_zero_rat ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_eq_0_iff
% 5.48/5.73 thf(fact_1393_mult__eq__0__iff,axiom,
% 5.48/5.73 ! [A: nat,B: nat] :
% 5.48/5.73 ( ( ( times_times_nat @ A @ B )
% 5.48/5.73 = zero_zero_nat )
% 5.48/5.73 = ( ( A = zero_zero_nat )
% 5.48/5.73 | ( B = zero_zero_nat ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_eq_0_iff
% 5.48/5.73 thf(fact_1394_mult__eq__0__iff,axiom,
% 5.48/5.73 ! [A: int,B: int] :
% 5.48/5.73 ( ( ( times_times_int @ A @ B )
% 5.48/5.73 = zero_zero_int )
% 5.48/5.73 = ( ( A = zero_zero_int )
% 5.48/5.73 | ( B = zero_zero_int ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_eq_0_iff
% 5.48/5.73 thf(fact_1395_mult__cancel__left,axiom,
% 5.48/5.73 ! [C: real,A: real,B: real] :
% 5.48/5.73 ( ( ( times_times_real @ C @ A )
% 5.48/5.73 = ( times_times_real @ C @ B ) )
% 5.48/5.73 = ( ( C = zero_zero_real )
% 5.48/5.73 | ( A = B ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_cancel_left
% 5.48/5.73 thf(fact_1396_mult__cancel__left,axiom,
% 5.48/5.73 ! [C: rat,A: rat,B: rat] :
% 5.48/5.73 ( ( ( times_times_rat @ C @ A )
% 5.48/5.73 = ( times_times_rat @ C @ B ) )
% 5.48/5.73 = ( ( C = zero_zero_rat )
% 5.48/5.73 | ( A = B ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_cancel_left
% 5.48/5.73 thf(fact_1397_mult__cancel__left,axiom,
% 5.48/5.73 ! [C: nat,A: nat,B: nat] :
% 5.48/5.73 ( ( ( times_times_nat @ C @ A )
% 5.48/5.73 = ( times_times_nat @ C @ B ) )
% 5.48/5.73 = ( ( C = zero_zero_nat )
% 5.48/5.73 | ( A = B ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_cancel_left
% 5.48/5.73 thf(fact_1398_mult__cancel__left,axiom,
% 5.48/5.73 ! [C: int,A: int,B: int] :
% 5.48/5.73 ( ( ( times_times_int @ C @ A )
% 5.48/5.73 = ( times_times_int @ C @ B ) )
% 5.48/5.73 = ( ( C = zero_zero_int )
% 5.48/5.73 | ( A = B ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_cancel_left
% 5.48/5.73 thf(fact_1399_mult__cancel__right,axiom,
% 5.48/5.73 ! [A: real,C: real,B: real] :
% 5.48/5.73 ( ( ( times_times_real @ A @ C )
% 5.48/5.73 = ( times_times_real @ B @ C ) )
% 5.48/5.73 = ( ( C = zero_zero_real )
% 5.48/5.73 | ( A = B ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_cancel_right
% 5.48/5.73 thf(fact_1400_mult__cancel__right,axiom,
% 5.48/5.73 ! [A: rat,C: rat,B: rat] :
% 5.48/5.73 ( ( ( times_times_rat @ A @ C )
% 5.48/5.73 = ( times_times_rat @ B @ C ) )
% 5.48/5.73 = ( ( C = zero_zero_rat )
% 5.48/5.73 | ( A = B ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_cancel_right
% 5.48/5.73 thf(fact_1401_mult__cancel__right,axiom,
% 5.48/5.73 ! [A: nat,C: nat,B: nat] :
% 5.48/5.73 ( ( ( times_times_nat @ A @ C )
% 5.48/5.73 = ( times_times_nat @ B @ C ) )
% 5.48/5.73 = ( ( C = zero_zero_nat )
% 5.48/5.73 | ( A = B ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_cancel_right
% 5.48/5.73 thf(fact_1402_mult__cancel__right,axiom,
% 5.48/5.73 ! [A: int,C: int,B: int] :
% 5.48/5.73 ( ( ( times_times_int @ A @ C )
% 5.48/5.73 = ( times_times_int @ B @ C ) )
% 5.48/5.73 = ( ( C = zero_zero_int )
% 5.48/5.73 | ( A = B ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % mult_cancel_right
% 5.48/5.73 thf(fact_1403_add_Oright__neutral,axiom,
% 5.48/5.73 ! [A: complex] :
% 5.48/5.73 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.48/5.73 = A ) ).
% 5.48/5.73
% 5.48/5.73 % add.right_neutral
% 5.48/5.73 thf(fact_1404_add_Oright__neutral,axiom,
% 5.48/5.73 ! [A: literal] :
% 5.48/5.73 ( ( plus_plus_literal @ A @ zero_zero_literal )
% 5.48/5.73 = A ) ).
% 5.48/5.73
% 5.48/5.73 % add.right_neutral
% 5.48/5.73 thf(fact_1405_add_Oright__neutral,axiom,
% 5.48/5.73 ! [A: real] :
% 5.48/5.73 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.48/5.73 = A ) ).
% 5.48/5.73
% 5.48/5.73 % add.right_neutral
% 5.48/5.73 thf(fact_1406_add_Oright__neutral,axiom,
% 5.48/5.73 ! [A: rat] :
% 5.48/5.73 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.48/5.73 = A ) ).
% 5.48/5.73
% 5.48/5.73 % add.right_neutral
% 5.48/5.73 thf(fact_1407_add_Oright__neutral,axiom,
% 5.48/5.73 ! [A: nat] :
% 5.48/5.73 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.48/5.73 = A ) ).
% 5.48/5.73
% 5.48/5.73 % add.right_neutral
% 5.48/5.73 thf(fact_1408_add_Oright__neutral,axiom,
% 5.48/5.73 ! [A: int] :
% 5.48/5.73 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.48/5.73 = A ) ).
% 5.48/5.73
% 5.48/5.73 % add.right_neutral
% 5.48/5.73 thf(fact_1409_double__zero__sym,axiom,
% 5.48/5.73 ! [A: real] :
% 5.48/5.73 ( ( zero_zero_real
% 5.48/5.73 = ( plus_plus_real @ A @ A ) )
% 5.48/5.73 = ( A = zero_zero_real ) ) ).
% 5.48/5.73
% 5.48/5.73 % double_zero_sym
% 5.48/5.73 thf(fact_1410_double__zero__sym,axiom,
% 5.48/5.73 ! [A: rat] :
% 5.48/5.73 ( ( zero_zero_rat
% 5.48/5.73 = ( plus_plus_rat @ A @ A ) )
% 5.48/5.73 = ( A = zero_zero_rat ) ) ).
% 5.48/5.73
% 5.48/5.73 % double_zero_sym
% 5.48/5.73 thf(fact_1411_double__zero__sym,axiom,
% 5.48/5.73 ! [A: int] :
% 5.48/5.73 ( ( zero_zero_int
% 5.48/5.73 = ( plus_plus_int @ A @ A ) )
% 5.48/5.73 = ( A = zero_zero_int ) ) ).
% 5.48/5.73
% 5.48/5.73 % double_zero_sym
% 5.48/5.73 thf(fact_1412_add__cancel__left__left,axiom,
% 5.48/5.73 ! [B: complex,A: complex] :
% 5.48/5.73 ( ( ( plus_plus_complex @ B @ A )
% 5.48/5.73 = A )
% 5.48/5.73 = ( B = zero_zero_complex ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_left_left
% 5.48/5.73 thf(fact_1413_add__cancel__left__left,axiom,
% 5.48/5.73 ! [B: real,A: real] :
% 5.48/5.73 ( ( ( plus_plus_real @ B @ A )
% 5.48/5.73 = A )
% 5.48/5.73 = ( B = zero_zero_real ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_left_left
% 5.48/5.73 thf(fact_1414_add__cancel__left__left,axiom,
% 5.48/5.73 ! [B: rat,A: rat] :
% 5.48/5.73 ( ( ( plus_plus_rat @ B @ A )
% 5.48/5.73 = A )
% 5.48/5.73 = ( B = zero_zero_rat ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_left_left
% 5.48/5.73 thf(fact_1415_add__cancel__left__left,axiom,
% 5.48/5.73 ! [B: nat,A: nat] :
% 5.48/5.73 ( ( ( plus_plus_nat @ B @ A )
% 5.48/5.73 = A )
% 5.48/5.73 = ( B = zero_zero_nat ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_left_left
% 5.48/5.73 thf(fact_1416_add__cancel__left__left,axiom,
% 5.48/5.73 ! [B: int,A: int] :
% 5.48/5.73 ( ( ( plus_plus_int @ B @ A )
% 5.48/5.73 = A )
% 5.48/5.73 = ( B = zero_zero_int ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_left_left
% 5.48/5.73 thf(fact_1417_add__cancel__left__right,axiom,
% 5.48/5.73 ! [A: complex,B: complex] :
% 5.48/5.73 ( ( ( plus_plus_complex @ A @ B )
% 5.48/5.73 = A )
% 5.48/5.73 = ( B = zero_zero_complex ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_left_right
% 5.48/5.73 thf(fact_1418_add__cancel__left__right,axiom,
% 5.48/5.73 ! [A: real,B: real] :
% 5.48/5.73 ( ( ( plus_plus_real @ A @ B )
% 5.48/5.73 = A )
% 5.48/5.73 = ( B = zero_zero_real ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_left_right
% 5.48/5.73 thf(fact_1419_add__cancel__left__right,axiom,
% 5.48/5.73 ! [A: rat,B: rat] :
% 5.48/5.73 ( ( ( plus_plus_rat @ A @ B )
% 5.48/5.73 = A )
% 5.48/5.73 = ( B = zero_zero_rat ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_left_right
% 5.48/5.73 thf(fact_1420_add__cancel__left__right,axiom,
% 5.48/5.73 ! [A: nat,B: nat] :
% 5.48/5.73 ( ( ( plus_plus_nat @ A @ B )
% 5.48/5.73 = A )
% 5.48/5.73 = ( B = zero_zero_nat ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_left_right
% 5.48/5.73 thf(fact_1421_add__cancel__left__right,axiom,
% 5.48/5.73 ! [A: int,B: int] :
% 5.48/5.73 ( ( ( plus_plus_int @ A @ B )
% 5.48/5.73 = A )
% 5.48/5.73 = ( B = zero_zero_int ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_left_right
% 5.48/5.73 thf(fact_1422_add__cancel__right__left,axiom,
% 5.48/5.73 ! [A: complex,B: complex] :
% 5.48/5.73 ( ( A
% 5.48/5.73 = ( plus_plus_complex @ B @ A ) )
% 5.48/5.73 = ( B = zero_zero_complex ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_right_left
% 5.48/5.73 thf(fact_1423_add__cancel__right__left,axiom,
% 5.48/5.73 ! [A: real,B: real] :
% 5.48/5.73 ( ( A
% 5.48/5.73 = ( plus_plus_real @ B @ A ) )
% 5.48/5.73 = ( B = zero_zero_real ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_right_left
% 5.48/5.73 thf(fact_1424_add__cancel__right__left,axiom,
% 5.48/5.73 ! [A: rat,B: rat] :
% 5.48/5.73 ( ( A
% 5.48/5.73 = ( plus_plus_rat @ B @ A ) )
% 5.48/5.73 = ( B = zero_zero_rat ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_right_left
% 5.48/5.73 thf(fact_1425_add__cancel__right__left,axiom,
% 5.48/5.73 ! [A: nat,B: nat] :
% 5.48/5.73 ( ( A
% 5.48/5.73 = ( plus_plus_nat @ B @ A ) )
% 5.48/5.73 = ( B = zero_zero_nat ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_right_left
% 5.48/5.73 thf(fact_1426_add__cancel__right__left,axiom,
% 5.48/5.73 ! [A: int,B: int] :
% 5.48/5.73 ( ( A
% 5.48/5.73 = ( plus_plus_int @ B @ A ) )
% 5.48/5.73 = ( B = zero_zero_int ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_right_left
% 5.48/5.73 thf(fact_1427_add__cancel__right__right,axiom,
% 5.48/5.73 ! [A: complex,B: complex] :
% 5.48/5.73 ( ( A
% 5.48/5.73 = ( plus_plus_complex @ A @ B ) )
% 5.48/5.73 = ( B = zero_zero_complex ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_right_right
% 5.48/5.73 thf(fact_1428_add__cancel__right__right,axiom,
% 5.48/5.73 ! [A: real,B: real] :
% 5.48/5.73 ( ( A
% 5.48/5.73 = ( plus_plus_real @ A @ B ) )
% 5.48/5.73 = ( B = zero_zero_real ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_right_right
% 5.48/5.73 thf(fact_1429_add__cancel__right__right,axiom,
% 5.48/5.73 ! [A: rat,B: rat] :
% 5.48/5.73 ( ( A
% 5.48/5.73 = ( plus_plus_rat @ A @ B ) )
% 5.48/5.73 = ( B = zero_zero_rat ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_right_right
% 5.48/5.73 thf(fact_1430_add__cancel__right__right,axiom,
% 5.48/5.73 ! [A: nat,B: nat] :
% 5.48/5.73 ( ( A
% 5.48/5.73 = ( plus_plus_nat @ A @ B ) )
% 5.48/5.73 = ( B = zero_zero_nat ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_right_right
% 5.48/5.73 thf(fact_1431_add__cancel__right__right,axiom,
% 5.48/5.73 ! [A: int,B: int] :
% 5.48/5.73 ( ( A
% 5.48/5.73 = ( plus_plus_int @ A @ B ) )
% 5.48/5.73 = ( B = zero_zero_int ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_cancel_right_right
% 5.48/5.73 thf(fact_1432_add__eq__0__iff__both__eq__0,axiom,
% 5.48/5.73 ! [X2: nat,Y2: nat] :
% 5.48/5.73 ( ( ( plus_plus_nat @ X2 @ Y2 )
% 5.48/5.73 = zero_zero_nat )
% 5.48/5.73 = ( ( X2 = zero_zero_nat )
% 5.48/5.73 & ( Y2 = zero_zero_nat ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % add_eq_0_iff_both_eq_0
% 5.48/5.73 thf(fact_1433_zero__eq__add__iff__both__eq__0,axiom,
% 5.48/5.73 ! [X2: nat,Y2: nat] :
% 5.48/5.73 ( ( zero_zero_nat
% 5.48/5.73 = ( plus_plus_nat @ X2 @ Y2 ) )
% 5.48/5.73 = ( ( X2 = zero_zero_nat )
% 5.48/5.73 & ( Y2 = zero_zero_nat ) ) ) ).
% 5.48/5.73
% 5.48/5.73 % zero_eq_add_iff_both_eq_0
% 5.48/5.73 thf(fact_1434_add__0,axiom,
% 5.48/5.73 ! [A: complex] :
% 5.48/5.73 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.48/5.73 = A ) ).
% 5.48/5.73
% 5.48/5.73 % add_0
% 5.48/5.73 thf(fact_1435_add__0,axiom,
% 5.48/5.73 ! [A: literal] :
% 5.48/5.73 ( ( plus_plus_literal @ zero_zero_literal @ A )
% 5.48/5.73 = A ) ).
% 5.48/5.73
% 5.48/5.73 % add_0
% 5.48/5.73 thf(fact_1436_add__0,axiom,
% 5.48/5.73 ! [A: real] :
% 5.48/5.73 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.48/5.73 = A ) ).
% 5.48/5.73
% 5.48/5.73 % add_0
% 5.48/5.73 thf(fact_1437_add__0,axiom,
% 5.48/5.73 ! [A: rat] :
% 5.48/5.73 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.48/5.73 = A ) ).
% 5.48/5.73
% 5.48/5.73 % add_0
% 5.48/5.73 thf(fact_1438_add__0,axiom,
% 5.48/5.73 ! [A: nat] :
% 5.48/5.73 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.48/5.73 = A ) ).
% 5.48/5.73
% 5.48/5.73 % add_0
% 5.48/5.73 thf(fact_1439_add__0,axiom,
% 5.48/5.73 ! [A: int] :
% 5.48/5.73 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.48/5.73 = A ) ).
% 5.48/5.73
% 5.48/5.73 % add_0
% 5.48/5.73 thf(fact_1440_diff__self,axiom,
% 5.48/5.73 ! [A: complex] :
% 5.48/5.73 ( ( minus_minus_complex @ A @ A )
% 5.48/5.73 = zero_zero_complex ) ).
% 5.48/5.73
% 5.48/5.73 % diff_self
% 5.48/5.73 thf(fact_1441_diff__self,axiom,
% 5.48/5.73 ! [A: real] :
% 5.48/5.73 ( ( minus_minus_real @ A @ A )
% 5.48/5.73 = zero_zero_real ) ).
% 5.48/5.73
% 5.48/5.73 % diff_self
% 5.48/5.73 thf(fact_1442_diff__self,axiom,
% 5.48/5.73 ! [A: rat] :
% 5.48/5.73 ( ( minus_minus_rat @ A @ A )
% 5.48/5.73 = zero_zero_rat ) ).
% 5.48/5.73
% 5.48/5.73 % diff_self
% 5.48/5.73 thf(fact_1443_diff__self,axiom,
% 5.48/5.73 ! [A: int] :
% 5.48/5.73 ( ( minus_minus_int @ A @ A )
% 5.48/5.73 = zero_zero_int ) ).
% 5.48/5.73
% 5.48/5.73 % diff_self
% 5.48/5.73 thf(fact_1444_diff__0__right,axiom,
% 5.48/5.74 ! [A: complex] :
% 5.48/5.74 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % diff_0_right
% 5.48/5.74 thf(fact_1445_diff__0__right,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % diff_0_right
% 5.48/5.74 thf(fact_1446_diff__0__right,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % diff_0_right
% 5.48/5.74 thf(fact_1447_diff__0__right,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % diff_0_right
% 5.48/5.74 thf(fact_1448_zero__diff,axiom,
% 5.48/5.74 ! [A: nat] :
% 5.48/5.74 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.48/5.74 = zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % zero_diff
% 5.48/5.74 thf(fact_1449_diff__zero,axiom,
% 5.48/5.74 ! [A: complex] :
% 5.48/5.74 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % diff_zero
% 5.48/5.74 thf(fact_1450_diff__zero,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % diff_zero
% 5.48/5.74 thf(fact_1451_diff__zero,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % diff_zero
% 5.48/5.74 thf(fact_1452_diff__zero,axiom,
% 5.48/5.74 ! [A: nat] :
% 5.48/5.74 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % diff_zero
% 5.48/5.74 thf(fact_1453_diff__zero,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % diff_zero
% 5.48/5.74 thf(fact_1454_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.48/5.74 ! [A: complex] :
% 5.48/5.74 ( ( minus_minus_complex @ A @ A )
% 5.48/5.74 = zero_zero_complex ) ).
% 5.48/5.74
% 5.48/5.74 % cancel_comm_monoid_add_class.diff_cancel
% 5.48/5.74 thf(fact_1455_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( minus_minus_real @ A @ A )
% 5.48/5.74 = zero_zero_real ) ).
% 5.48/5.74
% 5.48/5.74 % cancel_comm_monoid_add_class.diff_cancel
% 5.48/5.74 thf(fact_1456_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( minus_minus_rat @ A @ A )
% 5.48/5.74 = zero_zero_rat ) ).
% 5.48/5.74
% 5.48/5.74 % cancel_comm_monoid_add_class.diff_cancel
% 5.48/5.74 thf(fact_1457_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.48/5.74 ! [A: nat] :
% 5.48/5.74 ( ( minus_minus_nat @ A @ A )
% 5.48/5.74 = zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % cancel_comm_monoid_add_class.diff_cancel
% 5.48/5.74 thf(fact_1458_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( minus_minus_int @ A @ A )
% 5.48/5.74 = zero_zero_int ) ).
% 5.48/5.74
% 5.48/5.74 % cancel_comm_monoid_add_class.diff_cancel
% 5.48/5.74 thf(fact_1459_division__ring__divide__zero,axiom,
% 5.48/5.74 ! [A: complex] :
% 5.48/5.74 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.48/5.74 = zero_zero_complex ) ).
% 5.48/5.74
% 5.48/5.74 % division_ring_divide_zero
% 5.48/5.74 thf(fact_1460_division__ring__divide__zero,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.48/5.74 = zero_zero_real ) ).
% 5.48/5.74
% 5.48/5.74 % division_ring_divide_zero
% 5.48/5.74 thf(fact_1461_division__ring__divide__zero,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.48/5.74 = zero_zero_rat ) ).
% 5.48/5.74
% 5.48/5.74 % division_ring_divide_zero
% 5.48/5.74 thf(fact_1462_bits__div__by__0,axiom,
% 5.48/5.74 ! [A: nat] :
% 5.48/5.74 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.48/5.74 = zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % bits_div_by_0
% 5.48/5.74 thf(fact_1463_bits__div__by__0,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.48/5.74 = zero_zero_int ) ).
% 5.48/5.74
% 5.48/5.74 % bits_div_by_0
% 5.48/5.74 thf(fact_1464_bits__div__0,axiom,
% 5.48/5.74 ! [A: nat] :
% 5.48/5.74 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.48/5.74 = zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % bits_div_0
% 5.48/5.74 thf(fact_1465_bits__div__0,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.48/5.74 = zero_zero_int ) ).
% 5.48/5.74
% 5.48/5.74 % bits_div_0
% 5.48/5.74 thf(fact_1466_divide__cancel__right,axiom,
% 5.48/5.74 ! [A: complex,C: complex,B: complex] :
% 5.48/5.74 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.48/5.74 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.48/5.74 = ( ( C = zero_zero_complex )
% 5.48/5.74 | ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_cancel_right
% 5.48/5.74 thf(fact_1467_divide__cancel__right,axiom,
% 5.48/5.74 ! [A: real,C: real,B: real] :
% 5.48/5.74 ( ( ( divide_divide_real @ A @ C )
% 5.48/5.74 = ( divide_divide_real @ B @ C ) )
% 5.48/5.74 = ( ( C = zero_zero_real )
% 5.48/5.74 | ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_cancel_right
% 5.48/5.74 thf(fact_1468_divide__cancel__right,axiom,
% 5.48/5.74 ! [A: rat,C: rat,B: rat] :
% 5.48/5.74 ( ( ( divide_divide_rat @ A @ C )
% 5.48/5.74 = ( divide_divide_rat @ B @ C ) )
% 5.48/5.74 = ( ( C = zero_zero_rat )
% 5.48/5.74 | ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_cancel_right
% 5.48/5.74 thf(fact_1469_divide__cancel__left,axiom,
% 5.48/5.74 ! [C: complex,A: complex,B: complex] :
% 5.48/5.74 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.48/5.74 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.48/5.74 = ( ( C = zero_zero_complex )
% 5.48/5.74 | ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_cancel_left
% 5.48/5.74 thf(fact_1470_divide__cancel__left,axiom,
% 5.48/5.74 ! [C: real,A: real,B: real] :
% 5.48/5.74 ( ( ( divide_divide_real @ C @ A )
% 5.48/5.74 = ( divide_divide_real @ C @ B ) )
% 5.48/5.74 = ( ( C = zero_zero_real )
% 5.48/5.74 | ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_cancel_left
% 5.48/5.74 thf(fact_1471_divide__cancel__left,axiom,
% 5.48/5.74 ! [C: rat,A: rat,B: rat] :
% 5.48/5.74 ( ( ( divide_divide_rat @ C @ A )
% 5.48/5.74 = ( divide_divide_rat @ C @ B ) )
% 5.48/5.74 = ( ( C = zero_zero_rat )
% 5.48/5.74 | ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_cancel_left
% 5.48/5.74 thf(fact_1472_div__by__0,axiom,
% 5.48/5.74 ! [A: complex] :
% 5.48/5.74 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.48/5.74 = zero_zero_complex ) ).
% 5.48/5.74
% 5.48/5.74 % div_by_0
% 5.48/5.74 thf(fact_1473_div__by__0,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.48/5.74 = zero_zero_real ) ).
% 5.48/5.74
% 5.48/5.74 % div_by_0
% 5.48/5.74 thf(fact_1474_div__by__0,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.48/5.74 = zero_zero_rat ) ).
% 5.48/5.74
% 5.48/5.74 % div_by_0
% 5.48/5.74 thf(fact_1475_div__by__0,axiom,
% 5.48/5.74 ! [A: nat] :
% 5.48/5.74 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.48/5.74 = zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % div_by_0
% 5.48/5.74 thf(fact_1476_div__by__0,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.48/5.74 = zero_zero_int ) ).
% 5.48/5.74
% 5.48/5.74 % div_by_0
% 5.48/5.74 thf(fact_1477_divide__eq__0__iff,axiom,
% 5.48/5.74 ! [A: complex,B: complex] :
% 5.48/5.74 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.48/5.74 = zero_zero_complex )
% 5.48/5.74 = ( ( A = zero_zero_complex )
% 5.48/5.74 | ( B = zero_zero_complex ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_eq_0_iff
% 5.48/5.74 thf(fact_1478_divide__eq__0__iff,axiom,
% 5.48/5.74 ! [A: real,B: real] :
% 5.48/5.74 ( ( ( divide_divide_real @ A @ B )
% 5.48/5.74 = zero_zero_real )
% 5.48/5.74 = ( ( A = zero_zero_real )
% 5.48/5.74 | ( B = zero_zero_real ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_eq_0_iff
% 5.48/5.74 thf(fact_1479_divide__eq__0__iff,axiom,
% 5.48/5.74 ! [A: rat,B: rat] :
% 5.48/5.74 ( ( ( divide_divide_rat @ A @ B )
% 5.48/5.74 = zero_zero_rat )
% 5.48/5.74 = ( ( A = zero_zero_rat )
% 5.48/5.74 | ( B = zero_zero_rat ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_eq_0_iff
% 5.48/5.74 thf(fact_1480_div__0,axiom,
% 5.48/5.74 ! [A: complex] :
% 5.48/5.74 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.48/5.74 = zero_zero_complex ) ).
% 5.48/5.74
% 5.48/5.74 % div_0
% 5.48/5.74 thf(fact_1481_div__0,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.48/5.74 = zero_zero_real ) ).
% 5.48/5.74
% 5.48/5.74 % div_0
% 5.48/5.74 thf(fact_1482_div__0,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.48/5.74 = zero_zero_rat ) ).
% 5.48/5.74
% 5.48/5.74 % div_0
% 5.48/5.74 thf(fact_1483_div__0,axiom,
% 5.48/5.74 ! [A: nat] :
% 5.48/5.74 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.48/5.74 = zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % div_0
% 5.48/5.74 thf(fact_1484_div__0,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.48/5.74 = zero_zero_int ) ).
% 5.48/5.74
% 5.48/5.74 % div_0
% 5.48/5.74 thf(fact_1485_less__nat__zero__code,axiom,
% 5.48/5.74 ! [N: nat] :
% 5.48/5.74 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % less_nat_zero_code
% 5.48/5.74 thf(fact_1486_neq0__conv,axiom,
% 5.48/5.74 ! [N: nat] :
% 5.48/5.74 ( ( N != zero_zero_nat )
% 5.48/5.74 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.48/5.74
% 5.48/5.74 % neq0_conv
% 5.48/5.74 thf(fact_1487_bot__nat__0_Onot__eq__extremum,axiom,
% 5.48/5.74 ! [A: nat] :
% 5.48/5.74 ( ( A != zero_zero_nat )
% 5.48/5.74 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % bot_nat_0.not_eq_extremum
% 5.48/5.74 thf(fact_1488_bot__nat__0_Oextremum,axiom,
% 5.48/5.74 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.48/5.74
% 5.48/5.74 % bot_nat_0.extremum
% 5.48/5.74 thf(fact_1489_le0,axiom,
% 5.48/5.74 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.48/5.74
% 5.48/5.74 % le0
% 5.48/5.74 thf(fact_1490_add__is__0,axiom,
% 5.48/5.74 ! [M: nat,N: nat] :
% 5.48/5.74 ( ( ( plus_plus_nat @ M @ N )
% 5.48/5.74 = zero_zero_nat )
% 5.48/5.74 = ( ( M = zero_zero_nat )
% 5.48/5.74 & ( N = zero_zero_nat ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_is_0
% 5.48/5.74 thf(fact_1491_Nat_Oadd__0__right,axiom,
% 5.48/5.74 ! [M: nat] :
% 5.48/5.74 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.48/5.74 = M ) ).
% 5.48/5.74
% 5.48/5.74 % Nat.add_0_right
% 5.48/5.74 thf(fact_1492_diff__0__eq__0,axiom,
% 5.48/5.74 ! [N: nat] :
% 5.48/5.74 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 5.48/5.74 = zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % diff_0_eq_0
% 5.48/5.74 thf(fact_1493_diff__self__eq__0,axiom,
% 5.48/5.74 ! [M: nat] :
% 5.48/5.74 ( ( minus_minus_nat @ M @ M )
% 5.48/5.74 = zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % diff_self_eq_0
% 5.48/5.74 thf(fact_1494_mult__is__0,axiom,
% 5.48/5.74 ! [M: nat,N: nat] :
% 5.48/5.74 ( ( ( times_times_nat @ M @ N )
% 5.48/5.74 = zero_zero_nat )
% 5.48/5.74 = ( ( M = zero_zero_nat )
% 5.48/5.74 | ( N = zero_zero_nat ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_is_0
% 5.48/5.74 thf(fact_1495_mult__0__right,axiom,
% 5.48/5.74 ! [M: nat] :
% 5.48/5.74 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.48/5.74 = zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % mult_0_right
% 5.48/5.74 thf(fact_1496_mult__cancel1,axiom,
% 5.48/5.74 ! [K: nat,M: nat,N: nat] :
% 5.48/5.74 ( ( ( times_times_nat @ K @ M )
% 5.48/5.74 = ( times_times_nat @ K @ N ) )
% 5.48/5.74 = ( ( M = N )
% 5.48/5.74 | ( K = zero_zero_nat ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel1
% 5.48/5.74 thf(fact_1497_mult__cancel2,axiom,
% 5.48/5.74 ! [M: nat,K: nat,N: nat] :
% 5.48/5.74 ( ( ( times_times_nat @ M @ K )
% 5.48/5.74 = ( times_times_nat @ N @ K ) )
% 5.48/5.74 = ( ( M = N )
% 5.48/5.74 | ( K = zero_zero_nat ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel2
% 5.48/5.74 thf(fact_1498_add__le__same__cancel1,axiom,
% 5.48/5.74 ! [B: real,A: real] :
% 5.48/5.74 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.48/5.74 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_le_same_cancel1
% 5.48/5.74 thf(fact_1499_add__le__same__cancel1,axiom,
% 5.48/5.74 ! [B: rat,A: rat] :
% 5.48/5.74 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.48/5.74 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_le_same_cancel1
% 5.48/5.74 thf(fact_1500_add__le__same__cancel1,axiom,
% 5.48/5.74 ! [B: nat,A: nat] :
% 5.48/5.74 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.48/5.74 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_le_same_cancel1
% 5.48/5.74 thf(fact_1501_add__le__same__cancel1,axiom,
% 5.48/5.74 ! [B: int,A: int] :
% 5.48/5.74 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.48/5.74 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_le_same_cancel1
% 5.48/5.74 thf(fact_1502_add__le__same__cancel2,axiom,
% 5.48/5.74 ! [A: real,B: real] :
% 5.48/5.74 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.48/5.74 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_le_same_cancel2
% 5.48/5.74 thf(fact_1503_add__le__same__cancel2,axiom,
% 5.48/5.74 ! [A: rat,B: rat] :
% 5.48/5.74 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.48/5.74 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_le_same_cancel2
% 5.48/5.74 thf(fact_1504_add__le__same__cancel2,axiom,
% 5.48/5.74 ! [A: nat,B: nat] :
% 5.48/5.74 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.48/5.74 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_le_same_cancel2
% 5.48/5.74 thf(fact_1505_add__le__same__cancel2,axiom,
% 5.48/5.74 ! [A: int,B: int] :
% 5.48/5.74 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.48/5.74 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_le_same_cancel2
% 5.48/5.74 thf(fact_1506_le__add__same__cancel1,axiom,
% 5.48/5.74 ! [A: real,B: real] :
% 5.48/5.74 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.48/5.74 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % le_add_same_cancel1
% 5.48/5.74 thf(fact_1507_le__add__same__cancel1,axiom,
% 5.48/5.74 ! [A: rat,B: rat] :
% 5.48/5.74 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.48/5.74 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % le_add_same_cancel1
% 5.48/5.74 thf(fact_1508_le__add__same__cancel1,axiom,
% 5.48/5.74 ! [A: nat,B: nat] :
% 5.48/5.74 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.48/5.74 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % le_add_same_cancel1
% 5.48/5.74 thf(fact_1509_le__add__same__cancel1,axiom,
% 5.48/5.74 ! [A: int,B: int] :
% 5.48/5.74 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.48/5.74 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % le_add_same_cancel1
% 5.48/5.74 thf(fact_1510_le__add__same__cancel2,axiom,
% 5.48/5.74 ! [A: real,B: real] :
% 5.48/5.74 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.48/5.74 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % le_add_same_cancel2
% 5.48/5.74 thf(fact_1511_le__add__same__cancel2,axiom,
% 5.48/5.74 ! [A: rat,B: rat] :
% 5.48/5.74 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.48/5.74 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % le_add_same_cancel2
% 5.48/5.74 thf(fact_1512_le__add__same__cancel2,axiom,
% 5.48/5.74 ! [A: nat,B: nat] :
% 5.48/5.74 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.48/5.74 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % le_add_same_cancel2
% 5.48/5.74 thf(fact_1513_le__add__same__cancel2,axiom,
% 5.48/5.74 ! [A: int,B: int] :
% 5.48/5.74 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.48/5.74 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % le_add_same_cancel2
% 5.48/5.74 thf(fact_1514_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.48/5.74 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.48/5.74
% 5.48/5.74 % double_add_le_zero_iff_single_add_le_zero
% 5.48/5.74 thf(fact_1515_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.48/5.74 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.48/5.74
% 5.48/5.74 % double_add_le_zero_iff_single_add_le_zero
% 5.48/5.74 thf(fact_1516_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.48/5.74 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.48/5.74
% 5.48/5.74 % double_add_le_zero_iff_single_add_le_zero
% 5.48/5.74 thf(fact_1517_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.48/5.74 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % zero_le_double_add_iff_zero_le_single_add
% 5.48/5.74 thf(fact_1518_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.48/5.74 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % zero_le_double_add_iff_zero_le_single_add
% 5.48/5.74 thf(fact_1519_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.48/5.74 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % zero_le_double_add_iff_zero_le_single_add
% 5.48/5.74 thf(fact_1520_add__less__same__cancel1,axiom,
% 5.48/5.74 ! [B: real,A: real] :
% 5.48/5.74 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.48/5.74 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_less_same_cancel1
% 5.48/5.74 thf(fact_1521_add__less__same__cancel1,axiom,
% 5.48/5.74 ! [B: rat,A: rat] :
% 5.48/5.74 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.48/5.74 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_less_same_cancel1
% 5.48/5.74 thf(fact_1522_add__less__same__cancel1,axiom,
% 5.48/5.74 ! [B: nat,A: nat] :
% 5.48/5.74 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.48/5.74 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_less_same_cancel1
% 5.48/5.74 thf(fact_1523_add__less__same__cancel1,axiom,
% 5.48/5.74 ! [B: int,A: int] :
% 5.48/5.74 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.48/5.74 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_less_same_cancel1
% 5.48/5.74 thf(fact_1524_add__less__same__cancel2,axiom,
% 5.48/5.74 ! [A: real,B: real] :
% 5.48/5.74 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.48/5.74 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_less_same_cancel2
% 5.48/5.74 thf(fact_1525_add__less__same__cancel2,axiom,
% 5.48/5.74 ! [A: rat,B: rat] :
% 5.48/5.74 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.48/5.74 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_less_same_cancel2
% 5.48/5.74 thf(fact_1526_add__less__same__cancel2,axiom,
% 5.48/5.74 ! [A: nat,B: nat] :
% 5.48/5.74 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.48/5.74 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_less_same_cancel2
% 5.48/5.74 thf(fact_1527_add__less__same__cancel2,axiom,
% 5.48/5.74 ! [A: int,B: int] :
% 5.48/5.74 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.48/5.74 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_less_same_cancel2
% 5.48/5.74 thf(fact_1528_less__add__same__cancel1,axiom,
% 5.48/5.74 ! [A: real,B: real] :
% 5.48/5.74 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.48/5.74 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % less_add_same_cancel1
% 5.48/5.74 thf(fact_1529_less__add__same__cancel1,axiom,
% 5.48/5.74 ! [A: rat,B: rat] :
% 5.48/5.74 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.48/5.74 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % less_add_same_cancel1
% 5.48/5.74 thf(fact_1530_less__add__same__cancel1,axiom,
% 5.48/5.74 ! [A: nat,B: nat] :
% 5.48/5.74 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.48/5.74 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % less_add_same_cancel1
% 5.48/5.74 thf(fact_1531_less__add__same__cancel1,axiom,
% 5.48/5.74 ! [A: int,B: int] :
% 5.48/5.74 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.48/5.74 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % less_add_same_cancel1
% 5.48/5.74 thf(fact_1532_less__add__same__cancel2,axiom,
% 5.48/5.74 ! [A: real,B: real] :
% 5.48/5.74 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.48/5.74 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % less_add_same_cancel2
% 5.48/5.74 thf(fact_1533_less__add__same__cancel2,axiom,
% 5.48/5.74 ! [A: rat,B: rat] :
% 5.48/5.74 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.48/5.74 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % less_add_same_cancel2
% 5.48/5.74 thf(fact_1534_less__add__same__cancel2,axiom,
% 5.48/5.74 ! [A: nat,B: nat] :
% 5.48/5.74 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.48/5.74 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % less_add_same_cancel2
% 5.48/5.74 thf(fact_1535_less__add__same__cancel2,axiom,
% 5.48/5.74 ! [A: int,B: int] :
% 5.48/5.74 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.48/5.74 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.48/5.74
% 5.48/5.74 % less_add_same_cancel2
% 5.48/5.74 thf(fact_1536_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.48/5.74 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.48/5.74
% 5.48/5.74 % double_add_less_zero_iff_single_add_less_zero
% 5.48/5.74 thf(fact_1537_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.48/5.74 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.48/5.74
% 5.48/5.74 % double_add_less_zero_iff_single_add_less_zero
% 5.48/5.74 thf(fact_1538_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.48/5.74 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.48/5.74
% 5.48/5.74 % double_add_less_zero_iff_single_add_less_zero
% 5.48/5.74 thf(fact_1539_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.48/5.74 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % zero_less_double_add_iff_zero_less_single_add
% 5.48/5.74 thf(fact_1540_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.48/5.74 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % zero_less_double_add_iff_zero_less_single_add
% 5.48/5.74 thf(fact_1541_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.48/5.74 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % zero_less_double_add_iff_zero_less_single_add
% 5.48/5.74 thf(fact_1542_diff__ge__0__iff__ge,axiom,
% 5.48/5.74 ! [A: real,B: real] :
% 5.48/5.74 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.48/5.74 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % diff_ge_0_iff_ge
% 5.48/5.74 thf(fact_1543_diff__ge__0__iff__ge,axiom,
% 5.48/5.74 ! [A: rat,B: rat] :
% 5.48/5.74 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.48/5.74 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % diff_ge_0_iff_ge
% 5.48/5.74 thf(fact_1544_diff__ge__0__iff__ge,axiom,
% 5.48/5.74 ! [A: int,B: int] :
% 5.48/5.74 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.48/5.74 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % diff_ge_0_iff_ge
% 5.48/5.74 thf(fact_1545_diff__gt__0__iff__gt,axiom,
% 5.48/5.74 ! [A: real,B: real] :
% 5.48/5.74 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.48/5.74 = ( ord_less_real @ B @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % diff_gt_0_iff_gt
% 5.48/5.74 thf(fact_1546_diff__gt__0__iff__gt,axiom,
% 5.48/5.74 ! [A: rat,B: rat] :
% 5.48/5.74 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.48/5.74 = ( ord_less_rat @ B @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % diff_gt_0_iff_gt
% 5.48/5.74 thf(fact_1547_diff__gt__0__iff__gt,axiom,
% 5.48/5.74 ! [A: int,B: int] :
% 5.48/5.74 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.48/5.74 = ( ord_less_int @ B @ A ) ) ).
% 5.48/5.74
% 5.48/5.74 % diff_gt_0_iff_gt
% 5.48/5.74 thf(fact_1548_mult__cancel__left1,axiom,
% 5.48/5.74 ! [C: complex,B: complex] :
% 5.48/5.74 ( ( C
% 5.48/5.74 = ( times_times_complex @ C @ B ) )
% 5.48/5.74 = ( ( C = zero_zero_complex )
% 5.48/5.74 | ( B = one_one_complex ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_left1
% 5.48/5.74 thf(fact_1549_mult__cancel__left1,axiom,
% 5.48/5.74 ! [C: real,B: real] :
% 5.48/5.74 ( ( C
% 5.48/5.74 = ( times_times_real @ C @ B ) )
% 5.48/5.74 = ( ( C = zero_zero_real )
% 5.48/5.74 | ( B = one_one_real ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_left1
% 5.48/5.74 thf(fact_1550_mult__cancel__left1,axiom,
% 5.48/5.74 ! [C: rat,B: rat] :
% 5.48/5.74 ( ( C
% 5.48/5.74 = ( times_times_rat @ C @ B ) )
% 5.48/5.74 = ( ( C = zero_zero_rat )
% 5.48/5.74 | ( B = one_one_rat ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_left1
% 5.48/5.74 thf(fact_1551_mult__cancel__left1,axiom,
% 5.48/5.74 ! [C: int,B: int] :
% 5.48/5.74 ( ( C
% 5.48/5.74 = ( times_times_int @ C @ B ) )
% 5.48/5.74 = ( ( C = zero_zero_int )
% 5.48/5.74 | ( B = one_one_int ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_left1
% 5.48/5.74 thf(fact_1552_mult__cancel__left2,axiom,
% 5.48/5.74 ! [C: complex,A: complex] :
% 5.48/5.74 ( ( ( times_times_complex @ C @ A )
% 5.48/5.74 = C )
% 5.48/5.74 = ( ( C = zero_zero_complex )
% 5.48/5.74 | ( A = one_one_complex ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_left2
% 5.48/5.74 thf(fact_1553_mult__cancel__left2,axiom,
% 5.48/5.74 ! [C: real,A: real] :
% 5.48/5.74 ( ( ( times_times_real @ C @ A )
% 5.48/5.74 = C )
% 5.48/5.74 = ( ( C = zero_zero_real )
% 5.48/5.74 | ( A = one_one_real ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_left2
% 5.48/5.74 thf(fact_1554_mult__cancel__left2,axiom,
% 5.48/5.74 ! [C: rat,A: rat] :
% 5.48/5.74 ( ( ( times_times_rat @ C @ A )
% 5.48/5.74 = C )
% 5.48/5.74 = ( ( C = zero_zero_rat )
% 5.48/5.74 | ( A = one_one_rat ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_left2
% 5.48/5.74 thf(fact_1555_mult__cancel__left2,axiom,
% 5.48/5.74 ! [C: int,A: int] :
% 5.48/5.74 ( ( ( times_times_int @ C @ A )
% 5.48/5.74 = C )
% 5.48/5.74 = ( ( C = zero_zero_int )
% 5.48/5.74 | ( A = one_one_int ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_left2
% 5.48/5.74 thf(fact_1556_mult__cancel__right1,axiom,
% 5.48/5.74 ! [C: complex,B: complex] :
% 5.48/5.74 ( ( C
% 5.48/5.74 = ( times_times_complex @ B @ C ) )
% 5.48/5.74 = ( ( C = zero_zero_complex )
% 5.48/5.74 | ( B = one_one_complex ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_right1
% 5.48/5.74 thf(fact_1557_mult__cancel__right1,axiom,
% 5.48/5.74 ! [C: real,B: real] :
% 5.48/5.74 ( ( C
% 5.48/5.74 = ( times_times_real @ B @ C ) )
% 5.48/5.74 = ( ( C = zero_zero_real )
% 5.48/5.74 | ( B = one_one_real ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_right1
% 5.48/5.74 thf(fact_1558_mult__cancel__right1,axiom,
% 5.48/5.74 ! [C: rat,B: rat] :
% 5.48/5.74 ( ( C
% 5.48/5.74 = ( times_times_rat @ B @ C ) )
% 5.48/5.74 = ( ( C = zero_zero_rat )
% 5.48/5.74 | ( B = one_one_rat ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_right1
% 5.48/5.74 thf(fact_1559_mult__cancel__right1,axiom,
% 5.48/5.74 ! [C: int,B: int] :
% 5.48/5.74 ( ( C
% 5.48/5.74 = ( times_times_int @ B @ C ) )
% 5.48/5.74 = ( ( C = zero_zero_int )
% 5.48/5.74 | ( B = one_one_int ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_right1
% 5.48/5.74 thf(fact_1560_mult__cancel__right2,axiom,
% 5.48/5.74 ! [A: complex,C: complex] :
% 5.48/5.74 ( ( ( times_times_complex @ A @ C )
% 5.48/5.74 = C )
% 5.48/5.74 = ( ( C = zero_zero_complex )
% 5.48/5.74 | ( A = one_one_complex ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_right2
% 5.48/5.74 thf(fact_1561_mult__cancel__right2,axiom,
% 5.48/5.74 ! [A: real,C: real] :
% 5.48/5.74 ( ( ( times_times_real @ A @ C )
% 5.48/5.74 = C )
% 5.48/5.74 = ( ( C = zero_zero_real )
% 5.48/5.74 | ( A = one_one_real ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_right2
% 5.48/5.74 thf(fact_1562_mult__cancel__right2,axiom,
% 5.48/5.74 ! [A: rat,C: rat] :
% 5.48/5.74 ( ( ( times_times_rat @ A @ C )
% 5.48/5.74 = C )
% 5.48/5.74 = ( ( C = zero_zero_rat )
% 5.48/5.74 | ( A = one_one_rat ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_right2
% 5.48/5.74 thf(fact_1563_mult__cancel__right2,axiom,
% 5.48/5.74 ! [A: int,C: int] :
% 5.48/5.74 ( ( ( times_times_int @ A @ C )
% 5.48/5.74 = C )
% 5.48/5.74 = ( ( C = zero_zero_int )
% 5.48/5.74 | ( A = one_one_int ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_cancel_right2
% 5.48/5.74 thf(fact_1564_sum__squares__eq__zero__iff,axiom,
% 5.48/5.74 ! [X2: real,Y2: real] :
% 5.48/5.74 ( ( ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) )
% 5.48/5.74 = zero_zero_real )
% 5.48/5.74 = ( ( X2 = zero_zero_real )
% 5.48/5.74 & ( Y2 = zero_zero_real ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % sum_squares_eq_zero_iff
% 5.48/5.74 thf(fact_1565_sum__squares__eq__zero__iff,axiom,
% 5.48/5.74 ! [X2: rat,Y2: rat] :
% 5.48/5.74 ( ( ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y2 @ Y2 ) )
% 5.48/5.74 = zero_zero_rat )
% 5.48/5.74 = ( ( X2 = zero_zero_rat )
% 5.48/5.74 & ( Y2 = zero_zero_rat ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % sum_squares_eq_zero_iff
% 5.48/5.74 thf(fact_1566_sum__squares__eq__zero__iff,axiom,
% 5.48/5.74 ! [X2: int,Y2: int] :
% 5.48/5.74 ( ( ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y2 @ Y2 ) )
% 5.48/5.74 = zero_zero_int )
% 5.48/5.74 = ( ( X2 = zero_zero_int )
% 5.48/5.74 & ( Y2 = zero_zero_int ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % sum_squares_eq_zero_iff
% 5.48/5.74 thf(fact_1567_diff__numeral__special_I9_J,axiom,
% 5.48/5.74 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.48/5.74 = zero_zero_complex ) ).
% 5.48/5.74
% 5.48/5.74 % diff_numeral_special(9)
% 5.48/5.74 thf(fact_1568_diff__numeral__special_I9_J,axiom,
% 5.48/5.74 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.48/5.74 = zero_zero_real ) ).
% 5.48/5.74
% 5.48/5.74 % diff_numeral_special(9)
% 5.48/5.74 thf(fact_1569_diff__numeral__special_I9_J,axiom,
% 5.48/5.74 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.48/5.74 = zero_zero_rat ) ).
% 5.48/5.74
% 5.48/5.74 % diff_numeral_special(9)
% 5.48/5.74 thf(fact_1570_diff__numeral__special_I9_J,axiom,
% 5.48/5.74 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.48/5.74 = zero_zero_int ) ).
% 5.48/5.74
% 5.48/5.74 % diff_numeral_special(9)
% 5.48/5.74 thf(fact_1571_div__mult__mult1,axiom,
% 5.48/5.74 ! [C: nat,A: nat,B: nat] :
% 5.48/5.74 ( ( C != zero_zero_nat )
% 5.48/5.74 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.48/5.74 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % div_mult_mult1
% 5.48/5.74 thf(fact_1572_div__mult__mult1,axiom,
% 5.48/5.74 ! [C: int,A: int,B: int] :
% 5.48/5.74 ( ( C != zero_zero_int )
% 5.48/5.74 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.48/5.74 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % div_mult_mult1
% 5.48/5.74 thf(fact_1573_div__mult__mult2,axiom,
% 5.48/5.74 ! [C: nat,A: nat,B: nat] :
% 5.48/5.74 ( ( C != zero_zero_nat )
% 5.48/5.74 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.48/5.74 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % div_mult_mult2
% 5.48/5.74 thf(fact_1574_div__mult__mult2,axiom,
% 5.48/5.74 ! [C: int,A: int,B: int] :
% 5.48/5.74 ( ( C != zero_zero_int )
% 5.48/5.74 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.48/5.74 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % div_mult_mult2
% 5.48/5.74 thf(fact_1575_div__mult__mult1__if,axiom,
% 5.48/5.74 ! [C: nat,A: nat,B: nat] :
% 5.48/5.74 ( ( ( C = zero_zero_nat )
% 5.48/5.74 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.48/5.74 = zero_zero_nat ) )
% 5.48/5.74 & ( ( C != zero_zero_nat )
% 5.48/5.74 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.48/5.74 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % div_mult_mult1_if
% 5.48/5.74 thf(fact_1576_div__mult__mult1__if,axiom,
% 5.48/5.74 ! [C: int,A: int,B: int] :
% 5.48/5.74 ( ( ( C = zero_zero_int )
% 5.48/5.74 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.48/5.74 = zero_zero_int ) )
% 5.48/5.74 & ( ( C != zero_zero_int )
% 5.48/5.74 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.48/5.74 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % div_mult_mult1_if
% 5.48/5.74 thf(fact_1577_mult__divide__mult__cancel__left__if,axiom,
% 5.48/5.74 ! [C: complex,A: complex,B: complex] :
% 5.48/5.74 ( ( ( C = zero_zero_complex )
% 5.48/5.74 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.48/5.74 = zero_zero_complex ) )
% 5.48/5.74 & ( ( C != zero_zero_complex )
% 5.48/5.74 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.48/5.74 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_divide_mult_cancel_left_if
% 5.48/5.74 thf(fact_1578_mult__divide__mult__cancel__left__if,axiom,
% 5.48/5.74 ! [C: real,A: real,B: real] :
% 5.48/5.74 ( ( ( C = zero_zero_real )
% 5.48/5.74 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.48/5.74 = zero_zero_real ) )
% 5.48/5.74 & ( ( C != zero_zero_real )
% 5.48/5.74 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.48/5.74 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_divide_mult_cancel_left_if
% 5.48/5.74 thf(fact_1579_mult__divide__mult__cancel__left__if,axiom,
% 5.48/5.74 ! [C: rat,A: rat,B: rat] :
% 5.48/5.74 ( ( ( C = zero_zero_rat )
% 5.48/5.74 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.48/5.74 = zero_zero_rat ) )
% 5.48/5.74 & ( ( C != zero_zero_rat )
% 5.48/5.74 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.48/5.74 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_divide_mult_cancel_left_if
% 5.48/5.74 thf(fact_1580_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.48/5.74 ! [C: complex,A: complex,B: complex] :
% 5.48/5.74 ( ( C != zero_zero_complex )
% 5.48/5.74 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.48/5.74 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_divide_mult_cancel_left
% 5.48/5.74 thf(fact_1581_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.48/5.74 ! [C: real,A: real,B: real] :
% 5.48/5.74 ( ( C != zero_zero_real )
% 5.48/5.74 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.48/5.74 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_divide_mult_cancel_left
% 5.48/5.74 thf(fact_1582_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.48/5.74 ! [C: rat,A: rat,B: rat] :
% 5.48/5.74 ( ( C != zero_zero_rat )
% 5.48/5.74 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.48/5.74 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_divide_mult_cancel_left
% 5.48/5.74 thf(fact_1583_nonzero__mult__div__cancel__left,axiom,
% 5.48/5.74 ! [A: complex,B: complex] :
% 5.48/5.74 ( ( A != zero_zero_complex )
% 5.48/5.74 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.48/5.74 = B ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_div_cancel_left
% 5.48/5.74 thf(fact_1584_nonzero__mult__div__cancel__left,axiom,
% 5.48/5.74 ! [A: real,B: real] :
% 5.48/5.74 ( ( A != zero_zero_real )
% 5.48/5.74 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.48/5.74 = B ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_div_cancel_left
% 5.48/5.74 thf(fact_1585_nonzero__mult__div__cancel__left,axiom,
% 5.48/5.74 ! [A: rat,B: rat] :
% 5.48/5.74 ( ( A != zero_zero_rat )
% 5.48/5.74 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.48/5.74 = B ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_div_cancel_left
% 5.48/5.74 thf(fact_1586_nonzero__mult__div__cancel__left,axiom,
% 5.48/5.74 ! [A: nat,B: nat] :
% 5.48/5.74 ( ( A != zero_zero_nat )
% 5.48/5.74 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.48/5.74 = B ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_div_cancel_left
% 5.48/5.74 thf(fact_1587_nonzero__mult__div__cancel__left,axiom,
% 5.48/5.74 ! [A: int,B: int] :
% 5.48/5.74 ( ( A != zero_zero_int )
% 5.48/5.74 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.48/5.74 = B ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_div_cancel_left
% 5.48/5.74 thf(fact_1588_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.48/5.74 ! [C: complex,A: complex,B: complex] :
% 5.48/5.74 ( ( C != zero_zero_complex )
% 5.48/5.74 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.48/5.74 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_divide_mult_cancel_left2
% 5.48/5.74 thf(fact_1589_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.48/5.74 ! [C: real,A: real,B: real] :
% 5.48/5.74 ( ( C != zero_zero_real )
% 5.48/5.74 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.48/5.74 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_divide_mult_cancel_left2
% 5.48/5.74 thf(fact_1590_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.48/5.74 ! [C: rat,A: rat,B: rat] :
% 5.48/5.74 ( ( C != zero_zero_rat )
% 5.48/5.74 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.48/5.74 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_divide_mult_cancel_left2
% 5.48/5.74 thf(fact_1591_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.48/5.74 ! [C: complex,A: complex,B: complex] :
% 5.48/5.74 ( ( C != zero_zero_complex )
% 5.48/5.74 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.48/5.74 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_divide_mult_cancel_right
% 5.48/5.74 thf(fact_1592_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.48/5.74 ! [C: real,A: real,B: real] :
% 5.48/5.74 ( ( C != zero_zero_real )
% 5.48/5.74 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.48/5.74 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_divide_mult_cancel_right
% 5.48/5.74 thf(fact_1593_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.48/5.74 ! [C: rat,A: rat,B: rat] :
% 5.48/5.74 ( ( C != zero_zero_rat )
% 5.48/5.74 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.48/5.74 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_divide_mult_cancel_right
% 5.48/5.74 thf(fact_1594_nonzero__mult__div__cancel__right,axiom,
% 5.48/5.74 ! [B: complex,A: complex] :
% 5.48/5.74 ( ( B != zero_zero_complex )
% 5.48/5.74 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.48/5.74 = A ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_div_cancel_right
% 5.48/5.74 thf(fact_1595_nonzero__mult__div__cancel__right,axiom,
% 5.48/5.74 ! [B: real,A: real] :
% 5.48/5.74 ( ( B != zero_zero_real )
% 5.48/5.74 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.48/5.74 = A ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_div_cancel_right
% 5.48/5.74 thf(fact_1596_nonzero__mult__div__cancel__right,axiom,
% 5.48/5.74 ! [B: rat,A: rat] :
% 5.48/5.74 ( ( B != zero_zero_rat )
% 5.48/5.74 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.48/5.74 = A ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_div_cancel_right
% 5.48/5.74 thf(fact_1597_nonzero__mult__div__cancel__right,axiom,
% 5.48/5.74 ! [B: nat,A: nat] :
% 5.48/5.74 ( ( B != zero_zero_nat )
% 5.48/5.74 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.48/5.74 = A ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_div_cancel_right
% 5.48/5.74 thf(fact_1598_nonzero__mult__div__cancel__right,axiom,
% 5.48/5.74 ! [B: int,A: int] :
% 5.48/5.74 ( ( B != zero_zero_int )
% 5.48/5.74 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.48/5.74 = A ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_div_cancel_right
% 5.48/5.74 thf(fact_1599_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.48/5.74 ! [C: complex,A: complex,B: complex] :
% 5.48/5.74 ( ( C != zero_zero_complex )
% 5.48/5.74 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.48/5.74 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_divide_mult_cancel_right2
% 5.48/5.74 thf(fact_1600_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.48/5.74 ! [C: real,A: real,B: real] :
% 5.48/5.74 ( ( C != zero_zero_real )
% 5.48/5.74 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.48/5.74 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_divide_mult_cancel_right2
% 5.48/5.74 thf(fact_1601_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.48/5.74 ! [C: rat,A: rat,B: rat] :
% 5.48/5.74 ( ( C != zero_zero_rat )
% 5.48/5.74 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.48/5.74 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nonzero_mult_divide_mult_cancel_right2
% 5.48/5.74 thf(fact_1602_diff__add__zero,axiom,
% 5.48/5.74 ! [A: nat,B: nat] :
% 5.48/5.74 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.48/5.74 = zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % diff_add_zero
% 5.48/5.74 thf(fact_1603_divide__eq__1__iff,axiom,
% 5.48/5.74 ! [A: complex,B: complex] :
% 5.48/5.74 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.48/5.74 = one_one_complex )
% 5.48/5.74 = ( ( B != zero_zero_complex )
% 5.48/5.74 & ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_eq_1_iff
% 5.48/5.74 thf(fact_1604_divide__eq__1__iff,axiom,
% 5.48/5.74 ! [A: real,B: real] :
% 5.48/5.74 ( ( ( divide_divide_real @ A @ B )
% 5.48/5.74 = one_one_real )
% 5.48/5.74 = ( ( B != zero_zero_real )
% 5.48/5.74 & ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_eq_1_iff
% 5.48/5.74 thf(fact_1605_divide__eq__1__iff,axiom,
% 5.48/5.74 ! [A: rat,B: rat] :
% 5.48/5.74 ( ( ( divide_divide_rat @ A @ B )
% 5.48/5.74 = one_one_rat )
% 5.48/5.74 = ( ( B != zero_zero_rat )
% 5.48/5.74 & ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_eq_1_iff
% 5.48/5.74 thf(fact_1606_div__self,axiom,
% 5.48/5.74 ! [A: complex] :
% 5.48/5.74 ( ( A != zero_zero_complex )
% 5.48/5.74 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.48/5.74 = one_one_complex ) ) ).
% 5.48/5.74
% 5.48/5.74 % div_self
% 5.48/5.74 thf(fact_1607_div__self,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( A != zero_zero_real )
% 5.48/5.74 => ( ( divide_divide_real @ A @ A )
% 5.48/5.74 = one_one_real ) ) ).
% 5.48/5.74
% 5.48/5.74 % div_self
% 5.48/5.74 thf(fact_1608_div__self,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( A != zero_zero_rat )
% 5.48/5.74 => ( ( divide_divide_rat @ A @ A )
% 5.48/5.74 = one_one_rat ) ) ).
% 5.48/5.74
% 5.48/5.74 % div_self
% 5.48/5.74 thf(fact_1609_div__self,axiom,
% 5.48/5.74 ! [A: nat] :
% 5.48/5.74 ( ( A != zero_zero_nat )
% 5.48/5.74 => ( ( divide_divide_nat @ A @ A )
% 5.48/5.74 = one_one_nat ) ) ).
% 5.48/5.74
% 5.48/5.74 % div_self
% 5.48/5.74 thf(fact_1610_div__self,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( A != zero_zero_int )
% 5.48/5.74 => ( ( divide_divide_int @ A @ A )
% 5.48/5.74 = one_one_int ) ) ).
% 5.48/5.74
% 5.48/5.74 % div_self
% 5.48/5.74 thf(fact_1611_one__eq__divide__iff,axiom,
% 5.48/5.74 ! [A: complex,B: complex] :
% 5.48/5.74 ( ( one_one_complex
% 5.48/5.74 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.48/5.74 = ( ( B != zero_zero_complex )
% 5.48/5.74 & ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % one_eq_divide_iff
% 5.48/5.74 thf(fact_1612_one__eq__divide__iff,axiom,
% 5.48/5.74 ! [A: real,B: real] :
% 5.48/5.74 ( ( one_one_real
% 5.48/5.74 = ( divide_divide_real @ A @ B ) )
% 5.48/5.74 = ( ( B != zero_zero_real )
% 5.48/5.74 & ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % one_eq_divide_iff
% 5.48/5.74 thf(fact_1613_one__eq__divide__iff,axiom,
% 5.48/5.74 ! [A: rat,B: rat] :
% 5.48/5.74 ( ( one_one_rat
% 5.48/5.74 = ( divide_divide_rat @ A @ B ) )
% 5.48/5.74 = ( ( B != zero_zero_rat )
% 5.48/5.74 & ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % one_eq_divide_iff
% 5.48/5.74 thf(fact_1614_divide__self,axiom,
% 5.48/5.74 ! [A: complex] :
% 5.48/5.74 ( ( A != zero_zero_complex )
% 5.48/5.74 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.48/5.74 = one_one_complex ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_self
% 5.48/5.74 thf(fact_1615_divide__self,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( A != zero_zero_real )
% 5.48/5.74 => ( ( divide_divide_real @ A @ A )
% 5.48/5.74 = one_one_real ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_self
% 5.48/5.74 thf(fact_1616_divide__self,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( A != zero_zero_rat )
% 5.48/5.74 => ( ( divide_divide_rat @ A @ A )
% 5.48/5.74 = one_one_rat ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_self
% 5.48/5.74 thf(fact_1617_divide__self__if,axiom,
% 5.48/5.74 ! [A: complex] :
% 5.48/5.74 ( ( ( A = zero_zero_complex )
% 5.48/5.74 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.48/5.74 = zero_zero_complex ) )
% 5.48/5.74 & ( ( A != zero_zero_complex )
% 5.48/5.74 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.48/5.74 = one_one_complex ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_self_if
% 5.48/5.74 thf(fact_1618_divide__self__if,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( ( A = zero_zero_real )
% 5.48/5.74 => ( ( divide_divide_real @ A @ A )
% 5.48/5.74 = zero_zero_real ) )
% 5.48/5.74 & ( ( A != zero_zero_real )
% 5.48/5.74 => ( ( divide_divide_real @ A @ A )
% 5.48/5.74 = one_one_real ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_self_if
% 5.48/5.74 thf(fact_1619_divide__self__if,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( ( A = zero_zero_rat )
% 5.48/5.74 => ( ( divide_divide_rat @ A @ A )
% 5.48/5.74 = zero_zero_rat ) )
% 5.48/5.74 & ( ( A != zero_zero_rat )
% 5.48/5.74 => ( ( divide_divide_rat @ A @ A )
% 5.48/5.74 = one_one_rat ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_self_if
% 5.48/5.74 thf(fact_1620_divide__eq__eq__1,axiom,
% 5.48/5.74 ! [B: real,A: real] :
% 5.48/5.74 ( ( ( divide_divide_real @ B @ A )
% 5.48/5.74 = one_one_real )
% 5.48/5.74 = ( ( A != zero_zero_real )
% 5.48/5.74 & ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_eq_eq_1
% 5.48/5.74 thf(fact_1621_divide__eq__eq__1,axiom,
% 5.48/5.74 ! [B: rat,A: rat] :
% 5.48/5.74 ( ( ( divide_divide_rat @ B @ A )
% 5.48/5.74 = one_one_rat )
% 5.48/5.74 = ( ( A != zero_zero_rat )
% 5.48/5.74 & ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % divide_eq_eq_1
% 5.48/5.74 thf(fact_1622_eq__divide__eq__1,axiom,
% 5.48/5.74 ! [B: real,A: real] :
% 5.48/5.74 ( ( one_one_real
% 5.48/5.74 = ( divide_divide_real @ B @ A ) )
% 5.48/5.74 = ( ( A != zero_zero_real )
% 5.48/5.74 & ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % eq_divide_eq_1
% 5.48/5.74 thf(fact_1623_eq__divide__eq__1,axiom,
% 5.48/5.74 ! [B: rat,A: rat] :
% 5.48/5.74 ( ( one_one_rat
% 5.48/5.74 = ( divide_divide_rat @ B @ A ) )
% 5.48/5.74 = ( ( A != zero_zero_rat )
% 5.48/5.74 & ( A = B ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % eq_divide_eq_1
% 5.48/5.74 thf(fact_1624_one__divide__eq__0__iff,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.48/5.74 = zero_zero_real )
% 5.48/5.74 = ( A = zero_zero_real ) ) ).
% 5.48/5.74
% 5.48/5.74 % one_divide_eq_0_iff
% 5.48/5.74 thf(fact_1625_one__divide__eq__0__iff,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.48/5.74 = zero_zero_rat )
% 5.48/5.74 = ( A = zero_zero_rat ) ) ).
% 5.48/5.74
% 5.48/5.74 % one_divide_eq_0_iff
% 5.48/5.74 thf(fact_1626_zero__eq__1__divide__iff,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( zero_zero_real
% 5.48/5.74 = ( divide_divide_real @ one_one_real @ A ) )
% 5.48/5.74 = ( A = zero_zero_real ) ) ).
% 5.48/5.74
% 5.48/5.74 % zero_eq_1_divide_iff
% 5.48/5.74 thf(fact_1627_zero__eq__1__divide__iff,axiom,
% 5.48/5.74 ! [A: rat] :
% 5.48/5.74 ( ( zero_zero_rat
% 5.48/5.74 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.48/5.74 = ( A = zero_zero_rat ) ) ).
% 5.48/5.74
% 5.48/5.74 % zero_eq_1_divide_iff
% 5.48/5.74 thf(fact_1628_power__0__Suc,axiom,
% 5.48/5.74 ! [N: nat] :
% 5.48/5.74 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.48/5.74 = zero_zero_rat ) ).
% 5.48/5.74
% 5.48/5.74 % power_0_Suc
% 5.48/5.74 thf(fact_1629_power__0__Suc,axiom,
% 5.48/5.74 ! [N: nat] :
% 5.48/5.74 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.48/5.74 = zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % power_0_Suc
% 5.48/5.74 thf(fact_1630_power__0__Suc,axiom,
% 5.48/5.74 ! [N: nat] :
% 5.48/5.74 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.48/5.74 = zero_zero_real ) ).
% 5.48/5.74
% 5.48/5.74 % power_0_Suc
% 5.48/5.74 thf(fact_1631_power__0__Suc,axiom,
% 5.48/5.74 ! [N: nat] :
% 5.48/5.74 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.48/5.74 = zero_zero_int ) ).
% 5.48/5.74
% 5.48/5.74 % power_0_Suc
% 5.48/5.74 thf(fact_1632_power__0__Suc,axiom,
% 5.48/5.74 ! [N: nat] :
% 5.48/5.74 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.48/5.74 = zero_zero_complex ) ).
% 5.48/5.74
% 5.48/5.74 % power_0_Suc
% 5.48/5.74 thf(fact_1633_power__zero__numeral,axiom,
% 5.48/5.74 ! [K: num] :
% 5.48/5.74 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.48/5.74 = zero_zero_rat ) ).
% 5.48/5.74
% 5.48/5.74 % power_zero_numeral
% 5.48/5.74 thf(fact_1634_power__zero__numeral,axiom,
% 5.48/5.74 ! [K: num] :
% 5.48/5.74 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.48/5.74 = zero_zero_nat ) ).
% 5.48/5.74
% 5.48/5.74 % power_zero_numeral
% 5.48/5.74 thf(fact_1635_power__zero__numeral,axiom,
% 5.48/5.74 ! [K: num] :
% 5.48/5.74 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.48/5.74 = zero_zero_real ) ).
% 5.48/5.74
% 5.48/5.74 % power_zero_numeral
% 5.48/5.74 thf(fact_1636_power__zero__numeral,axiom,
% 5.48/5.74 ! [K: num] :
% 5.48/5.74 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.48/5.74 = zero_zero_int ) ).
% 5.48/5.74
% 5.48/5.74 % power_zero_numeral
% 5.48/5.74 thf(fact_1637_power__zero__numeral,axiom,
% 5.48/5.74 ! [K: num] :
% 5.48/5.74 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.48/5.74 = zero_zero_complex ) ).
% 5.48/5.74
% 5.48/5.74 % power_zero_numeral
% 5.48/5.74 thf(fact_1638_power__Suc0__right,axiom,
% 5.48/5.74 ! [A: nat] :
% 5.48/5.74 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % power_Suc0_right
% 5.48/5.74 thf(fact_1639_power__Suc0__right,axiom,
% 5.48/5.74 ! [A: real] :
% 5.48/5.74 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % power_Suc0_right
% 5.48/5.74 thf(fact_1640_power__Suc0__right,axiom,
% 5.48/5.74 ! [A: int] :
% 5.48/5.74 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % power_Suc0_right
% 5.48/5.74 thf(fact_1641_power__Suc0__right,axiom,
% 5.48/5.74 ! [A: complex] :
% 5.48/5.74 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.48/5.74 = A ) ).
% 5.48/5.74
% 5.48/5.74 % power_Suc0_right
% 5.48/5.74 thf(fact_1642_zero__less__Suc,axiom,
% 5.48/5.74 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.48/5.74
% 5.48/5.74 % zero_less_Suc
% 5.48/5.74 thf(fact_1643_less__Suc0,axiom,
% 5.48/5.74 ! [N: nat] :
% 5.48/5.74 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.48/5.74 = ( N = zero_zero_nat ) ) ).
% 5.48/5.74
% 5.48/5.74 % less_Suc0
% 5.48/5.74 thf(fact_1644_add__gr__0,axiom,
% 5.48/5.74 ! [M: nat,N: nat] :
% 5.48/5.74 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 5.48/5.74 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.48/5.74 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % add_gr_0
% 5.48/5.74 thf(fact_1645_mult__eq__1__iff,axiom,
% 5.48/5.74 ! [M: nat,N: nat] :
% 5.48/5.74 ( ( ( times_times_nat @ M @ N )
% 5.48/5.74 = ( suc @ zero_zero_nat ) )
% 5.48/5.74 = ( ( M
% 5.48/5.74 = ( suc @ zero_zero_nat ) )
% 5.48/5.74 & ( N
% 5.48/5.74 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % mult_eq_1_iff
% 5.48/5.74 thf(fact_1646_one__eq__mult__iff,axiom,
% 5.48/5.74 ! [M: nat,N: nat] :
% 5.48/5.74 ( ( ( suc @ zero_zero_nat )
% 5.48/5.74 = ( times_times_nat @ M @ N ) )
% 5.48/5.74 = ( ( M
% 5.48/5.74 = ( suc @ zero_zero_nat ) )
% 5.48/5.74 & ( N
% 5.48/5.74 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % one_eq_mult_iff
% 5.48/5.74 thf(fact_1647_less__one,axiom,
% 5.48/5.74 ! [N: nat] :
% 5.48/5.74 ( ( ord_less_nat @ N @ one_one_nat )
% 5.48/5.74 = ( N = zero_zero_nat ) ) ).
% 5.48/5.74
% 5.48/5.74 % less_one
% 5.48/5.74 thf(fact_1648_div__by__Suc__0,axiom,
% 5.48/5.74 ! [M: nat] :
% 5.48/5.74 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.48/5.74 = M ) ).
% 5.48/5.74
% 5.48/5.74 % div_by_Suc_0
% 5.48/5.74 thf(fact_1649_zero__less__diff,axiom,
% 5.48/5.74 ! [N: nat,M: nat] :
% 5.48/5.74 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 5.48/5.74 = ( ord_less_nat @ M @ N ) ) ).
% 5.48/5.74
% 5.48/5.74 % zero_less_diff
% 5.48/5.74 thf(fact_1650_nat__mult__less__cancel__disj,axiom,
% 5.48/5.74 ! [K: nat,M: nat,N: nat] :
% 5.48/5.74 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.48/5.74 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.48/5.74 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.48/5.74
% 5.48/5.74 % nat_mult_less_cancel_disj
% 5.48/5.74 thf(fact_1651_mult__less__cancel2,axiom,
% 5.52/5.74 ! [M: nat,K: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.52/5.74 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.74 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_less_cancel2
% 5.52/5.74 thf(fact_1652_nat__0__less__mult__iff,axiom,
% 5.52/5.74 ! [M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 5.52/5.74 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.74 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nat_0_less_mult_iff
% 5.52/5.74 thf(fact_1653_div__less,axiom,
% 5.52/5.74 ! [M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ M @ N )
% 5.52/5.74 => ( ( divide_divide_nat @ M @ N )
% 5.52/5.74 = zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % div_less
% 5.52/5.74 thf(fact_1654_diff__is__0__eq,axiom,
% 5.52/5.74 ! [M: nat,N: nat] :
% 5.52/5.74 ( ( ( minus_minus_nat @ M @ N )
% 5.52/5.74 = zero_zero_nat )
% 5.52/5.74 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.74
% 5.52/5.74 % diff_is_0_eq
% 5.52/5.74 thf(fact_1655_diff__is__0__eq_H,axiom,
% 5.52/5.74 ! [M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.74 => ( ( minus_minus_nat @ M @ N )
% 5.52/5.74 = zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % diff_is_0_eq'
% 5.52/5.74 thf(fact_1656_power__Suc__0,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.52/5.74 = ( suc @ zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_Suc_0
% 5.52/5.74 thf(fact_1657_nat__power__eq__Suc__0__iff,axiom,
% 5.52/5.74 ! [X2: nat,M: nat] :
% 5.52/5.74 ( ( ( power_power_nat @ X2 @ M )
% 5.52/5.74 = ( suc @ zero_zero_nat ) )
% 5.52/5.74 = ( ( M = zero_zero_nat )
% 5.52/5.74 | ( X2
% 5.52/5.74 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nat_power_eq_Suc_0_iff
% 5.52/5.74 thf(fact_1658_nat__zero__less__power__iff,axiom,
% 5.52/5.74 ! [X2: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X2 @ N ) )
% 5.52/5.74 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.52/5.74 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nat_zero_less_power_iff
% 5.52/5.74 thf(fact_1659_nat__mult__div__cancel__disj,axiom,
% 5.52/5.74 ! [K: nat,M: nat,N: nat] :
% 5.52/5.74 ( ( ( K = zero_zero_nat )
% 5.52/5.74 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.52/5.74 = zero_zero_nat ) )
% 5.52/5.74 & ( ( K != zero_zero_nat )
% 5.52/5.74 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.52/5.74 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nat_mult_div_cancel_disj
% 5.52/5.74 thf(fact_1660_divide__le__0__1__iff,axiom,
% 5.52/5.74 ! [A: real] :
% 5.52/5.74 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.52/5.74 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_le_0_1_iff
% 5.52/5.74 thf(fact_1661_divide__le__0__1__iff,axiom,
% 5.52/5.74 ! [A: rat] :
% 5.52/5.74 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.52/5.74 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_le_0_1_iff
% 5.52/5.74 thf(fact_1662_zero__le__divide__1__iff,axiom,
% 5.52/5.74 ! [A: real] :
% 5.52/5.74 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.52/5.74 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_le_divide_1_iff
% 5.52/5.74 thf(fact_1663_zero__le__divide__1__iff,axiom,
% 5.52/5.74 ! [A: rat] :
% 5.52/5.74 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.52/5.74 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_le_divide_1_iff
% 5.52/5.74 thf(fact_1664_zero__less__divide__1__iff,axiom,
% 5.52/5.74 ! [A: real] :
% 5.52/5.74 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.52/5.74 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_less_divide_1_iff
% 5.52/5.74 thf(fact_1665_zero__less__divide__1__iff,axiom,
% 5.52/5.74 ! [A: rat] :
% 5.52/5.74 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.52/5.74 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_less_divide_1_iff
% 5.52/5.74 thf(fact_1666_less__divide__eq__1__pos,axiom,
% 5.52/5.74 ! [A: real,B: real] :
% 5.52/5.74 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.74 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.52/5.74 = ( ord_less_real @ A @ B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % less_divide_eq_1_pos
% 5.52/5.74 thf(fact_1667_less__divide__eq__1__pos,axiom,
% 5.52/5.74 ! [A: rat,B: rat] :
% 5.52/5.74 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.74 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.52/5.74 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % less_divide_eq_1_pos
% 5.52/5.74 thf(fact_1668_less__divide__eq__1__neg,axiom,
% 5.52/5.74 ! [A: real,B: real] :
% 5.52/5.74 ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.74 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.52/5.74 = ( ord_less_real @ B @ A ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % less_divide_eq_1_neg
% 5.52/5.74 thf(fact_1669_less__divide__eq__1__neg,axiom,
% 5.52/5.74 ! [A: rat,B: rat] :
% 5.52/5.74 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.74 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.52/5.74 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % less_divide_eq_1_neg
% 5.52/5.74 thf(fact_1670_divide__less__eq__1__pos,axiom,
% 5.52/5.74 ! [A: real,B: real] :
% 5.52/5.74 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.74 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.52/5.74 = ( ord_less_real @ B @ A ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_less_eq_1_pos
% 5.52/5.74 thf(fact_1671_divide__less__eq__1__pos,axiom,
% 5.52/5.74 ! [A: rat,B: rat] :
% 5.52/5.74 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.74 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.52/5.74 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_less_eq_1_pos
% 5.52/5.74 thf(fact_1672_divide__less__eq__1__neg,axiom,
% 5.52/5.74 ! [A: real,B: real] :
% 5.52/5.74 ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.74 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.52/5.74 = ( ord_less_real @ A @ B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_less_eq_1_neg
% 5.52/5.74 thf(fact_1673_divide__less__eq__1__neg,axiom,
% 5.52/5.74 ! [A: rat,B: rat] :
% 5.52/5.74 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.74 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.52/5.74 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_less_eq_1_neg
% 5.52/5.74 thf(fact_1674_divide__less__0__1__iff,axiom,
% 5.52/5.74 ! [A: real] :
% 5.52/5.74 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.52/5.74 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_less_0_1_iff
% 5.52/5.74 thf(fact_1675_divide__less__0__1__iff,axiom,
% 5.52/5.74 ! [A: rat] :
% 5.52/5.74 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.52/5.74 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_less_0_1_iff
% 5.52/5.74 thf(fact_1676_divide__eq__eq__numeral1_I1_J,axiom,
% 5.52/5.74 ! [B: complex,W: num,A: complex] :
% 5.52/5.74 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 5.52/5.74 = A )
% 5.52/5.74 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.52/5.74 != zero_zero_complex )
% 5.52/5.74 => ( B
% 5.52/5.74 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.52/5.74 & ( ( ( numera6690914467698888265omplex @ W )
% 5.52/5.74 = zero_zero_complex )
% 5.52/5.74 => ( A = zero_zero_complex ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_eq_eq_numeral1(1)
% 5.52/5.74 thf(fact_1677_divide__eq__eq__numeral1_I1_J,axiom,
% 5.52/5.74 ! [B: real,W: num,A: real] :
% 5.52/5.74 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 5.52/5.74 = A )
% 5.52/5.74 = ( ( ( ( numeral_numeral_real @ W )
% 5.52/5.74 != zero_zero_real )
% 5.52/5.74 => ( B
% 5.52/5.74 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.52/5.74 & ( ( ( numeral_numeral_real @ W )
% 5.52/5.74 = zero_zero_real )
% 5.52/5.74 => ( A = zero_zero_real ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_eq_eq_numeral1(1)
% 5.52/5.74 thf(fact_1678_divide__eq__eq__numeral1_I1_J,axiom,
% 5.52/5.74 ! [B: rat,W: num,A: rat] :
% 5.52/5.74 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 5.52/5.74 = A )
% 5.52/5.74 = ( ( ( ( numeral_numeral_rat @ W )
% 5.52/5.74 != zero_zero_rat )
% 5.52/5.74 => ( B
% 5.52/5.74 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 5.52/5.74 & ( ( ( numeral_numeral_rat @ W )
% 5.52/5.74 = zero_zero_rat )
% 5.52/5.74 => ( A = zero_zero_rat ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_eq_eq_numeral1(1)
% 5.52/5.74 thf(fact_1679_eq__divide__eq__numeral1_I1_J,axiom,
% 5.52/5.74 ! [A: complex,B: complex,W: num] :
% 5.52/5.74 ( ( A
% 5.52/5.74 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 5.52/5.74 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.52/5.74 != zero_zero_complex )
% 5.52/5.74 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.52/5.74 = B ) )
% 5.52/5.74 & ( ( ( numera6690914467698888265omplex @ W )
% 5.52/5.74 = zero_zero_complex )
% 5.52/5.74 => ( A = zero_zero_complex ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % eq_divide_eq_numeral1(1)
% 5.52/5.74 thf(fact_1680_eq__divide__eq__numeral1_I1_J,axiom,
% 5.52/5.74 ! [A: real,B: real,W: num] :
% 5.52/5.74 ( ( A
% 5.52/5.74 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.52/5.74 = ( ( ( ( numeral_numeral_real @ W )
% 5.52/5.74 != zero_zero_real )
% 5.52/5.74 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.52/5.74 = B ) )
% 5.52/5.74 & ( ( ( numeral_numeral_real @ W )
% 5.52/5.74 = zero_zero_real )
% 5.52/5.74 => ( A = zero_zero_real ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % eq_divide_eq_numeral1(1)
% 5.52/5.74 thf(fact_1681_eq__divide__eq__numeral1_I1_J,axiom,
% 5.52/5.74 ! [A: rat,B: rat,W: num] :
% 5.52/5.74 ( ( A
% 5.52/5.74 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.52/5.74 = ( ( ( ( numeral_numeral_rat @ W )
% 5.52/5.74 != zero_zero_rat )
% 5.52/5.74 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 5.52/5.74 = B ) )
% 5.52/5.74 & ( ( ( numeral_numeral_rat @ W )
% 5.52/5.74 = zero_zero_rat )
% 5.52/5.74 => ( A = zero_zero_rat ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % eq_divide_eq_numeral1(1)
% 5.52/5.74 thf(fact_1682_nonzero__divide__mult__cancel__left,axiom,
% 5.52/5.74 ! [A: complex,B: complex] :
% 5.52/5.74 ( ( A != zero_zero_complex )
% 5.52/5.74 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.52/5.74 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nonzero_divide_mult_cancel_left
% 5.52/5.74 thf(fact_1683_nonzero__divide__mult__cancel__left,axiom,
% 5.52/5.74 ! [A: real,B: real] :
% 5.52/5.74 ( ( A != zero_zero_real )
% 5.52/5.74 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.52/5.74 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nonzero_divide_mult_cancel_left
% 5.52/5.74 thf(fact_1684_nonzero__divide__mult__cancel__left,axiom,
% 5.52/5.74 ! [A: rat,B: rat] :
% 5.52/5.74 ( ( A != zero_zero_rat )
% 5.52/5.74 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.52/5.74 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nonzero_divide_mult_cancel_left
% 5.52/5.74 thf(fact_1685_nonzero__divide__mult__cancel__right,axiom,
% 5.52/5.74 ! [B: complex,A: complex] :
% 5.52/5.74 ( ( B != zero_zero_complex )
% 5.52/5.74 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.52/5.74 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nonzero_divide_mult_cancel_right
% 5.52/5.74 thf(fact_1686_nonzero__divide__mult__cancel__right,axiom,
% 5.52/5.74 ! [B: real,A: real] :
% 5.52/5.74 ( ( B != zero_zero_real )
% 5.52/5.74 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.52/5.74 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nonzero_divide_mult_cancel_right
% 5.52/5.74 thf(fact_1687_nonzero__divide__mult__cancel__right,axiom,
% 5.52/5.74 ! [B: rat,A: rat] :
% 5.52/5.74 ( ( B != zero_zero_rat )
% 5.52/5.74 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.52/5.74 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nonzero_divide_mult_cancel_right
% 5.52/5.74 thf(fact_1688_div__mult__self1,axiom,
% 5.52/5.74 ! [B: nat,A: nat,C: nat] :
% 5.52/5.74 ( ( B != zero_zero_nat )
% 5.52/5.74 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.52/5.74 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % div_mult_self1
% 5.52/5.74 thf(fact_1689_div__mult__self1,axiom,
% 5.52/5.74 ! [B: int,A: int,C: int] :
% 5.52/5.74 ( ( B != zero_zero_int )
% 5.52/5.74 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.52/5.74 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % div_mult_self1
% 5.52/5.74 thf(fact_1690_div__mult__self2,axiom,
% 5.52/5.74 ! [B: nat,A: nat,C: nat] :
% 5.52/5.74 ( ( B != zero_zero_nat )
% 5.52/5.74 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.52/5.74 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % div_mult_self2
% 5.52/5.74 thf(fact_1691_div__mult__self2,axiom,
% 5.52/5.74 ! [B: int,A: int,C: int] :
% 5.52/5.74 ( ( B != zero_zero_int )
% 5.52/5.74 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.52/5.74 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % div_mult_self2
% 5.52/5.74 thf(fact_1692_div__mult__self3,axiom,
% 5.52/5.74 ! [B: nat,C: nat,A: nat] :
% 5.52/5.74 ( ( B != zero_zero_nat )
% 5.52/5.74 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.52/5.74 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % div_mult_self3
% 5.52/5.74 thf(fact_1693_div__mult__self3,axiom,
% 5.52/5.74 ! [B: int,C: int,A: int] :
% 5.52/5.74 ( ( B != zero_zero_int )
% 5.52/5.74 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.52/5.74 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % div_mult_self3
% 5.52/5.74 thf(fact_1694_div__mult__self4,axiom,
% 5.52/5.74 ! [B: nat,C: nat,A: nat] :
% 5.52/5.74 ( ( B != zero_zero_nat )
% 5.52/5.74 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.52/5.74 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % div_mult_self4
% 5.52/5.74 thf(fact_1695_div__mult__self4,axiom,
% 5.52/5.74 ! [B: int,C: int,A: int] :
% 5.52/5.74 ( ( B != zero_zero_int )
% 5.52/5.74 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.52/5.74 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % div_mult_self4
% 5.52/5.74 thf(fact_1696_power__eq__0__iff,axiom,
% 5.52/5.74 ! [A: rat,N: nat] :
% 5.52/5.74 ( ( ( power_power_rat @ A @ N )
% 5.52/5.74 = zero_zero_rat )
% 5.52/5.74 = ( ( A = zero_zero_rat )
% 5.52/5.74 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_0_iff
% 5.52/5.74 thf(fact_1697_power__eq__0__iff,axiom,
% 5.52/5.74 ! [A: nat,N: nat] :
% 5.52/5.74 ( ( ( power_power_nat @ A @ N )
% 5.52/5.74 = zero_zero_nat )
% 5.52/5.74 = ( ( A = zero_zero_nat )
% 5.52/5.74 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_0_iff
% 5.52/5.74 thf(fact_1698_power__eq__0__iff,axiom,
% 5.52/5.74 ! [A: real,N: nat] :
% 5.52/5.74 ( ( ( power_power_real @ A @ N )
% 5.52/5.74 = zero_zero_real )
% 5.52/5.74 = ( ( A = zero_zero_real )
% 5.52/5.74 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_0_iff
% 5.52/5.74 thf(fact_1699_power__eq__0__iff,axiom,
% 5.52/5.74 ! [A: int,N: nat] :
% 5.52/5.74 ( ( ( power_power_int @ A @ N )
% 5.52/5.74 = zero_zero_int )
% 5.52/5.74 = ( ( A = zero_zero_int )
% 5.52/5.74 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_0_iff
% 5.52/5.74 thf(fact_1700_power__eq__0__iff,axiom,
% 5.52/5.74 ! [A: complex,N: nat] :
% 5.52/5.74 ( ( ( power_power_complex @ A @ N )
% 5.52/5.74 = zero_zero_complex )
% 5.52/5.74 = ( ( A = zero_zero_complex )
% 5.52/5.74 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_0_iff
% 5.52/5.74 thf(fact_1701_Suc__pred,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.52/5.74 = N ) ) ).
% 5.52/5.74
% 5.52/5.74 % Suc_pred
% 5.52/5.74 thf(fact_1702_one__le__mult__iff,axiom,
% 5.52/5.74 ! [M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 5.52/5.74 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.52/5.74 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % one_le_mult_iff
% 5.52/5.74 thf(fact_1703_nat__mult__le__cancel__disj,axiom,
% 5.52/5.74 ! [K: nat,M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.52/5.74 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.74 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nat_mult_le_cancel_disj
% 5.52/5.74 thf(fact_1704_mult__le__cancel2,axiom,
% 5.52/5.74 ! [M: nat,K: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.52/5.74 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.74 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_le_cancel2
% 5.52/5.74 thf(fact_1705_div__mult__self1__is__m,axiom,
% 5.52/5.74 ! [N: nat,M: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 5.52/5.74 = M ) ) ).
% 5.52/5.74
% 5.52/5.74 % div_mult_self1_is_m
% 5.52/5.74 thf(fact_1706_div__mult__self__is__m,axiom,
% 5.52/5.74 ! [N: nat,M: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 5.52/5.74 = M ) ) ).
% 5.52/5.74
% 5.52/5.74 % div_mult_self_is_m
% 5.52/5.74 thf(fact_1707_divide__le__eq__1__neg,axiom,
% 5.52/5.74 ! [A: real,B: real] :
% 5.52/5.74 ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.74 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.52/5.74 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_le_eq_1_neg
% 5.52/5.74 thf(fact_1708_divide__le__eq__1__neg,axiom,
% 5.52/5.74 ! [A: rat,B: rat] :
% 5.52/5.74 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.74 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.52/5.74 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_le_eq_1_neg
% 5.52/5.74 thf(fact_1709_divide__le__eq__1__pos,axiom,
% 5.52/5.74 ! [A: real,B: real] :
% 5.52/5.74 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.74 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.52/5.74 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_le_eq_1_pos
% 5.52/5.74 thf(fact_1710_divide__le__eq__1__pos,axiom,
% 5.52/5.74 ! [A: rat,B: rat] :
% 5.52/5.74 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.74 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.52/5.74 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divide_le_eq_1_pos
% 5.52/5.74 thf(fact_1711_le__divide__eq__1__neg,axiom,
% 5.52/5.74 ! [A: real,B: real] :
% 5.52/5.74 ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.74 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.52/5.74 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % le_divide_eq_1_neg
% 5.52/5.74 thf(fact_1712_le__divide__eq__1__neg,axiom,
% 5.52/5.74 ! [A: rat,B: rat] :
% 5.52/5.74 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.74 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.52/5.74 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % le_divide_eq_1_neg
% 5.52/5.74 thf(fact_1713_le__divide__eq__1__pos,axiom,
% 5.52/5.74 ! [A: real,B: real] :
% 5.52/5.74 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.74 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.52/5.74 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % le_divide_eq_1_pos
% 5.52/5.74 thf(fact_1714_le__divide__eq__1__pos,axiom,
% 5.52/5.74 ! [A: rat,B: rat] :
% 5.52/5.74 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.74 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.52/5.74 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % le_divide_eq_1_pos
% 5.52/5.74 thf(fact_1715_power__strict__decreasing__iff,axiom,
% 5.52/5.74 ! [B: real,M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.74 => ( ( ord_less_real @ B @ one_one_real )
% 5.52/5.74 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.52/5.74 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_strict_decreasing_iff
% 5.52/5.74 thf(fact_1716_power__strict__decreasing__iff,axiom,
% 5.52/5.74 ! [B: rat,M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.52/5.74 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.52/5.74 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.52/5.74 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_strict_decreasing_iff
% 5.52/5.74 thf(fact_1717_power__strict__decreasing__iff,axiom,
% 5.52/5.74 ! [B: nat,M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.74 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.52/5.74 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.52/5.74 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_strict_decreasing_iff
% 5.52/5.74 thf(fact_1718_power__strict__decreasing__iff,axiom,
% 5.52/5.74 ! [B: int,M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.74 => ( ( ord_less_int @ B @ one_one_int )
% 5.52/5.74 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.52/5.74 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_strict_decreasing_iff
% 5.52/5.74 thf(fact_1719_zero__eq__power2,axiom,
% 5.52/5.74 ! [A: rat] :
% 5.52/5.74 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.74 = zero_zero_rat )
% 5.52/5.74 = ( A = zero_zero_rat ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_eq_power2
% 5.52/5.74 thf(fact_1720_zero__eq__power2,axiom,
% 5.52/5.74 ! [A: nat] :
% 5.52/5.74 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.74 = zero_zero_nat )
% 5.52/5.74 = ( A = zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_eq_power2
% 5.52/5.74 thf(fact_1721_zero__eq__power2,axiom,
% 5.52/5.74 ! [A: real] :
% 5.52/5.74 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.74 = zero_zero_real )
% 5.52/5.74 = ( A = zero_zero_real ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_eq_power2
% 5.52/5.74 thf(fact_1722_zero__eq__power2,axiom,
% 5.52/5.74 ! [A: int] :
% 5.52/5.74 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.74 = zero_zero_int )
% 5.52/5.74 = ( A = zero_zero_int ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_eq_power2
% 5.52/5.74 thf(fact_1723_zero__eq__power2,axiom,
% 5.52/5.74 ! [A: complex] :
% 5.52/5.74 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.74 = zero_zero_complex )
% 5.52/5.74 = ( A = zero_zero_complex ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_eq_power2
% 5.52/5.74 thf(fact_1724_power__mono__iff,axiom,
% 5.52/5.74 ! [A: real,B: real,N: nat] :
% 5.52/5.74 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.74 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.52/5.74 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_mono_iff
% 5.52/5.74 thf(fact_1725_power__mono__iff,axiom,
% 5.52/5.74 ! [A: rat,B: rat,N: nat] :
% 5.52/5.74 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.52/5.74 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_mono_iff
% 5.52/5.74 thf(fact_1726_power__mono__iff,axiom,
% 5.52/5.74 ! [A: nat,B: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.52/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.52/5.74 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_mono_iff
% 5.52/5.74 thf(fact_1727_power__mono__iff,axiom,
% 5.52/5.74 ! [A: int,B: int,N: nat] :
% 5.52/5.74 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.52/5.74 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_mono_iff
% 5.52/5.74 thf(fact_1728_Suc__diff__1,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.52/5.74 = N ) ) ).
% 5.52/5.74
% 5.52/5.74 % Suc_diff_1
% 5.52/5.74 thf(fact_1729_one__div__two__eq__zero,axiom,
% 5.52/5.74 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.74 = zero_zero_nat ) ).
% 5.52/5.74
% 5.52/5.74 % one_div_two_eq_zero
% 5.52/5.74 thf(fact_1730_one__div__two__eq__zero,axiom,
% 5.52/5.74 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.74 = zero_zero_int ) ).
% 5.52/5.74
% 5.52/5.74 % one_div_two_eq_zero
% 5.52/5.74 thf(fact_1731_bits__1__div__2,axiom,
% 5.52/5.74 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.74 = zero_zero_nat ) ).
% 5.52/5.74
% 5.52/5.74 % bits_1_div_2
% 5.52/5.74 thf(fact_1732_bits__1__div__2,axiom,
% 5.52/5.74 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.74 = zero_zero_int ) ).
% 5.52/5.74
% 5.52/5.74 % bits_1_div_2
% 5.52/5.74 thf(fact_1733_power__decreasing__iff,axiom,
% 5.52/5.74 ! [B: real,M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.74 => ( ( ord_less_real @ B @ one_one_real )
% 5.52/5.74 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.52/5.74 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_decreasing_iff
% 5.52/5.74 thf(fact_1734_power__decreasing__iff,axiom,
% 5.52/5.74 ! [B: rat,M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.52/5.74 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.52/5.74 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.52/5.74 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_decreasing_iff
% 5.52/5.74 thf(fact_1735_power__decreasing__iff,axiom,
% 5.52/5.74 ! [B: nat,M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.74 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.52/5.74 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.52/5.74 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_decreasing_iff
% 5.52/5.74 thf(fact_1736_power__decreasing__iff,axiom,
% 5.52/5.74 ! [B: int,M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.74 => ( ( ord_less_int @ B @ one_one_int )
% 5.52/5.74 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.52/5.74 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_decreasing_iff
% 5.52/5.74 thf(fact_1737_power2__less__eq__zero__iff,axiom,
% 5.52/5.74 ! [A: real] :
% 5.52/5.74 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.52/5.74 = ( A = zero_zero_real ) ) ).
% 5.52/5.74
% 5.52/5.74 % power2_less_eq_zero_iff
% 5.52/5.74 thf(fact_1738_power2__less__eq__zero__iff,axiom,
% 5.52/5.74 ! [A: rat] :
% 5.52/5.74 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.52/5.74 = ( A = zero_zero_rat ) ) ).
% 5.52/5.74
% 5.52/5.74 % power2_less_eq_zero_iff
% 5.52/5.74 thf(fact_1739_power2__less__eq__zero__iff,axiom,
% 5.52/5.74 ! [A: int] :
% 5.52/5.74 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.52/5.74 = ( A = zero_zero_int ) ) ).
% 5.52/5.74
% 5.52/5.74 % power2_less_eq_zero_iff
% 5.52/5.74 thf(fact_1740_power2__eq__iff__nonneg,axiom,
% 5.52/5.74 ! [X2: real,Y2: real] :
% 5.52/5.74 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.74 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.74 => ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.74 = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.74 = ( X2 = Y2 ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power2_eq_iff_nonneg
% 5.52/5.74 thf(fact_1741_power2__eq__iff__nonneg,axiom,
% 5.52/5.74 ! [X2: rat,Y2: rat] :
% 5.52/5.74 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.52/5.74 => ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.74 = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.74 = ( X2 = Y2 ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power2_eq_iff_nonneg
% 5.52/5.74 thf(fact_1742_power2__eq__iff__nonneg,axiom,
% 5.52/5.74 ! [X2: nat,Y2: nat] :
% 5.52/5.74 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.52/5.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.52/5.74 => ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.74 = ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.74 = ( X2 = Y2 ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power2_eq_iff_nonneg
% 5.52/5.74 thf(fact_1743_power2__eq__iff__nonneg,axiom,
% 5.52/5.74 ! [X2: int,Y2: int] :
% 5.52/5.74 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.74 => ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.74 = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.74 = ( X2 = Y2 ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power2_eq_iff_nonneg
% 5.52/5.74 thf(fact_1744_zero__less__power2,axiom,
% 5.52/5.74 ! [A: real] :
% 5.52/5.74 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.74 = ( A != zero_zero_real ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_less_power2
% 5.52/5.74 thf(fact_1745_zero__less__power2,axiom,
% 5.52/5.74 ! [A: rat] :
% 5.52/5.74 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.74 = ( A != zero_zero_rat ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_less_power2
% 5.52/5.74 thf(fact_1746_zero__less__power2,axiom,
% 5.52/5.74 ! [A: int] :
% 5.52/5.74 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.74 = ( A != zero_zero_int ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_less_power2
% 5.52/5.74 thf(fact_1747_sum__power2__eq__zero__iff,axiom,
% 5.52/5.74 ! [X2: rat,Y2: rat] :
% 5.52/5.74 ( ( ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.74 = zero_zero_rat )
% 5.52/5.74 = ( ( X2 = zero_zero_rat )
% 5.52/5.74 & ( Y2 = zero_zero_rat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % sum_power2_eq_zero_iff
% 5.52/5.74 thf(fact_1748_sum__power2__eq__zero__iff,axiom,
% 5.52/5.74 ! [X2: real,Y2: real] :
% 5.52/5.74 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.74 = zero_zero_real )
% 5.52/5.74 = ( ( X2 = zero_zero_real )
% 5.52/5.74 & ( Y2 = zero_zero_real ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % sum_power2_eq_zero_iff
% 5.52/5.74 thf(fact_1749_sum__power2__eq__zero__iff,axiom,
% 5.52/5.74 ! [X2: int,Y2: int] :
% 5.52/5.74 ( ( ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.74 = zero_zero_int )
% 5.52/5.74 = ( ( X2 = zero_zero_int )
% 5.52/5.74 & ( Y2 = zero_zero_int ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % sum_power2_eq_zero_iff
% 5.52/5.74 thf(fact_1750_zero__reorient,axiom,
% 5.52/5.74 ! [X2: literal] :
% 5.52/5.74 ( ( zero_zero_literal = X2 )
% 5.52/5.74 = ( X2 = zero_zero_literal ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_reorient
% 5.52/5.74 thf(fact_1751_zero__reorient,axiom,
% 5.52/5.74 ! [X2: real] :
% 5.52/5.74 ( ( zero_zero_real = X2 )
% 5.52/5.74 = ( X2 = zero_zero_real ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_reorient
% 5.52/5.74 thf(fact_1752_zero__reorient,axiom,
% 5.52/5.74 ! [X2: rat] :
% 5.52/5.74 ( ( zero_zero_rat = X2 )
% 5.52/5.74 = ( X2 = zero_zero_rat ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_reorient
% 5.52/5.74 thf(fact_1753_zero__reorient,axiom,
% 5.52/5.74 ! [X2: nat] :
% 5.52/5.74 ( ( zero_zero_nat = X2 )
% 5.52/5.74 = ( X2 = zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_reorient
% 5.52/5.74 thf(fact_1754_zero__reorient,axiom,
% 5.52/5.74 ! [X2: int] :
% 5.52/5.74 ( ( zero_zero_int = X2 )
% 5.52/5.74 = ( X2 = zero_zero_int ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_reorient
% 5.52/5.74 thf(fact_1755_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I1_J,axiom,
% 5.52/5.74 ! [A: $o,B: $o,X2: nat] :
% 5.52/5.74 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.52/5.74 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(1)
% 5.52/5.74 thf(fact_1756_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.52/5.74 ! [X2: produc9072475918466114483BT_nat] :
% 5.52/5.74 ( ! [A3: $o,B2: $o,X4: nat] :
% 5.52/5.74 ( X2
% 5.52/5.74 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X4 ) )
% 5.52/5.74 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.52/5.74 ( X2
% 5.52/5.74 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.52/5.74 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT,X4: nat] :
% 5.52/5.74 ( X2
% 5.52/5.74 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) @ X4 ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % VEBT_internal.naive_member.cases
% 5.52/5.74 thf(fact_1757_invar__vebt_Ointros_I1_J,axiom,
% 5.52/5.74 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % invar_vebt.intros(1)
% 5.52/5.74 thf(fact_1758_power__0__left,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ( N = zero_zero_nat )
% 5.52/5.74 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.52/5.74 = one_one_rat ) )
% 5.52/5.74 & ( ( N != zero_zero_nat )
% 5.52/5.74 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.52/5.74 = zero_zero_rat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_0_left
% 5.52/5.74 thf(fact_1759_power__0__left,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ( N = zero_zero_nat )
% 5.52/5.74 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.52/5.74 = one_one_nat ) )
% 5.52/5.74 & ( ( N != zero_zero_nat )
% 5.52/5.74 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.52/5.74 = zero_zero_nat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_0_left
% 5.52/5.74 thf(fact_1760_power__0__left,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ( N = zero_zero_nat )
% 5.52/5.74 => ( ( power_power_real @ zero_zero_real @ N )
% 5.52/5.74 = one_one_real ) )
% 5.52/5.74 & ( ( N != zero_zero_nat )
% 5.52/5.74 => ( ( power_power_real @ zero_zero_real @ N )
% 5.52/5.74 = zero_zero_real ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_0_left
% 5.52/5.74 thf(fact_1761_power__0__left,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ( N = zero_zero_nat )
% 5.52/5.74 => ( ( power_power_int @ zero_zero_int @ N )
% 5.52/5.74 = one_one_int ) )
% 5.52/5.74 & ( ( N != zero_zero_nat )
% 5.52/5.74 => ( ( power_power_int @ zero_zero_int @ N )
% 5.52/5.74 = zero_zero_int ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_0_left
% 5.52/5.74 thf(fact_1762_power__0__left,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ( N = zero_zero_nat )
% 5.52/5.74 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.52/5.74 = one_one_complex ) )
% 5.52/5.74 & ( ( N != zero_zero_nat )
% 5.52/5.74 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.52/5.74 = zero_zero_complex ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_0_left
% 5.52/5.74 thf(fact_1763_zero__power,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.52/5.74 = zero_zero_rat ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_power
% 5.52/5.74 thf(fact_1764_zero__power,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.52/5.74 = zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_power
% 5.52/5.74 thf(fact_1765_zero__power,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( power_power_real @ zero_zero_real @ N )
% 5.52/5.74 = zero_zero_real ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_power
% 5.52/5.74 thf(fact_1766_zero__power,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( power_power_int @ zero_zero_int @ N )
% 5.52/5.74 = zero_zero_int ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_power
% 5.52/5.74 thf(fact_1767_zero__power,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.52/5.74 = zero_zero_complex ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_power
% 5.52/5.74 thf(fact_1768_vebt__member_Osimps_I1_J,axiom,
% 5.52/5.74 ! [A: $o,B: $o,X2: nat] :
% 5.52/5.74 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.52/5.74 = ( ( ( X2 = zero_zero_nat )
% 5.52/5.74 => A )
% 5.52/5.74 & ( ( X2 != zero_zero_nat )
% 5.52/5.74 => ( ( ( X2 = one_one_nat )
% 5.52/5.74 => B )
% 5.52/5.74 & ( X2 = one_one_nat ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % vebt_member.simps(1)
% 5.52/5.74 thf(fact_1769_VEBT_Odistinct_I1_J,axiom,
% 5.52/5.74 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.52/5.74 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.52/5.74 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.52/5.74
% 5.52/5.74 % VEBT.distinct(1)
% 5.52/5.74 thf(fact_1770_VEBT_Oexhaust,axiom,
% 5.52/5.74 ! [Y2: vEBT_VEBT] :
% 5.52/5.74 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.52/5.74 ( Y2
% 5.52/5.74 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.52/5.74 => ~ ! [X212: $o,X223: $o] :
% 5.52/5.74 ( Y2
% 5.52/5.74 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % VEBT.exhaust
% 5.52/5.74 thf(fact_1771_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.52/5.74 ! [X2: produc9072475918466114483BT_nat] :
% 5.52/5.74 ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 5.52/5.74 ( X2
% 5.52/5.74 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 5.52/5.74 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.52/5.74 ( X2
% 5.52/5.74 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % VEBT_internal.valid'.cases
% 5.52/5.74 thf(fact_1772_vebt__insert_Osimps_I1_J,axiom,
% 5.52/5.74 ! [X2: nat,A: $o,B: $o] :
% 5.52/5.74 ( ( ( X2 = zero_zero_nat )
% 5.52/5.74 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.52/5.74 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.52/5.74 & ( ( X2 != zero_zero_nat )
% 5.52/5.74 => ( ( ( X2 = one_one_nat )
% 5.52/5.74 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.52/5.74 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.52/5.74 & ( ( X2 != one_one_nat )
% 5.52/5.74 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.52/5.74 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % vebt_insert.simps(1)
% 5.52/5.74 thf(fact_1773_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.52/5.74 ! [A: $o,B: $o,X2: nat] :
% 5.52/5.74 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.52/5.74 = ( ( ( X2 = zero_zero_nat )
% 5.52/5.74 => A )
% 5.52/5.74 & ( ( X2 != zero_zero_nat )
% 5.52/5.74 => ( ( ( X2 = one_one_nat )
% 5.52/5.74 => B )
% 5.52/5.74 & ( X2 = one_one_nat ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % VEBT_internal.naive_member.simps(1)
% 5.52/5.74 thf(fact_1774_vebt__pred_Osimps_I1_J,axiom,
% 5.52/5.74 ! [Uu: $o,Uv: $o] :
% 5.52/5.74 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 5.52/5.74 = none_nat ) ).
% 5.52/5.74
% 5.52/5.74 % vebt_pred.simps(1)
% 5.52/5.74 thf(fact_1775_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I1_J,axiom,
% 5.52/5.74 ! [Uu: $o,B: $o] :
% 5.52/5.74 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.52/5.74 = one_one_nat ) ).
% 5.52/5.74
% 5.52/5.74 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(1)
% 5.52/5.74 thf(fact_1776_zero__le,axiom,
% 5.52/5.74 ! [X2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X2 ) ).
% 5.52/5.74
% 5.52/5.74 % zero_le
% 5.52/5.74 thf(fact_1777_le__numeral__extra_I3_J,axiom,
% 5.52/5.74 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.52/5.74
% 5.52/5.74 % le_numeral_extra(3)
% 5.52/5.74 thf(fact_1778_le__numeral__extra_I3_J,axiom,
% 5.52/5.74 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.52/5.74
% 5.52/5.74 % le_numeral_extra(3)
% 5.52/5.74 thf(fact_1779_le__numeral__extra_I3_J,axiom,
% 5.52/5.74 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.52/5.74
% 5.52/5.74 % le_numeral_extra(3)
% 5.52/5.74 thf(fact_1780_le__numeral__extra_I3_J,axiom,
% 5.52/5.74 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.52/5.74
% 5.52/5.74 % le_numeral_extra(3)
% 5.52/5.74 thf(fact_1781_field__lbound__gt__zero,axiom,
% 5.52/5.74 ! [D1: real,D22: real] :
% 5.52/5.74 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.52/5.74 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.52/5.74 => ? [E2: real] :
% 5.52/5.74 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.52/5.74 & ( ord_less_real @ E2 @ D1 )
% 5.52/5.74 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % field_lbound_gt_zero
% 5.52/5.74 thf(fact_1782_field__lbound__gt__zero,axiom,
% 5.52/5.74 ! [D1: rat,D22: rat] :
% 5.52/5.74 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.52/5.74 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.52/5.74 => ? [E2: rat] :
% 5.52/5.74 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.52/5.74 & ( ord_less_rat @ E2 @ D1 )
% 5.52/5.74 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % field_lbound_gt_zero
% 5.52/5.74 thf(fact_1783_zero__less__iff__neq__zero,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 = ( N != zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_less_iff_neq_zero
% 5.52/5.74 thf(fact_1784_gr__implies__not__zero,axiom,
% 5.52/5.74 ! [M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ M @ N )
% 5.52/5.74 => ( N != zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % gr_implies_not_zero
% 5.52/5.74 thf(fact_1785_not__less__zero,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.52/5.74
% 5.52/5.74 % not_less_zero
% 5.52/5.74 thf(fact_1786_gr__zeroI,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( N != zero_zero_nat )
% 5.52/5.74 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.52/5.74
% 5.52/5.74 % gr_zeroI
% 5.52/5.74 thf(fact_1787_less__numeral__extra_I3_J,axiom,
% 5.52/5.74 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.52/5.74
% 5.52/5.74 % less_numeral_extra(3)
% 5.52/5.74 thf(fact_1788_less__numeral__extra_I3_J,axiom,
% 5.52/5.74 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.52/5.74
% 5.52/5.74 % less_numeral_extra(3)
% 5.52/5.74 thf(fact_1789_less__numeral__extra_I3_J,axiom,
% 5.52/5.74 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.52/5.74
% 5.52/5.74 % less_numeral_extra(3)
% 5.52/5.74 thf(fact_1790_less__numeral__extra_I3_J,axiom,
% 5.52/5.74 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.52/5.74
% 5.52/5.74 % less_numeral_extra(3)
% 5.52/5.74 thf(fact_1791_zero__neq__numeral,axiom,
% 5.52/5.74 ! [N: num] :
% 5.52/5.74 ( zero_zero_complex
% 5.52/5.74 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_neq_numeral
% 5.52/5.74 thf(fact_1792_zero__neq__numeral,axiom,
% 5.52/5.74 ! [N: num] :
% 5.52/5.74 ( zero_zero_real
% 5.52/5.74 != ( numeral_numeral_real @ N ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_neq_numeral
% 5.52/5.74 thf(fact_1793_zero__neq__numeral,axiom,
% 5.52/5.74 ! [N: num] :
% 5.52/5.74 ( zero_zero_rat
% 5.52/5.74 != ( numeral_numeral_rat @ N ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_neq_numeral
% 5.52/5.74 thf(fact_1794_zero__neq__numeral,axiom,
% 5.52/5.74 ! [N: num] :
% 5.52/5.74 ( zero_zero_nat
% 5.52/5.74 != ( numeral_numeral_nat @ N ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_neq_numeral
% 5.52/5.74 thf(fact_1795_zero__neq__numeral,axiom,
% 5.52/5.74 ! [N: num] :
% 5.52/5.74 ( zero_zero_int
% 5.52/5.74 != ( numeral_numeral_int @ N ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_neq_numeral
% 5.52/5.74 thf(fact_1796_mult__not__zero,axiom,
% 5.52/5.74 ! [A: real,B: real] :
% 5.52/5.74 ( ( ( times_times_real @ A @ B )
% 5.52/5.74 != zero_zero_real )
% 5.52/5.74 => ( ( A != zero_zero_real )
% 5.52/5.74 & ( B != zero_zero_real ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_not_zero
% 5.52/5.74 thf(fact_1797_mult__not__zero,axiom,
% 5.52/5.74 ! [A: rat,B: rat] :
% 5.52/5.74 ( ( ( times_times_rat @ A @ B )
% 5.52/5.74 != zero_zero_rat )
% 5.52/5.74 => ( ( A != zero_zero_rat )
% 5.52/5.74 & ( B != zero_zero_rat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_not_zero
% 5.52/5.74 thf(fact_1798_mult__not__zero,axiom,
% 5.52/5.74 ! [A: nat,B: nat] :
% 5.52/5.74 ( ( ( times_times_nat @ A @ B )
% 5.52/5.74 != zero_zero_nat )
% 5.52/5.74 => ( ( A != zero_zero_nat )
% 5.52/5.74 & ( B != zero_zero_nat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_not_zero
% 5.52/5.74 thf(fact_1799_mult__not__zero,axiom,
% 5.52/5.74 ! [A: int,B: int] :
% 5.52/5.74 ( ( ( times_times_int @ A @ B )
% 5.52/5.74 != zero_zero_int )
% 5.52/5.74 => ( ( A != zero_zero_int )
% 5.52/5.74 & ( B != zero_zero_int ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_not_zero
% 5.52/5.74 thf(fact_1800_divisors__zero,axiom,
% 5.52/5.74 ! [A: real,B: real] :
% 5.52/5.74 ( ( ( times_times_real @ A @ B )
% 5.52/5.74 = zero_zero_real )
% 5.52/5.74 => ( ( A = zero_zero_real )
% 5.52/5.74 | ( B = zero_zero_real ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divisors_zero
% 5.52/5.74 thf(fact_1801_divisors__zero,axiom,
% 5.52/5.74 ! [A: rat,B: rat] :
% 5.52/5.74 ( ( ( times_times_rat @ A @ B )
% 5.52/5.74 = zero_zero_rat )
% 5.52/5.74 => ( ( A = zero_zero_rat )
% 5.52/5.74 | ( B = zero_zero_rat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divisors_zero
% 5.52/5.74 thf(fact_1802_divisors__zero,axiom,
% 5.52/5.74 ! [A: nat,B: nat] :
% 5.52/5.74 ( ( ( times_times_nat @ A @ B )
% 5.52/5.74 = zero_zero_nat )
% 5.52/5.74 => ( ( A = zero_zero_nat )
% 5.52/5.74 | ( B = zero_zero_nat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divisors_zero
% 5.52/5.74 thf(fact_1803_divisors__zero,axiom,
% 5.52/5.74 ! [A: int,B: int] :
% 5.52/5.74 ( ( ( times_times_int @ A @ B )
% 5.52/5.74 = zero_zero_int )
% 5.52/5.74 => ( ( A = zero_zero_int )
% 5.52/5.74 | ( B = zero_zero_int ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % divisors_zero
% 5.52/5.74 thf(fact_1804_no__zero__divisors,axiom,
% 5.52/5.74 ! [A: real,B: real] :
% 5.52/5.74 ( ( A != zero_zero_real )
% 5.52/5.74 => ( ( B != zero_zero_real )
% 5.52/5.74 => ( ( times_times_real @ A @ B )
% 5.52/5.74 != zero_zero_real ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % no_zero_divisors
% 5.52/5.74 thf(fact_1805_no__zero__divisors,axiom,
% 5.52/5.74 ! [A: rat,B: rat] :
% 5.52/5.74 ( ( A != zero_zero_rat )
% 5.52/5.74 => ( ( B != zero_zero_rat )
% 5.52/5.74 => ( ( times_times_rat @ A @ B )
% 5.52/5.74 != zero_zero_rat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % no_zero_divisors
% 5.52/5.74 thf(fact_1806_no__zero__divisors,axiom,
% 5.52/5.74 ! [A: nat,B: nat] :
% 5.52/5.74 ( ( A != zero_zero_nat )
% 5.52/5.74 => ( ( B != zero_zero_nat )
% 5.52/5.74 => ( ( times_times_nat @ A @ B )
% 5.52/5.74 != zero_zero_nat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % no_zero_divisors
% 5.52/5.74 thf(fact_1807_no__zero__divisors,axiom,
% 5.52/5.74 ! [A: int,B: int] :
% 5.52/5.74 ( ( A != zero_zero_int )
% 5.52/5.74 => ( ( B != zero_zero_int )
% 5.52/5.74 => ( ( times_times_int @ A @ B )
% 5.52/5.74 != zero_zero_int ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % no_zero_divisors
% 5.52/5.74 thf(fact_1808_mult__left__cancel,axiom,
% 5.52/5.74 ! [C: real,A: real,B: real] :
% 5.52/5.74 ( ( C != zero_zero_real )
% 5.52/5.74 => ( ( ( times_times_real @ C @ A )
% 5.52/5.74 = ( times_times_real @ C @ B ) )
% 5.52/5.74 = ( A = B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_left_cancel
% 5.52/5.74 thf(fact_1809_mult__left__cancel,axiom,
% 5.52/5.74 ! [C: rat,A: rat,B: rat] :
% 5.52/5.74 ( ( C != zero_zero_rat )
% 5.52/5.74 => ( ( ( times_times_rat @ C @ A )
% 5.52/5.74 = ( times_times_rat @ C @ B ) )
% 5.52/5.74 = ( A = B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_left_cancel
% 5.52/5.74 thf(fact_1810_mult__left__cancel,axiom,
% 5.52/5.74 ! [C: nat,A: nat,B: nat] :
% 5.52/5.74 ( ( C != zero_zero_nat )
% 5.52/5.74 => ( ( ( times_times_nat @ C @ A )
% 5.52/5.74 = ( times_times_nat @ C @ B ) )
% 5.52/5.74 = ( A = B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_left_cancel
% 5.52/5.74 thf(fact_1811_mult__left__cancel,axiom,
% 5.52/5.74 ! [C: int,A: int,B: int] :
% 5.52/5.74 ( ( C != zero_zero_int )
% 5.52/5.74 => ( ( ( times_times_int @ C @ A )
% 5.52/5.74 = ( times_times_int @ C @ B ) )
% 5.52/5.74 = ( A = B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_left_cancel
% 5.52/5.74 thf(fact_1812_mult__right__cancel,axiom,
% 5.52/5.74 ! [C: real,A: real,B: real] :
% 5.52/5.74 ( ( C != zero_zero_real )
% 5.52/5.74 => ( ( ( times_times_real @ A @ C )
% 5.52/5.74 = ( times_times_real @ B @ C ) )
% 5.52/5.74 = ( A = B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_right_cancel
% 5.52/5.74 thf(fact_1813_mult__right__cancel,axiom,
% 5.52/5.74 ! [C: rat,A: rat,B: rat] :
% 5.52/5.74 ( ( C != zero_zero_rat )
% 5.52/5.74 => ( ( ( times_times_rat @ A @ C )
% 5.52/5.74 = ( times_times_rat @ B @ C ) )
% 5.52/5.74 = ( A = B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_right_cancel
% 5.52/5.74 thf(fact_1814_mult__right__cancel,axiom,
% 5.52/5.74 ! [C: nat,A: nat,B: nat] :
% 5.52/5.74 ( ( C != zero_zero_nat )
% 5.52/5.74 => ( ( ( times_times_nat @ A @ C )
% 5.52/5.74 = ( times_times_nat @ B @ C ) )
% 5.52/5.74 = ( A = B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_right_cancel
% 5.52/5.74 thf(fact_1815_mult__right__cancel,axiom,
% 5.52/5.74 ! [C: int,A: int,B: int] :
% 5.52/5.74 ( ( C != zero_zero_int )
% 5.52/5.74 => ( ( ( times_times_int @ A @ C )
% 5.52/5.74 = ( times_times_int @ B @ C ) )
% 5.52/5.74 = ( A = B ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % mult_right_cancel
% 5.52/5.74 thf(fact_1816_zero__neq__one,axiom,
% 5.52/5.74 zero_zero_complex != one_one_complex ).
% 5.52/5.74
% 5.52/5.74 % zero_neq_one
% 5.52/5.74 thf(fact_1817_zero__neq__one,axiom,
% 5.52/5.74 zero_zero_real != one_one_real ).
% 5.52/5.74
% 5.52/5.74 % zero_neq_one
% 5.52/5.74 thf(fact_1818_zero__neq__one,axiom,
% 5.52/5.74 zero_zero_rat != one_one_rat ).
% 5.52/5.74
% 5.52/5.74 % zero_neq_one
% 5.52/5.74 thf(fact_1819_zero__neq__one,axiom,
% 5.52/5.74 zero_zero_nat != one_one_nat ).
% 5.52/5.74
% 5.52/5.74 % zero_neq_one
% 5.52/5.74 thf(fact_1820_zero__neq__one,axiom,
% 5.52/5.74 zero_zero_int != one_one_int ).
% 5.52/5.74
% 5.52/5.74 % zero_neq_one
% 5.52/5.74 thf(fact_1821_comm__monoid__add__class_Oadd__0,axiom,
% 5.52/5.74 ! [A: complex] :
% 5.52/5.74 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % comm_monoid_add_class.add_0
% 5.52/5.74 thf(fact_1822_comm__monoid__add__class_Oadd__0,axiom,
% 5.52/5.74 ! [A: real] :
% 5.52/5.74 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % comm_monoid_add_class.add_0
% 5.52/5.74 thf(fact_1823_comm__monoid__add__class_Oadd__0,axiom,
% 5.52/5.74 ! [A: rat] :
% 5.52/5.74 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % comm_monoid_add_class.add_0
% 5.52/5.74 thf(fact_1824_comm__monoid__add__class_Oadd__0,axiom,
% 5.52/5.74 ! [A: nat] :
% 5.52/5.74 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % comm_monoid_add_class.add_0
% 5.52/5.74 thf(fact_1825_comm__monoid__add__class_Oadd__0,axiom,
% 5.52/5.74 ! [A: int] :
% 5.52/5.74 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % comm_monoid_add_class.add_0
% 5.52/5.74 thf(fact_1826_add_Ocomm__neutral,axiom,
% 5.52/5.74 ! [A: complex] :
% 5.52/5.74 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % add.comm_neutral
% 5.52/5.74 thf(fact_1827_add_Ocomm__neutral,axiom,
% 5.52/5.74 ! [A: real] :
% 5.52/5.74 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % add.comm_neutral
% 5.52/5.74 thf(fact_1828_add_Ocomm__neutral,axiom,
% 5.52/5.74 ! [A: rat] :
% 5.52/5.74 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % add.comm_neutral
% 5.52/5.74 thf(fact_1829_add_Ocomm__neutral,axiom,
% 5.52/5.74 ! [A: nat] :
% 5.52/5.74 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % add.comm_neutral
% 5.52/5.74 thf(fact_1830_add_Ocomm__neutral,axiom,
% 5.52/5.74 ! [A: int] :
% 5.52/5.74 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % add.comm_neutral
% 5.52/5.74 thf(fact_1831_add_Ogroup__left__neutral,axiom,
% 5.52/5.74 ! [A: complex] :
% 5.52/5.74 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % add.group_left_neutral
% 5.52/5.74 thf(fact_1832_add_Ogroup__left__neutral,axiom,
% 5.52/5.74 ! [A: real] :
% 5.52/5.74 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % add.group_left_neutral
% 5.52/5.74 thf(fact_1833_add_Ogroup__left__neutral,axiom,
% 5.52/5.74 ! [A: rat] :
% 5.52/5.74 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % add.group_left_neutral
% 5.52/5.74 thf(fact_1834_add_Ogroup__left__neutral,axiom,
% 5.52/5.74 ! [A: int] :
% 5.52/5.74 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.52/5.74 = A ) ).
% 5.52/5.74
% 5.52/5.74 % add.group_left_neutral
% 5.52/5.74 thf(fact_1835_eq__iff__diff__eq__0,axiom,
% 5.52/5.74 ( ( ^ [Y5: complex,Z4: complex] : ( Y5 = Z4 ) )
% 5.52/5.74 = ( ^ [A4: complex,B3: complex] :
% 5.52/5.74 ( ( minus_minus_complex @ A4 @ B3 )
% 5.52/5.74 = zero_zero_complex ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % eq_iff_diff_eq_0
% 5.52/5.74 thf(fact_1836_eq__iff__diff__eq__0,axiom,
% 5.52/5.74 ( ( ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) )
% 5.52/5.74 = ( ^ [A4: real,B3: real] :
% 5.52/5.74 ( ( minus_minus_real @ A4 @ B3 )
% 5.52/5.74 = zero_zero_real ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % eq_iff_diff_eq_0
% 5.52/5.74 thf(fact_1837_eq__iff__diff__eq__0,axiom,
% 5.52/5.74 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.52/5.74 = ( ^ [A4: rat,B3: rat] :
% 5.52/5.74 ( ( minus_minus_rat @ A4 @ B3 )
% 5.52/5.74 = zero_zero_rat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % eq_iff_diff_eq_0
% 5.52/5.74 thf(fact_1838_eq__iff__diff__eq__0,axiom,
% 5.52/5.74 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.52/5.74 = ( ^ [A4: int,B3: int] :
% 5.52/5.74 ( ( minus_minus_int @ A4 @ B3 )
% 5.52/5.74 = zero_zero_int ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % eq_iff_diff_eq_0
% 5.52/5.74 thf(fact_1839_power__not__zero,axiom,
% 5.52/5.74 ! [A: rat,N: nat] :
% 5.52/5.74 ( ( A != zero_zero_rat )
% 5.52/5.74 => ( ( power_power_rat @ A @ N )
% 5.52/5.74 != zero_zero_rat ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_not_zero
% 5.52/5.74 thf(fact_1840_power__not__zero,axiom,
% 5.52/5.74 ! [A: nat,N: nat] :
% 5.52/5.74 ( ( A != zero_zero_nat )
% 5.52/5.74 => ( ( power_power_nat @ A @ N )
% 5.52/5.74 != zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_not_zero
% 5.52/5.74 thf(fact_1841_power__not__zero,axiom,
% 5.52/5.74 ! [A: real,N: nat] :
% 5.52/5.74 ( ( A != zero_zero_real )
% 5.52/5.74 => ( ( power_power_real @ A @ N )
% 5.52/5.74 != zero_zero_real ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_not_zero
% 5.52/5.74 thf(fact_1842_power__not__zero,axiom,
% 5.52/5.74 ! [A: int,N: nat] :
% 5.52/5.74 ( ( A != zero_zero_int )
% 5.52/5.74 => ( ( power_power_int @ A @ N )
% 5.52/5.74 != zero_zero_int ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_not_zero
% 5.52/5.74 thf(fact_1843_power__not__zero,axiom,
% 5.52/5.74 ! [A: complex,N: nat] :
% 5.52/5.74 ( ( A != zero_zero_complex )
% 5.52/5.74 => ( ( power_power_complex @ A @ N )
% 5.52/5.74 != zero_zero_complex ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_not_zero
% 5.52/5.74 thf(fact_1844_num_Osize_I4_J,axiom,
% 5.52/5.74 ( ( size_size_num @ one )
% 5.52/5.74 = zero_zero_nat ) ).
% 5.52/5.74
% 5.52/5.74 % num.size(4)
% 5.52/5.74 thf(fact_1845_nat_Odistinct_I1_J,axiom,
% 5.52/5.74 ! [X23: nat] :
% 5.52/5.74 ( zero_zero_nat
% 5.52/5.74 != ( suc @ X23 ) ) ).
% 5.52/5.74
% 5.52/5.74 % nat.distinct(1)
% 5.52/5.74 thf(fact_1846_old_Onat_Odistinct_I2_J,axiom,
% 5.52/5.74 ! [Nat2: nat] :
% 5.52/5.74 ( ( suc @ Nat2 )
% 5.52/5.74 != zero_zero_nat ) ).
% 5.52/5.74
% 5.52/5.74 % old.nat.distinct(2)
% 5.52/5.74 thf(fact_1847_old_Onat_Odistinct_I1_J,axiom,
% 5.52/5.74 ! [Nat2: nat] :
% 5.52/5.74 ( zero_zero_nat
% 5.52/5.74 != ( suc @ Nat2 ) ) ).
% 5.52/5.74
% 5.52/5.74 % old.nat.distinct(1)
% 5.52/5.74 thf(fact_1848_nat_OdiscI,axiom,
% 5.52/5.74 ! [Nat: nat,X23: nat] :
% 5.52/5.74 ( ( Nat
% 5.52/5.74 = ( suc @ X23 ) )
% 5.52/5.74 => ( Nat != zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % nat.discI
% 5.52/5.74 thf(fact_1849_old_Onat_Oexhaust,axiom,
% 5.52/5.74 ! [Y2: nat] :
% 5.52/5.74 ( ( Y2 != zero_zero_nat )
% 5.52/5.74 => ~ ! [Nat3: nat] :
% 5.52/5.74 ( Y2
% 5.52/5.74 != ( suc @ Nat3 ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % old.nat.exhaust
% 5.52/5.74 thf(fact_1850_nat__induct,axiom,
% 5.52/5.74 ! [P: nat > $o,N: nat] :
% 5.52/5.74 ( ( P @ zero_zero_nat )
% 5.52/5.74 => ( ! [N2: nat] :
% 5.52/5.74 ( ( P @ N2 )
% 5.52/5.74 => ( P @ ( suc @ N2 ) ) )
% 5.52/5.74 => ( P @ N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nat_induct
% 5.52/5.74 thf(fact_1851_diff__induct,axiom,
% 5.52/5.74 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.52/5.74 ( ! [X4: nat] : ( P @ X4 @ zero_zero_nat )
% 5.52/5.74 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 5.52/5.74 => ( ! [X4: nat,Y3: nat] :
% 5.52/5.74 ( ( P @ X4 @ Y3 )
% 5.52/5.74 => ( P @ ( suc @ X4 ) @ ( suc @ Y3 ) ) )
% 5.52/5.74 => ( P @ M @ N ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % diff_induct
% 5.52/5.74 thf(fact_1852_zero__induct,axiom,
% 5.52/5.74 ! [P: nat > $o,K: nat] :
% 5.52/5.74 ( ( P @ K )
% 5.52/5.74 => ( ! [N2: nat] :
% 5.52/5.74 ( ( P @ ( suc @ N2 ) )
% 5.52/5.74 => ( P @ N2 ) )
% 5.52/5.74 => ( P @ zero_zero_nat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % zero_induct
% 5.52/5.74 thf(fact_1853_Suc__neq__Zero,axiom,
% 5.52/5.74 ! [M: nat] :
% 5.52/5.74 ( ( suc @ M )
% 5.52/5.74 != zero_zero_nat ) ).
% 5.52/5.74
% 5.52/5.74 % Suc_neq_Zero
% 5.52/5.74 thf(fact_1854_Zero__neq__Suc,axiom,
% 5.52/5.74 ! [M: nat] :
% 5.52/5.74 ( zero_zero_nat
% 5.52/5.74 != ( suc @ M ) ) ).
% 5.52/5.74
% 5.52/5.74 % Zero_neq_Suc
% 5.52/5.74 thf(fact_1855_Zero__not__Suc,axiom,
% 5.52/5.74 ! [M: nat] :
% 5.52/5.74 ( zero_zero_nat
% 5.52/5.74 != ( suc @ M ) ) ).
% 5.52/5.74
% 5.52/5.74 % Zero_not_Suc
% 5.52/5.74 thf(fact_1856_not0__implies__Suc,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( N != zero_zero_nat )
% 5.52/5.74 => ? [M4: nat] :
% 5.52/5.74 ( N
% 5.52/5.74 = ( suc @ M4 ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % not0_implies_Suc
% 5.52/5.74 thf(fact_1857_infinite__descent0,axiom,
% 5.52/5.74 ! [P: nat > $o,N: nat] :
% 5.52/5.74 ( ( P @ zero_zero_nat )
% 5.52/5.74 => ( ! [N2: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.52/5.74 => ( ~ ( P @ N2 )
% 5.52/5.74 => ? [M2: nat] :
% 5.52/5.74 ( ( ord_less_nat @ M2 @ N2 )
% 5.52/5.74 & ~ ( P @ M2 ) ) ) )
% 5.52/5.74 => ( P @ N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % infinite_descent0
% 5.52/5.74 thf(fact_1858_gr__implies__not0,axiom,
% 5.52/5.74 ! [M: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ M @ N )
% 5.52/5.74 => ( N != zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % gr_implies_not0
% 5.52/5.74 thf(fact_1859_less__zeroE,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.52/5.74
% 5.52/5.74 % less_zeroE
% 5.52/5.74 thf(fact_1860_not__less0,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.52/5.74
% 5.52/5.74 % not_less0
% 5.52/5.74 thf(fact_1861_not__gr0,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.52/5.74 = ( N = zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % not_gr0
% 5.52/5.74 thf(fact_1862_gr0I,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( N != zero_zero_nat )
% 5.52/5.74 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.52/5.74
% 5.52/5.74 % gr0I
% 5.52/5.74 thf(fact_1863_bot__nat__0_Oextremum__strict,axiom,
% 5.52/5.74 ! [A: nat] :
% 5.52/5.74 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.52/5.74
% 5.52/5.74 % bot_nat_0.extremum_strict
% 5.52/5.74 thf(fact_1864_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I2_J,axiom,
% 5.52/5.74 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.52/5.74 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X2 )
% 5.52/5.74 = one_one_nat ) ).
% 5.52/5.74
% 5.52/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(2)
% 5.52/5.74 thf(fact_1865_less__eq__nat_Osimps_I1_J,axiom,
% 5.52/5.74 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.52/5.74
% 5.52/5.74 % less_eq_nat.simps(1)
% 5.52/5.74 thf(fact_1866_bot__nat__0_Oextremum__unique,axiom,
% 5.52/5.74 ! [A: nat] :
% 5.52/5.74 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.52/5.74 = ( A = zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % bot_nat_0.extremum_unique
% 5.52/5.74 thf(fact_1867_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.52/5.74 ! [A: nat] :
% 5.52/5.74 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.52/5.74 => ( A = zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % bot_nat_0.extremum_uniqueI
% 5.52/5.74 thf(fact_1868_le__0__eq,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.52/5.74 = ( N = zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % le_0_eq
% 5.52/5.74 thf(fact_1869_plus__nat_Oadd__0,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.52/5.74 = N ) ).
% 5.52/5.74
% 5.52/5.74 % plus_nat.add_0
% 5.52/5.74 thf(fact_1870_add__eq__self__zero,axiom,
% 5.52/5.74 ! [M: nat,N: nat] :
% 5.52/5.74 ( ( ( plus_plus_nat @ M @ N )
% 5.52/5.74 = M )
% 5.52/5.74 => ( N = zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % add_eq_self_zero
% 5.52/5.74 thf(fact_1871_minus__nat_Odiff__0,axiom,
% 5.52/5.74 ! [M: nat] :
% 5.52/5.74 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.52/5.74 = M ) ).
% 5.52/5.74
% 5.52/5.74 % minus_nat.diff_0
% 5.52/5.74 thf(fact_1872_diffs0__imp__equal,axiom,
% 5.52/5.74 ! [M: nat,N: nat] :
% 5.52/5.74 ( ( ( minus_minus_nat @ M @ N )
% 5.52/5.74 = zero_zero_nat )
% 5.52/5.74 => ( ( ( minus_minus_nat @ N @ M )
% 5.52/5.74 = zero_zero_nat )
% 5.52/5.74 => ( M = N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % diffs0_imp_equal
% 5.52/5.74 thf(fact_1873_nat__mult__eq__cancel__disj,axiom,
% 5.52/5.74 ! [K: nat,M: nat,N: nat] :
% 5.52/5.74 ( ( ( times_times_nat @ K @ M )
% 5.52/5.74 = ( times_times_nat @ K @ N ) )
% 5.52/5.74 = ( ( K = zero_zero_nat )
% 5.52/5.74 | ( M = N ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % nat_mult_eq_cancel_disj
% 5.52/5.74 thf(fact_1874_mult__0,axiom,
% 5.52/5.74 ! [N: nat] :
% 5.52/5.74 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.52/5.74 = zero_zero_nat ) ).
% 5.52/5.74
% 5.52/5.74 % mult_0
% 5.52/5.74 thf(fact_1875_power__eq__imp__eq__base,axiom,
% 5.52/5.74 ! [A: real,N: nat,B: real] :
% 5.52/5.74 ( ( ( power_power_real @ A @ N )
% 5.52/5.74 = ( power_power_real @ B @ N ) )
% 5.52/5.74 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.74 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( A = B ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_imp_eq_base
% 5.52/5.74 thf(fact_1876_power__eq__imp__eq__base,axiom,
% 5.52/5.74 ! [A: rat,N: nat,B: rat] :
% 5.52/5.74 ( ( ( power_power_rat @ A @ N )
% 5.52/5.74 = ( power_power_rat @ B @ N ) )
% 5.52/5.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( A = B ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_imp_eq_base
% 5.52/5.74 thf(fact_1877_power__eq__imp__eq__base,axiom,
% 5.52/5.74 ! [A: nat,N: nat,B: nat] :
% 5.52/5.74 ( ( ( power_power_nat @ A @ N )
% 5.52/5.74 = ( power_power_nat @ B @ N ) )
% 5.52/5.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.52/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( A = B ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_imp_eq_base
% 5.52/5.74 thf(fact_1878_power__eq__imp__eq__base,axiom,
% 5.52/5.74 ! [A: int,N: nat,B: int] :
% 5.52/5.74 ( ( ( power_power_int @ A @ N )
% 5.52/5.74 = ( power_power_int @ B @ N ) )
% 5.52/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( A = B ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_imp_eq_base
% 5.52/5.74 thf(fact_1879_power__eq__iff__eq__base,axiom,
% 5.52/5.74 ! [N: nat,A: real,B: real] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.74 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.74 => ( ( ( power_power_real @ A @ N )
% 5.52/5.74 = ( power_power_real @ B @ N ) )
% 5.52/5.74 = ( A = B ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_iff_eq_base
% 5.52/5.74 thf(fact_1880_power__eq__iff__eq__base,axiom,
% 5.52/5.74 ! [N: nat,A: rat,B: rat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.74 => ( ( ( power_power_rat @ A @ N )
% 5.52/5.74 = ( power_power_rat @ B @ N ) )
% 5.52/5.74 = ( A = B ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_iff_eq_base
% 5.52/5.74 thf(fact_1881_power__eq__iff__eq__base,axiom,
% 5.52/5.74 ! [N: nat,A: nat,B: nat] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.52/5.74 => ( ( ( power_power_nat @ A @ N )
% 5.52/5.74 = ( power_power_nat @ B @ N ) )
% 5.52/5.74 = ( A = B ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_iff_eq_base
% 5.52/5.74 thf(fact_1882_power__eq__iff__eq__base,axiom,
% 5.52/5.74 ! [N: nat,A: int,B: int] :
% 5.52/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.74 => ( ( ( power_power_int @ A @ N )
% 5.52/5.74 = ( power_power_int @ B @ N ) )
% 5.52/5.74 = ( A = B ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_eq_iff_eq_base
% 5.52/5.74 thf(fact_1883_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I1_J,axiom,
% 5.52/5.74 ! [Uu: $o,B: $o] :
% 5.52/5.74 ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.52/5.74 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(1)
% 5.52/5.74 thf(fact_1884_lambda__zero,axiom,
% 5.52/5.74 ( ( ^ [H: real] : zero_zero_real )
% 5.52/5.74 = ( times_times_real @ zero_zero_real ) ) ).
% 5.52/5.74
% 5.52/5.74 % lambda_zero
% 5.52/5.74 thf(fact_1885_lambda__zero,axiom,
% 5.52/5.74 ( ( ^ [H: rat] : zero_zero_rat )
% 5.52/5.74 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.52/5.74
% 5.52/5.74 % lambda_zero
% 5.52/5.74 thf(fact_1886_lambda__zero,axiom,
% 5.52/5.74 ( ( ^ [H: nat] : zero_zero_nat )
% 5.52/5.74 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.52/5.74
% 5.52/5.74 % lambda_zero
% 5.52/5.74 thf(fact_1887_lambda__zero,axiom,
% 5.52/5.74 ( ( ^ [H: int] : zero_zero_int )
% 5.52/5.74 = ( times_times_int @ zero_zero_int ) ) ).
% 5.52/5.74
% 5.52/5.74 % lambda_zero
% 5.52/5.74 thf(fact_1888_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I1_J,axiom,
% 5.52/5.74 ! [A: $o,B: $o] :
% 5.52/5.74 ( ( vEBT_T_m_i_n_t @ ( vEBT_Leaf @ A @ B ) )
% 5.52/5.74 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(1)
% 5.52/5.74 thf(fact_1889_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I3_J,axiom,
% 5.52/5.74 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.52/5.74 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X2 )
% 5.52/5.74 = one_one_nat ) ).
% 5.52/5.74
% 5.52/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(3)
% 5.52/5.74 thf(fact_1890_power__strict__mono,axiom,
% 5.52/5.74 ! [A: real,B: real,N: nat] :
% 5.52/5.74 ( ( ord_less_real @ A @ B )
% 5.52/5.74 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_strict_mono
% 5.52/5.74 thf(fact_1891_power__strict__mono,axiom,
% 5.52/5.74 ! [A: rat,B: rat,N: nat] :
% 5.52/5.74 ( ( ord_less_rat @ A @ B )
% 5.52/5.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_strict_mono
% 5.52/5.74 thf(fact_1892_power__strict__mono,axiom,
% 5.52/5.74 ! [A: nat,B: nat,N: nat] :
% 5.52/5.74 ( ( ord_less_nat @ A @ B )
% 5.52/5.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_strict_mono
% 5.52/5.74 thf(fact_1893_power__strict__mono,axiom,
% 5.52/5.74 ! [A: int,B: int,N: nat] :
% 5.52/5.74 ( ( ord_less_int @ A @ B )
% 5.52/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.74 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % power_strict_mono
% 5.52/5.74 thf(fact_1894_vebt__succ_Osimps_I1_J,axiom,
% 5.52/5.74 ! [B: $o,Uu: $o] :
% 5.52/5.74 ( ( B
% 5.52/5.74 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.52/5.74 = ( some_nat @ one_one_nat ) ) )
% 5.52/5.74 & ( ~ B
% 5.52/5.74 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.52/5.74 = none_nat ) ) ) ).
% 5.52/5.74
% 5.52/5.74 % vebt_succ.simps(1)
% 5.52/5.74 thf(fact_1895_vebt__maxt_Osimps_I1_J,axiom,
% 5.52/5.74 ! [B: $o,A: $o] :
% 5.52/5.74 ( ( B
% 5.52/5.74 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.52/5.74 = ( some_nat @ one_one_nat ) ) )
% 5.52/5.74 & ( ~ B
% 5.52/5.75 => ( ( A
% 5.52/5.75 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.52/5.75 = ( some_nat @ zero_zero_nat ) ) )
% 5.52/5.75 & ( ~ A
% 5.52/5.75 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.52/5.75 = none_nat ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % vebt_maxt.simps(1)
% 5.52/5.75 thf(fact_1896_vebt__pred_Osimps_I2_J,axiom,
% 5.52/5.75 ! [A: $o,Uw: $o] :
% 5.52/5.75 ( ( A
% 5.52/5.75 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.52/5.75 = ( some_nat @ zero_zero_nat ) ) )
% 5.52/5.75 & ( ~ A
% 5.52/5.75 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.52/5.75 = none_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % vebt_pred.simps(2)
% 5.52/5.75 thf(fact_1897_vebt__mint_Osimps_I1_J,axiom,
% 5.52/5.75 ! [A: $o,B: $o] :
% 5.52/5.75 ( ( A
% 5.52/5.75 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.52/5.75 = ( some_nat @ zero_zero_nat ) ) )
% 5.52/5.75 & ( ~ A
% 5.52/5.75 => ( ( B
% 5.52/5.75 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.52/5.75 = ( some_nat @ one_one_nat ) ) )
% 5.52/5.75 & ( ~ B
% 5.52/5.75 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.52/5.75 = none_nat ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % vebt_mint.simps(1)
% 5.52/5.75 thf(fact_1898_zero__le__numeral,axiom,
% 5.52/5.75 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_numeral
% 5.52/5.75 thf(fact_1899_zero__le__numeral,axiom,
% 5.52/5.75 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_numeral
% 5.52/5.75 thf(fact_1900_zero__le__numeral,axiom,
% 5.52/5.75 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_numeral
% 5.52/5.75 thf(fact_1901_zero__le__numeral,axiom,
% 5.52/5.75 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_numeral
% 5.52/5.75 thf(fact_1902_not__numeral__le__zero,axiom,
% 5.52/5.75 ! [N: num] :
% 5.52/5.75 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.52/5.75
% 5.52/5.75 % not_numeral_le_zero
% 5.52/5.75 thf(fact_1903_not__numeral__le__zero,axiom,
% 5.52/5.75 ! [N: num] :
% 5.52/5.75 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.52/5.75
% 5.52/5.75 % not_numeral_le_zero
% 5.52/5.75 thf(fact_1904_not__numeral__le__zero,axiom,
% 5.52/5.75 ! [N: num] :
% 5.52/5.75 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.52/5.75
% 5.52/5.75 % not_numeral_le_zero
% 5.52/5.75 thf(fact_1905_not__numeral__le__zero,axiom,
% 5.52/5.75 ! [N: num] :
% 5.52/5.75 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.52/5.75
% 5.52/5.75 % not_numeral_le_zero
% 5.52/5.75 thf(fact_1906_mult__mono,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real,D2: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_real @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_mono
% 5.52/5.75 thf(fact_1907_mult__mono,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_mono
% 5.52/5.75 thf(fact_1908_mult__mono,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_mono
% 5.52/5.75 thf(fact_1909_mult__mono,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int,D2: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_int @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_mono
% 5.52/5.75 thf(fact_1910_mult__mono_H,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real,D2: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_real @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_mono'
% 5.52/5.75 thf(fact_1911_mult__mono_H,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_mono'
% 5.52/5.75 thf(fact_1912_mult__mono_H,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_mono'
% 5.52/5.75 thf(fact_1913_mult__mono_H,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int,D2: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_int @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_mono'
% 5.52/5.75 thf(fact_1914_zero__le__square,axiom,
% 5.52/5.75 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_square
% 5.52/5.75 thf(fact_1915_zero__le__square,axiom,
% 5.52/5.75 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_square
% 5.52/5.75 thf(fact_1916_zero__le__square,axiom,
% 5.52/5.75 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_square
% 5.52/5.75 thf(fact_1917_split__mult__pos__le,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.52/5.75 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.75 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.52/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % split_mult_pos_le
% 5.52/5.75 thf(fact_1918_split__mult__pos__le,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.52/5.75 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.75 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.52/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % split_mult_pos_le
% 5.52/5.75 thf(fact_1919_split__mult__pos__le,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.52/5.75 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.75 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.52/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % split_mult_pos_le
% 5.52/5.75 thf(fact_1920_mult__left__mono__neg,axiom,
% 5.52/5.75 ! [B: real,A: real,C: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ B @ A )
% 5.52/5.75 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_mono_neg
% 5.52/5.75 thf(fact_1921_mult__left__mono__neg,axiom,
% 5.52/5.75 ! [B: rat,A: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ B @ A )
% 5.52/5.75 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_mono_neg
% 5.52/5.75 thf(fact_1922_mult__left__mono__neg,axiom,
% 5.52/5.75 ! [B: int,A: int,C: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ B @ A )
% 5.52/5.75 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.52/5.75 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_mono_neg
% 5.52/5.75 thf(fact_1923_mult__nonpos__nonpos,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.52/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonpos_nonpos
% 5.52/5.75 thf(fact_1924_mult__nonpos__nonpos,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonpos_nonpos
% 5.52/5.75 thf(fact_1925_mult__nonpos__nonpos,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.52/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonpos_nonpos
% 5.52/5.75 thf(fact_1926_mult__left__mono,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_mono
% 5.52/5.75 thf(fact_1927_mult__left__mono,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_mono
% 5.52/5.75 thf(fact_1928_mult__left__mono,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_mono
% 5.52/5.75 thf(fact_1929_mult__left__mono,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_mono
% 5.52/5.75 thf(fact_1930_mult__right__mono__neg,axiom,
% 5.52/5.75 ! [B: real,A: real,C: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ B @ A )
% 5.52/5.75 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_mono_neg
% 5.52/5.75 thf(fact_1931_mult__right__mono__neg,axiom,
% 5.52/5.75 ! [B: rat,A: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ B @ A )
% 5.52/5.75 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_mono_neg
% 5.52/5.75 thf(fact_1932_mult__right__mono__neg,axiom,
% 5.52/5.75 ! [B: int,A: int,C: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ B @ A )
% 5.52/5.75 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.52/5.75 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_mono_neg
% 5.52/5.75 thf(fact_1933_mult__right__mono,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_mono
% 5.52/5.75 thf(fact_1934_mult__right__mono,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_mono
% 5.52/5.75 thf(fact_1935_mult__right__mono,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_mono
% 5.52/5.75 thf(fact_1936_mult__right__mono,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_mono
% 5.52/5.75 thf(fact_1937_mult__le__0__iff,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.52/5.75 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.52/5.75 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.75 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_0_iff
% 5.52/5.75 thf(fact_1938_mult__le__0__iff,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.52/5.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.52/5.75 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.75 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_0_iff
% 5.52/5.75 thf(fact_1939_mult__le__0__iff,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.52/5.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.52/5.75 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.75 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_0_iff
% 5.52/5.75 thf(fact_1940_split__mult__neg__le,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.52/5.75 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.75 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.52/5.75 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.52/5.75
% 5.52/5.75 % split_mult_neg_le
% 5.52/5.75 thf(fact_1941_split__mult__neg__le,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.52/5.75 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.75 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.52/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.52/5.75
% 5.52/5.75 % split_mult_neg_le
% 5.52/5.75 thf(fact_1942_split__mult__neg__le,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.52/5.75 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.52/5.75 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.52/5.75 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.52/5.75
% 5.52/5.75 % split_mult_neg_le
% 5.52/5.75 thf(fact_1943_split__mult__neg__le,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.52/5.75 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.75 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.52/5.75 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.52/5.75
% 5.52/5.75 % split_mult_neg_le
% 5.52/5.75 thf(fact_1944_mult__nonneg__nonneg,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonneg_nonneg
% 5.52/5.75 thf(fact_1945_mult__nonneg__nonneg,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonneg_nonneg
% 5.52/5.75 thf(fact_1946_mult__nonneg__nonneg,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.52/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonneg_nonneg
% 5.52/5.75 thf(fact_1947_mult__nonneg__nonneg,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonneg_nonneg
% 5.52/5.75 thf(fact_1948_mult__nonneg__nonpos,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.52/5.75 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonneg_nonpos
% 5.52/5.75 thf(fact_1949_mult__nonneg__nonpos,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonneg_nonpos
% 5.52/5.75 thf(fact_1950_mult__nonneg__nonpos,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.52/5.75 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonneg_nonpos
% 5.52/5.75 thf(fact_1951_mult__nonneg__nonpos,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.52/5.75 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonneg_nonpos
% 5.52/5.75 thf(fact_1952_mult__nonpos__nonneg,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.75 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonpos_nonneg
% 5.52/5.75 thf(fact_1953_mult__nonpos__nonneg,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonpos_nonneg
% 5.52/5.75 thf(fact_1954_mult__nonpos__nonneg,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.52/5.75 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonpos_nonneg
% 5.52/5.75 thf(fact_1955_mult__nonpos__nonneg,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.75 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonpos_nonneg
% 5.52/5.75 thf(fact_1956_mult__nonneg__nonpos2,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.52/5.75 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonneg_nonpos2
% 5.52/5.75 thf(fact_1957_mult__nonneg__nonpos2,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonneg_nonpos2
% 5.52/5.75 thf(fact_1958_mult__nonneg__nonpos2,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.52/5.75 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonneg_nonpos2
% 5.52/5.75 thf(fact_1959_mult__nonneg__nonpos2,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.52/5.75 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_nonneg_nonpos2
% 5.52/5.75 thf(fact_1960_zero__le__mult__iff,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.52/5.75 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.52/5.75 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.75 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_mult_iff
% 5.52/5.75 thf(fact_1961_zero__le__mult__iff,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.52/5.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.52/5.75 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.75 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_mult_iff
% 5.52/5.75 thf(fact_1962_zero__le__mult__iff,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.52/5.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.52/5.75 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.75 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_mult_iff
% 5.52/5.75 thf(fact_1963_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.52/5.75 thf(fact_1964_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.52/5.75 thf(fact_1965_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.52/5.75 thf(fact_1966_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.52/5.75 thf(fact_1967_not__numeral__less__zero,axiom,
% 5.52/5.75 ! [N: num] :
% 5.52/5.75 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.52/5.75
% 5.52/5.75 % not_numeral_less_zero
% 5.52/5.75 thf(fact_1968_not__numeral__less__zero,axiom,
% 5.52/5.75 ! [N: num] :
% 5.52/5.75 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.52/5.75
% 5.52/5.75 % not_numeral_less_zero
% 5.52/5.75 thf(fact_1969_not__numeral__less__zero,axiom,
% 5.52/5.75 ! [N: num] :
% 5.52/5.75 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.52/5.75
% 5.52/5.75 % not_numeral_less_zero
% 5.52/5.75 thf(fact_1970_not__numeral__less__zero,axiom,
% 5.52/5.75 ! [N: num] :
% 5.52/5.75 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.52/5.75
% 5.52/5.75 % not_numeral_less_zero
% 5.52/5.75 thf(fact_1971_zero__less__numeral,axiom,
% 5.52/5.75 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_numeral
% 5.52/5.75 thf(fact_1972_zero__less__numeral,axiom,
% 5.52/5.75 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_numeral
% 5.52/5.75 thf(fact_1973_zero__less__numeral,axiom,
% 5.52/5.75 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_numeral
% 5.52/5.75 thf(fact_1974_zero__less__numeral,axiom,
% 5.52/5.75 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_numeral
% 5.52/5.75 thf(fact_1975_zero__less__one__class_Ozero__le__one,axiom,
% 5.52/5.75 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.52/5.75
% 5.52/5.75 % zero_less_one_class.zero_le_one
% 5.52/5.75 thf(fact_1976_zero__less__one__class_Ozero__le__one,axiom,
% 5.52/5.75 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.52/5.75
% 5.52/5.75 % zero_less_one_class.zero_le_one
% 5.52/5.75 thf(fact_1977_zero__less__one__class_Ozero__le__one,axiom,
% 5.52/5.75 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.52/5.75
% 5.52/5.75 % zero_less_one_class.zero_le_one
% 5.52/5.75 thf(fact_1978_zero__less__one__class_Ozero__le__one,axiom,
% 5.52/5.75 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.52/5.75
% 5.52/5.75 % zero_less_one_class.zero_le_one
% 5.52/5.75 thf(fact_1979_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.52/5.75 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.52/5.75
% 5.52/5.75 % linordered_nonzero_semiring_class.zero_le_one
% 5.52/5.75 thf(fact_1980_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.52/5.75 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.52/5.75
% 5.52/5.75 % linordered_nonzero_semiring_class.zero_le_one
% 5.52/5.75 thf(fact_1981_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.52/5.75 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.52/5.75
% 5.52/5.75 % linordered_nonzero_semiring_class.zero_le_one
% 5.52/5.75 thf(fact_1982_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.52/5.75 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.52/5.75
% 5.52/5.75 % linordered_nonzero_semiring_class.zero_le_one
% 5.52/5.75 thf(fact_1983_not__one__le__zero,axiom,
% 5.52/5.75 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.52/5.75
% 5.52/5.75 % not_one_le_zero
% 5.52/5.75 thf(fact_1984_not__one__le__zero,axiom,
% 5.52/5.75 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.52/5.75
% 5.52/5.75 % not_one_le_zero
% 5.52/5.75 thf(fact_1985_not__one__le__zero,axiom,
% 5.52/5.75 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.52/5.75
% 5.52/5.75 % not_one_le_zero
% 5.52/5.75 thf(fact_1986_not__one__le__zero,axiom,
% 5.52/5.75 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.52/5.75
% 5.52/5.75 % not_one_le_zero
% 5.52/5.75 thf(fact_1987_add__decreasing,axiom,
% 5.52/5.75 ! [A: real,C: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_eq_real @ C @ B )
% 5.52/5.75 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_decreasing
% 5.52/5.75 thf(fact_1988_add__decreasing,axiom,
% 5.52/5.75 ! [A: rat,C: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_eq_rat @ C @ B )
% 5.52/5.75 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_decreasing
% 5.52/5.75 thf(fact_1989_add__decreasing,axiom,
% 5.52/5.75 ! [A: nat,C: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.52/5.75 => ( ( ord_less_eq_nat @ C @ B )
% 5.52/5.75 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_decreasing
% 5.52/5.75 thf(fact_1990_add__decreasing,axiom,
% 5.52/5.75 ! [A: int,C: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_eq_int @ C @ B )
% 5.52/5.75 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_decreasing
% 5.52/5.75 thf(fact_1991_add__increasing,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_eq_real @ B @ C )
% 5.52/5.75 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_increasing
% 5.52/5.75 thf(fact_1992_add__increasing,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_eq_rat @ B @ C )
% 5.52/5.75 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_increasing
% 5.52/5.75 thf(fact_1993_add__increasing,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_eq_nat @ B @ C )
% 5.52/5.75 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_increasing
% 5.52/5.75 thf(fact_1994_add__increasing,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_eq_int @ B @ C )
% 5.52/5.75 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_increasing
% 5.52/5.75 thf(fact_1995_add__decreasing2,axiom,
% 5.52/5.75 ! [C: real,A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_eq_real @ A @ B )
% 5.52/5.75 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_decreasing2
% 5.52/5.75 thf(fact_1996_add__decreasing2,axiom,
% 5.52/5.75 ! [C: rat,A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.75 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_decreasing2
% 5.52/5.75 thf(fact_1997_add__decreasing2,axiom,
% 5.52/5.75 ! [C: nat,A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.52/5.75 => ( ( ord_less_eq_nat @ A @ B )
% 5.52/5.75 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_decreasing2
% 5.52/5.75 thf(fact_1998_add__decreasing2,axiom,
% 5.52/5.75 ! [C: int,A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_eq_int @ A @ B )
% 5.52/5.75 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_decreasing2
% 5.52/5.75 thf(fact_1999_add__increasing2,axiom,
% 5.52/5.75 ! [C: real,B: real,A: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ( ord_less_eq_real @ B @ A )
% 5.52/5.75 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_increasing2
% 5.52/5.75 thf(fact_2000_add__increasing2,axiom,
% 5.52/5.75 ! [C: rat,B: rat,A: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ( ord_less_eq_rat @ B @ A )
% 5.52/5.75 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_increasing2
% 5.52/5.75 thf(fact_2001_add__increasing2,axiom,
% 5.52/5.75 ! [C: nat,B: nat,A: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ( ord_less_eq_nat @ B @ A )
% 5.52/5.75 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_increasing2
% 5.52/5.75 thf(fact_2002_add__increasing2,axiom,
% 5.52/5.75 ! [C: int,B: int,A: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ( ord_less_eq_int @ B @ A )
% 5.52/5.75 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_increasing2
% 5.52/5.75 thf(fact_2003_add__nonneg__nonneg,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonneg_nonneg
% 5.52/5.75 thf(fact_2004_add__nonneg__nonneg,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonneg_nonneg
% 5.52/5.75 thf(fact_2005_add__nonneg__nonneg,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.52/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonneg_nonneg
% 5.52/5.75 thf(fact_2006_add__nonneg__nonneg,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonneg_nonneg
% 5.52/5.75 thf(fact_2007_add__nonpos__nonpos,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.52/5.75 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonpos_nonpos
% 5.52/5.75 thf(fact_2008_add__nonpos__nonpos,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonpos_nonpos
% 5.52/5.75 thf(fact_2009_add__nonpos__nonpos,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.52/5.75 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.52/5.75 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonpos_nonpos
% 5.52/5.75 thf(fact_2010_add__nonpos__nonpos,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.52/5.75 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonpos_nonpos
% 5.52/5.75 thf(fact_2011_add__nonneg__eq__0__iff,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.75 => ( ( ( plus_plus_real @ X2 @ Y2 )
% 5.52/5.75 = zero_zero_real )
% 5.52/5.75 = ( ( X2 = zero_zero_real )
% 5.52/5.75 & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonneg_eq_0_iff
% 5.52/5.75 thf(fact_2012_add__nonneg__eq__0__iff,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.52/5.75 => ( ( ( plus_plus_rat @ X2 @ Y2 )
% 5.52/5.75 = zero_zero_rat )
% 5.52/5.75 = ( ( X2 = zero_zero_rat )
% 5.52/5.75 & ( Y2 = zero_zero_rat ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonneg_eq_0_iff
% 5.52/5.75 thf(fact_2013_add__nonneg__eq__0__iff,axiom,
% 5.52/5.75 ! [X2: nat,Y2: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.52/5.75 => ( ( ( plus_plus_nat @ X2 @ Y2 )
% 5.52/5.75 = zero_zero_nat )
% 5.52/5.75 = ( ( X2 = zero_zero_nat )
% 5.52/5.75 & ( Y2 = zero_zero_nat ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonneg_eq_0_iff
% 5.52/5.75 thf(fact_2014_add__nonneg__eq__0__iff,axiom,
% 5.52/5.75 ! [X2: int,Y2: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.75 => ( ( ( plus_plus_int @ X2 @ Y2 )
% 5.52/5.75 = zero_zero_int )
% 5.52/5.75 = ( ( X2 = zero_zero_int )
% 5.52/5.75 & ( Y2 = zero_zero_int ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonneg_eq_0_iff
% 5.52/5.75 thf(fact_2015_add__nonpos__eq__0__iff,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.52/5.75 => ( ( ( plus_plus_real @ X2 @ Y2 )
% 5.52/5.75 = zero_zero_real )
% 5.52/5.75 = ( ( X2 = zero_zero_real )
% 5.52/5.75 & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonpos_eq_0_iff
% 5.52/5.75 thf(fact_2016_add__nonpos__eq__0__iff,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 5.52/5.75 => ( ( ( plus_plus_rat @ X2 @ Y2 )
% 5.52/5.75 = zero_zero_rat )
% 5.52/5.75 = ( ( X2 = zero_zero_rat )
% 5.52/5.75 & ( Y2 = zero_zero_rat ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonpos_eq_0_iff
% 5.52/5.75 thf(fact_2017_add__nonpos__eq__0__iff,axiom,
% 5.52/5.75 ! [X2: nat,Y2: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ X2 @ zero_zero_nat )
% 5.52/5.75 => ( ( ord_less_eq_nat @ Y2 @ zero_zero_nat )
% 5.52/5.75 => ( ( ( plus_plus_nat @ X2 @ Y2 )
% 5.52/5.75 = zero_zero_nat )
% 5.52/5.75 = ( ( X2 = zero_zero_nat )
% 5.52/5.75 & ( Y2 = zero_zero_nat ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonpos_eq_0_iff
% 5.52/5.75 thf(fact_2018_add__nonpos__eq__0__iff,axiom,
% 5.52/5.75 ! [X2: int,Y2: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_eq_int @ Y2 @ zero_zero_int )
% 5.52/5.75 => ( ( ( plus_plus_int @ X2 @ Y2 )
% 5.52/5.75 = zero_zero_int )
% 5.52/5.75 = ( ( X2 = zero_zero_int )
% 5.52/5.75 & ( Y2 = zero_zero_int ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonpos_eq_0_iff
% 5.52/5.75 thf(fact_2019_mult__neg__neg,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_neg_neg
% 5.52/5.75 thf(fact_2020_mult__neg__neg,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_neg_neg
% 5.52/5.75 thf(fact_2021_mult__neg__neg,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ A @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.52/5.75 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_neg_neg
% 5.52/5.75 thf(fact_2022_not__square__less__zero,axiom,
% 5.52/5.75 ! [A: real] :
% 5.52/5.75 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.52/5.75
% 5.52/5.75 % not_square_less_zero
% 5.52/5.75 thf(fact_2023_not__square__less__zero,axiom,
% 5.52/5.75 ! [A: rat] :
% 5.52/5.75 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.52/5.75
% 5.52/5.75 % not_square_less_zero
% 5.52/5.75 thf(fact_2024_not__square__less__zero,axiom,
% 5.52/5.75 ! [A: int] :
% 5.52/5.75 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.52/5.75
% 5.52/5.75 % not_square_less_zero
% 5.52/5.75 thf(fact_2025_mult__less__0__iff,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.52/5.75 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.52/5.75 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.75 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_0_iff
% 5.52/5.75 thf(fact_2026_mult__less__0__iff,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.52/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.52/5.75 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.75 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_0_iff
% 5.52/5.75 thf(fact_2027_mult__less__0__iff,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.52/5.75 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.52/5.75 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.52/5.75 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_0_iff
% 5.52/5.75 thf(fact_2028_mult__neg__pos,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.75 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_neg_pos
% 5.52/5.75 thf(fact_2029_mult__neg__pos,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.52/5.75 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_neg_pos
% 5.52/5.75 thf(fact_2030_mult__neg__pos,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.75 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_neg_pos
% 5.52/5.75 thf(fact_2031_mult__neg__pos,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ A @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.75 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_neg_pos
% 5.52/5.75 thf(fact_2032_mult__pos__neg,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_pos_neg
% 5.52/5.75 thf(fact_2033_mult__pos__neg,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_pos_neg
% 5.52/5.75 thf(fact_2034_mult__pos__neg,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.52/5.75 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_pos_neg
% 5.52/5.75 thf(fact_2035_mult__pos__neg,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.52/5.75 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_pos_neg
% 5.52/5.75 thf(fact_2036_mult__pos__pos,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.75 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_pos_pos
% 5.52/5.75 thf(fact_2037_mult__pos__pos,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.52/5.75 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_pos_pos
% 5.52/5.75 thf(fact_2038_mult__pos__pos,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_pos_pos
% 5.52/5.75 thf(fact_2039_mult__pos__pos,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.75 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_pos_pos
% 5.52/5.75 thf(fact_2040_mult__pos__neg2,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_pos_neg2
% 5.52/5.75 thf(fact_2041_mult__pos__neg2,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_pos_neg2
% 5.52/5.75 thf(fact_2042_mult__pos__neg2,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.52/5.75 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_pos_neg2
% 5.52/5.75 thf(fact_2043_mult__pos__neg2,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.52/5.75 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_pos_neg2
% 5.52/5.75 thf(fact_2044_zero__less__mult__iff,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.52/5.75 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.52/5.75 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.75 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_mult_iff
% 5.52/5.75 thf(fact_2045_zero__less__mult__iff,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.52/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.52/5.75 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.75 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_mult_iff
% 5.52/5.75 thf(fact_2046_zero__less__mult__iff,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.52/5.75 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.52/5.75 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.52/5.75 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_mult_iff
% 5.52/5.75 thf(fact_2047_zero__less__mult__pos,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_mult_pos
% 5.52/5.75 thf(fact_2048_zero__less__mult__pos,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_mult_pos
% 5.52/5.75 thf(fact_2049_zero__less__mult__pos,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_mult_pos
% 5.52/5.75 thf(fact_2050_zero__less__mult__pos,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_mult_pos
% 5.52/5.75 thf(fact_2051_zero__less__mult__pos2,axiom,
% 5.52/5.75 ! [B: real,A: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_mult_pos2
% 5.52/5.75 thf(fact_2052_zero__less__mult__pos2,axiom,
% 5.52/5.75 ! [B: rat,A: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_mult_pos2
% 5.52/5.75 thf(fact_2053_zero__less__mult__pos2,axiom,
% 5.52/5.75 ! [B: nat,A: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_mult_pos2
% 5.52/5.75 thf(fact_2054_zero__less__mult__pos2,axiom,
% 5.52/5.75 ! [B: int,A: int] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_mult_pos2
% 5.52/5.75 thf(fact_2055_mult__less__cancel__left__neg,axiom,
% 5.52/5.75 ! [C: real,A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.52/5.75 = ( ord_less_real @ B @ A ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_left_neg
% 5.52/5.75 thf(fact_2056_mult__less__cancel__left__neg,axiom,
% 5.52/5.75 ! [C: rat,A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.52/5.75 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_left_neg
% 5.52/5.75 thf(fact_2057_mult__less__cancel__left__neg,axiom,
% 5.52/5.75 ! [C: int,A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ C @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.52/5.75 = ( ord_less_int @ B @ A ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_left_neg
% 5.52/5.75 thf(fact_2058_mult__less__cancel__left__pos,axiom,
% 5.52/5.75 ! [C: real,A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.52/5.75 = ( ord_less_real @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_left_pos
% 5.52/5.75 thf(fact_2059_mult__less__cancel__left__pos,axiom,
% 5.52/5.75 ! [C: rat,A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.52/5.75 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_left_pos
% 5.52/5.75 thf(fact_2060_mult__less__cancel__left__pos,axiom,
% 5.52/5.75 ! [C: int,A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.52/5.75 = ( ord_less_int @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_left_pos
% 5.52/5.75 thf(fact_2061_mult__strict__left__mono__neg,axiom,
% 5.52/5.75 ! [B: real,A: real,C: real] :
% 5.52/5.75 ( ( ord_less_real @ B @ A )
% 5.52/5.75 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_left_mono_neg
% 5.52/5.75 thf(fact_2062_mult__strict__left__mono__neg,axiom,
% 5.52/5.75 ! [B: rat,A: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_rat @ B @ A )
% 5.52/5.75 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_left_mono_neg
% 5.52/5.75 thf(fact_2063_mult__strict__left__mono__neg,axiom,
% 5.52/5.75 ! [B: int,A: int,C: int] :
% 5.52/5.75 ( ( ord_less_int @ B @ A )
% 5.52/5.75 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.52/5.75 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_left_mono_neg
% 5.52/5.75 thf(fact_2064_mult__strict__left__mono,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_left_mono
% 5.52/5.75 thf(fact_2065_mult__strict__left__mono,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_left_mono
% 5.52/5.75 thf(fact_2066_mult__strict__left__mono,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat] :
% 5.52/5.75 ( ( ord_less_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_left_mono
% 5.52/5.75 thf(fact_2067_mult__strict__left__mono,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int] :
% 5.52/5.75 ( ( ord_less_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_left_mono
% 5.52/5.75 thf(fact_2068_mult__less__cancel__left__disj,axiom,
% 5.52/5.75 ! [C: real,A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.52/5.75 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 & ( ord_less_real @ A @ B ) )
% 5.52/5.75 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.75 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_left_disj
% 5.52/5.75 thf(fact_2069_mult__less__cancel__left__disj,axiom,
% 5.52/5.75 ! [C: rat,A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.52/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 & ( ord_less_rat @ A @ B ) )
% 5.52/5.75 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.75 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_left_disj
% 5.52/5.75 thf(fact_2070_mult__less__cancel__left__disj,axiom,
% 5.52/5.75 ! [C: int,A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.52/5.75 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.75 & ( ord_less_int @ A @ B ) )
% 5.52/5.75 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.52/5.75 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_left_disj
% 5.52/5.75 thf(fact_2071_mult__strict__right__mono__neg,axiom,
% 5.52/5.75 ! [B: real,A: real,C: real] :
% 5.52/5.75 ( ( ord_less_real @ B @ A )
% 5.52/5.75 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_right_mono_neg
% 5.52/5.75 thf(fact_2072_mult__strict__right__mono__neg,axiom,
% 5.52/5.75 ! [B: rat,A: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_rat @ B @ A )
% 5.52/5.75 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_right_mono_neg
% 5.52/5.75 thf(fact_2073_mult__strict__right__mono__neg,axiom,
% 5.52/5.75 ! [B: int,A: int,C: int] :
% 5.52/5.75 ( ( ord_less_int @ B @ A )
% 5.52/5.75 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.52/5.75 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_right_mono_neg
% 5.52/5.75 thf(fact_2074_mult__strict__right__mono,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_right_mono
% 5.52/5.75 thf(fact_2075_mult__strict__right__mono,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_right_mono
% 5.52/5.75 thf(fact_2076_mult__strict__right__mono,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat] :
% 5.52/5.75 ( ( ord_less_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_right_mono
% 5.52/5.75 thf(fact_2077_mult__strict__right__mono,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int] :
% 5.52/5.75 ( ( ord_less_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_right_mono
% 5.52/5.75 thf(fact_2078_mult__less__cancel__right__disj,axiom,
% 5.52/5.75 ! [A: real,C: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.52/5.75 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 & ( ord_less_real @ A @ B ) )
% 5.52/5.75 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.75 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_right_disj
% 5.52/5.75 thf(fact_2079_mult__less__cancel__right__disj,axiom,
% 5.52/5.75 ! [A: rat,C: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.52/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 & ( ord_less_rat @ A @ B ) )
% 5.52/5.75 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.75 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_right_disj
% 5.52/5.75 thf(fact_2080_mult__less__cancel__right__disj,axiom,
% 5.52/5.75 ! [A: int,C: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.52/5.75 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.75 & ( ord_less_int @ A @ B ) )
% 5.52/5.75 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.52/5.75 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_right_disj
% 5.52/5.75 thf(fact_2081_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.52/5.75 thf(fact_2082_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.52/5.75 thf(fact_2083_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat] :
% 5.52/5.75 ( ( ord_less_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.52/5.75 thf(fact_2084_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int] :
% 5.52/5.75 ( ( ord_less_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.52/5.75 thf(fact_2085_less__numeral__extra_I1_J,axiom,
% 5.52/5.75 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.52/5.75
% 5.52/5.75 % less_numeral_extra(1)
% 5.52/5.75 thf(fact_2086_less__numeral__extra_I1_J,axiom,
% 5.52/5.75 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.52/5.75
% 5.52/5.75 % less_numeral_extra(1)
% 5.52/5.75 thf(fact_2087_less__numeral__extra_I1_J,axiom,
% 5.52/5.75 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.52/5.75
% 5.52/5.75 % less_numeral_extra(1)
% 5.52/5.75 thf(fact_2088_less__numeral__extra_I1_J,axiom,
% 5.52/5.75 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.52/5.75
% 5.52/5.75 % less_numeral_extra(1)
% 5.52/5.75 thf(fact_2089_zero__less__one,axiom,
% 5.52/5.75 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.52/5.75
% 5.52/5.75 % zero_less_one
% 5.52/5.75 thf(fact_2090_zero__less__one,axiom,
% 5.52/5.75 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.52/5.75
% 5.52/5.75 % zero_less_one
% 5.52/5.75 thf(fact_2091_zero__less__one,axiom,
% 5.52/5.75 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.52/5.75
% 5.52/5.75 % zero_less_one
% 5.52/5.75 thf(fact_2092_zero__less__one,axiom,
% 5.52/5.75 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.52/5.75
% 5.52/5.75 % zero_less_one
% 5.52/5.75 thf(fact_2093_not__one__less__zero,axiom,
% 5.52/5.75 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.52/5.75
% 5.52/5.75 % not_one_less_zero
% 5.52/5.75 thf(fact_2094_not__one__less__zero,axiom,
% 5.52/5.75 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.52/5.75
% 5.52/5.75 % not_one_less_zero
% 5.52/5.75 thf(fact_2095_not__one__less__zero,axiom,
% 5.52/5.75 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.52/5.75
% 5.52/5.75 % not_one_less_zero
% 5.52/5.75 thf(fact_2096_not__one__less__zero,axiom,
% 5.52/5.75 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.52/5.75
% 5.52/5.75 % not_one_less_zero
% 5.52/5.75 thf(fact_2097_add__neg__neg,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_neg_neg
% 5.52/5.75 thf(fact_2098_add__neg__neg,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_neg_neg
% 5.52/5.75 thf(fact_2099_add__neg__neg,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.52/5.75 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.52/5.75 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_neg_neg
% 5.52/5.75 thf(fact_2100_add__neg__neg,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ A @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.52/5.75 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_neg_neg
% 5.52/5.75 thf(fact_2101_add__pos__pos,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.75 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_pos_pos
% 5.52/5.75 thf(fact_2102_add__pos__pos,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.52/5.75 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_pos_pos
% 5.52/5.75 thf(fact_2103_add__pos__pos,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_pos_pos
% 5.52/5.75 thf(fact_2104_add__pos__pos,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.75 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_pos_pos
% 5.52/5.75 thf(fact_2105_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_nat @ A @ B )
% 5.52/5.75 => ~ ! [C2: nat] :
% 5.52/5.75 ( ( B
% 5.52/5.75 = ( plus_plus_nat @ A @ C2 ) )
% 5.52/5.75 => ( C2 = zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % canonically_ordered_monoid_add_class.lessE
% 5.52/5.75 thf(fact_2106_pos__add__strict,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_real @ B @ C )
% 5.52/5.75 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % pos_add_strict
% 5.52/5.75 thf(fact_2107_pos__add__strict,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_rat @ B @ C )
% 5.52/5.75 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % pos_add_strict
% 5.52/5.75 thf(fact_2108_pos__add__strict,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_nat @ B @ C )
% 5.52/5.75 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % pos_add_strict
% 5.52/5.75 thf(fact_2109_pos__add__strict,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_int @ B @ C )
% 5.52/5.75 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % pos_add_strict
% 5.52/5.75 thf(fact_2110_add__less__zeroD,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y2 ) @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.52/5.75 | ( ord_less_real @ Y2 @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_less_zeroD
% 5.52/5.75 thf(fact_2111_add__less__zeroD,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ( ord_less_rat @ ( plus_plus_rat @ X2 @ Y2 ) @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.52/5.75 | ( ord_less_rat @ Y2 @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_less_zeroD
% 5.52/5.75 thf(fact_2112_add__less__zeroD,axiom,
% 5.52/5.75 ! [X2: int,Y2: int] :
% 5.52/5.75 ( ( ord_less_int @ ( plus_plus_int @ X2 @ Y2 ) @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.52/5.75 | ( ord_less_int @ Y2 @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_less_zeroD
% 5.52/5.75 thf(fact_2113_le__iff__diff__le__0,axiom,
% 5.52/5.75 ( ord_less_eq_real
% 5.52/5.75 = ( ^ [A4: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % le_iff_diff_le_0
% 5.52/5.75 thf(fact_2114_le__iff__diff__le__0,axiom,
% 5.52/5.75 ( ord_less_eq_rat
% 5.52/5.75 = ( ^ [A4: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % le_iff_diff_le_0
% 5.52/5.75 thf(fact_2115_le__iff__diff__le__0,axiom,
% 5.52/5.75 ( ord_less_eq_int
% 5.52/5.75 = ( ^ [A4: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % le_iff_diff_le_0
% 5.52/5.75 thf(fact_2116_divide__le__0__iff,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.52/5.75 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.52/5.75 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.75 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_le_0_iff
% 5.52/5.75 thf(fact_2117_divide__le__0__iff,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.52/5.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.52/5.75 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.75 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_le_0_iff
% 5.52/5.75 thf(fact_2118_divide__right__mono,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_right_mono
% 5.52/5.75 thf(fact_2119_divide__right__mono,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_right_mono
% 5.52/5.75 thf(fact_2120_zero__le__divide__iff,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.52/5.75 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.52/5.75 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.75 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_divide_iff
% 5.52/5.75 thf(fact_2121_zero__le__divide__iff,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.52/5.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.52/5.75 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.75 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_divide_iff
% 5.52/5.75 thf(fact_2122_divide__nonneg__nonneg,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_nonneg_nonneg
% 5.52/5.75 thf(fact_2123_divide__nonneg__nonneg,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.52/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_nonneg_nonneg
% 5.52/5.75 thf(fact_2124_divide__nonneg__nonpos,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.75 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.52/5.75 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_nonneg_nonpos
% 5.52/5.75 thf(fact_2125_divide__nonneg__nonpos,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.75 => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_nonneg_nonpos
% 5.52/5.75 thf(fact_2126_divide__nonpos__nonneg,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.75 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_nonpos_nonneg
% 5.52/5.75 thf(fact_2127_divide__nonpos__nonneg,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.52/5.75 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_nonpos_nonneg
% 5.52/5.75 thf(fact_2128_divide__nonpos__nonpos,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.52/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_nonpos_nonpos
% 5.52/5.75 thf(fact_2129_divide__nonpos__nonpos,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_nonpos_nonpos
% 5.52/5.75 thf(fact_2130_divide__right__mono__neg,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_right_mono_neg
% 5.52/5.75 thf(fact_2131_divide__right__mono__neg,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_right_mono_neg
% 5.52/5.75 thf(fact_2132_less__iff__diff__less__0,axiom,
% 5.52/5.75 ( ord_less_real
% 5.52/5.75 = ( ^ [A4: real,B3: real] : ( ord_less_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % less_iff_diff_less_0
% 5.52/5.75 thf(fact_2133_less__iff__diff__less__0,axiom,
% 5.52/5.75 ( ord_less_rat
% 5.52/5.75 = ( ^ [A4: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % less_iff_diff_less_0
% 5.52/5.75 thf(fact_2134_less__iff__diff__less__0,axiom,
% 5.52/5.75 ( ord_less_int
% 5.52/5.75 = ( ^ [A4: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % less_iff_diff_less_0
% 5.52/5.75 thf(fact_2135_divide__strict__right__mono__neg,axiom,
% 5.52/5.75 ! [B: real,A: real,C: real] :
% 5.52/5.75 ( ( ord_less_real @ B @ A )
% 5.52/5.75 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_strict_right_mono_neg
% 5.52/5.75 thf(fact_2136_divide__strict__right__mono__neg,axiom,
% 5.52/5.75 ! [B: rat,A: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_rat @ B @ A )
% 5.52/5.75 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_strict_right_mono_neg
% 5.52/5.75 thf(fact_2137_divide__strict__right__mono,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_strict_right_mono
% 5.52/5.75 thf(fact_2138_divide__strict__right__mono,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_strict_right_mono
% 5.52/5.75 thf(fact_2139_zero__less__divide__iff,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.52/5.75 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.52/5.75 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.75 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_divide_iff
% 5.52/5.75 thf(fact_2140_zero__less__divide__iff,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.52/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.52/5.75 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.75 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_divide_iff
% 5.52/5.75 thf(fact_2141_divide__less__cancel,axiom,
% 5.52/5.75 ! [A: real,C: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.52/5.75 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ B @ A ) )
% 5.52/5.75 & ( C != zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_less_cancel
% 5.52/5.75 thf(fact_2142_divide__less__cancel,axiom,
% 5.52/5.75 ! [A: rat,C: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ B @ A ) )
% 5.52/5.75 & ( C != zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_less_cancel
% 5.52/5.75 thf(fact_2143_divide__less__0__iff,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.52/5.75 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.52/5.75 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.75 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_less_0_iff
% 5.52/5.75 thf(fact_2144_divide__less__0__iff,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.52/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.52/5.75 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.75 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_less_0_iff
% 5.52/5.75 thf(fact_2145_divide__pos__pos,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.75 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_pos_pos
% 5.52/5.75 thf(fact_2146_divide__pos__pos,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.52/5.75 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_pos_pos
% 5.52/5.75 thf(fact_2147_divide__pos__neg,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.75 => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_pos_neg
% 5.52/5.75 thf(fact_2148_divide__pos__neg,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.52/5.75 => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_pos_neg
% 5.52/5.75 thf(fact_2149_divide__neg__pos,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.75 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_neg_pos
% 5.52/5.75 thf(fact_2150_divide__neg__pos,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.52/5.75 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_neg_pos
% 5.52/5.75 thf(fact_2151_divide__neg__neg,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_neg_neg
% 5.52/5.75 thf(fact_2152_divide__neg__neg,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_neg_neg
% 5.52/5.75 thf(fact_2153_zero__le__power,axiom,
% 5.52/5.75 ! [A: real,N: nat] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_power
% 5.52/5.75 thf(fact_2154_zero__le__power,axiom,
% 5.52/5.75 ! [A: rat,N: nat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_power
% 5.52/5.75 thf(fact_2155_zero__le__power,axiom,
% 5.52/5.75 ! [A: nat,N: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_power
% 5.52/5.75 thf(fact_2156_zero__le__power,axiom,
% 5.52/5.75 ! [A: int,N: nat] :
% 5.52/5.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_le_power
% 5.52/5.75 thf(fact_2157_power__mono,axiom,
% 5.52/5.75 ! [A: real,B: real,N: nat] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % power_mono
% 5.52/5.75 thf(fact_2158_power__mono,axiom,
% 5.52/5.75 ! [A: rat,B: rat,N: nat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % power_mono
% 5.52/5.75 thf(fact_2159_power__mono,axiom,
% 5.52/5.75 ! [A: nat,B: nat,N: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % power_mono
% 5.52/5.75 thf(fact_2160_power__mono,axiom,
% 5.52/5.75 ! [A: int,B: int,N: nat] :
% 5.52/5.75 ( ( ord_less_eq_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % power_mono
% 5.52/5.75 thf(fact_2161_zero__less__power,axiom,
% 5.52/5.75 ! [A: real,N: nat] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_power
% 5.52/5.75 thf(fact_2162_zero__less__power,axiom,
% 5.52/5.75 ! [A: rat,N: nat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_power
% 5.52/5.75 thf(fact_2163_zero__less__power,axiom,
% 5.52/5.75 ! [A: nat,N: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_power
% 5.52/5.75 thf(fact_2164_zero__less__power,axiom,
% 5.52/5.75 ! [A: int,N: nat] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % zero_less_power
% 5.52/5.75 thf(fact_2165_frac__eq__eq,axiom,
% 5.52/5.75 ! [Y2: complex,Z: complex,X2: complex,W: complex] :
% 5.52/5.75 ( ( Y2 != zero_zero_complex )
% 5.52/5.75 => ( ( Z != zero_zero_complex )
% 5.52/5.75 => ( ( ( divide1717551699836669952omplex @ X2 @ Y2 )
% 5.52/5.75 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.52/5.75 = ( ( times_times_complex @ X2 @ Z )
% 5.52/5.75 = ( times_times_complex @ W @ Y2 ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % frac_eq_eq
% 5.52/5.75 thf(fact_2166_frac__eq__eq,axiom,
% 5.52/5.75 ! [Y2: real,Z: real,X2: real,W: real] :
% 5.52/5.75 ( ( Y2 != zero_zero_real )
% 5.52/5.75 => ( ( Z != zero_zero_real )
% 5.52/5.75 => ( ( ( divide_divide_real @ X2 @ Y2 )
% 5.52/5.75 = ( divide_divide_real @ W @ Z ) )
% 5.52/5.75 = ( ( times_times_real @ X2 @ Z )
% 5.52/5.75 = ( times_times_real @ W @ Y2 ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % frac_eq_eq
% 5.52/5.75 thf(fact_2167_frac__eq__eq,axiom,
% 5.52/5.75 ! [Y2: rat,Z: rat,X2: rat,W: rat] :
% 5.52/5.75 ( ( Y2 != zero_zero_rat )
% 5.52/5.75 => ( ( Z != zero_zero_rat )
% 5.52/5.75 => ( ( ( divide_divide_rat @ X2 @ Y2 )
% 5.52/5.75 = ( divide_divide_rat @ W @ Z ) )
% 5.52/5.75 = ( ( times_times_rat @ X2 @ Z )
% 5.52/5.75 = ( times_times_rat @ W @ Y2 ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % frac_eq_eq
% 5.52/5.75 thf(fact_2168_divide__eq__eq,axiom,
% 5.52/5.75 ! [B: complex,C: complex,A: complex] :
% 5.52/5.75 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.52/5.75 = A )
% 5.52/5.75 = ( ( ( C != zero_zero_complex )
% 5.52/5.75 => ( B
% 5.52/5.75 = ( times_times_complex @ A @ C ) ) )
% 5.52/5.75 & ( ( C = zero_zero_complex )
% 5.52/5.75 => ( A = zero_zero_complex ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_eq_eq
% 5.52/5.75 thf(fact_2169_divide__eq__eq,axiom,
% 5.52/5.75 ! [B: real,C: real,A: real] :
% 5.52/5.75 ( ( ( divide_divide_real @ B @ C )
% 5.52/5.75 = A )
% 5.52/5.75 = ( ( ( C != zero_zero_real )
% 5.52/5.75 => ( B
% 5.52/5.75 = ( times_times_real @ A @ C ) ) )
% 5.52/5.75 & ( ( C = zero_zero_real )
% 5.52/5.75 => ( A = zero_zero_real ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_eq_eq
% 5.52/5.75 thf(fact_2170_divide__eq__eq,axiom,
% 5.52/5.75 ! [B: rat,C: rat,A: rat] :
% 5.52/5.75 ( ( ( divide_divide_rat @ B @ C )
% 5.52/5.75 = A )
% 5.52/5.75 = ( ( ( C != zero_zero_rat )
% 5.52/5.75 => ( B
% 5.52/5.75 = ( times_times_rat @ A @ C ) ) )
% 5.52/5.75 & ( ( C = zero_zero_rat )
% 5.52/5.75 => ( A = zero_zero_rat ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_eq_eq
% 5.52/5.75 thf(fact_2171_eq__divide__eq,axiom,
% 5.52/5.75 ! [A: complex,B: complex,C: complex] :
% 5.52/5.75 ( ( A
% 5.52/5.75 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.52/5.75 = ( ( ( C != zero_zero_complex )
% 5.52/5.75 => ( ( times_times_complex @ A @ C )
% 5.52/5.75 = B ) )
% 5.52/5.75 & ( ( C = zero_zero_complex )
% 5.52/5.75 => ( A = zero_zero_complex ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % eq_divide_eq
% 5.52/5.75 thf(fact_2172_eq__divide__eq,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( A
% 5.52/5.75 = ( divide_divide_real @ B @ C ) )
% 5.52/5.75 = ( ( ( C != zero_zero_real )
% 5.52/5.75 => ( ( times_times_real @ A @ C )
% 5.52/5.75 = B ) )
% 5.52/5.75 & ( ( C = zero_zero_real )
% 5.52/5.75 => ( A = zero_zero_real ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % eq_divide_eq
% 5.52/5.75 thf(fact_2173_eq__divide__eq,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( A
% 5.52/5.75 = ( divide_divide_rat @ B @ C ) )
% 5.52/5.75 = ( ( ( C != zero_zero_rat )
% 5.52/5.75 => ( ( times_times_rat @ A @ C )
% 5.52/5.75 = B ) )
% 5.52/5.75 & ( ( C = zero_zero_rat )
% 5.52/5.75 => ( A = zero_zero_rat ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % eq_divide_eq
% 5.52/5.75 thf(fact_2174_divide__eq__imp,axiom,
% 5.52/5.75 ! [C: complex,B: complex,A: complex] :
% 5.52/5.75 ( ( C != zero_zero_complex )
% 5.52/5.75 => ( ( B
% 5.52/5.75 = ( times_times_complex @ A @ C ) )
% 5.52/5.75 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.52/5.75 = A ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_eq_imp
% 5.52/5.75 thf(fact_2175_divide__eq__imp,axiom,
% 5.52/5.75 ! [C: real,B: real,A: real] :
% 5.52/5.75 ( ( C != zero_zero_real )
% 5.52/5.75 => ( ( B
% 5.52/5.75 = ( times_times_real @ A @ C ) )
% 5.52/5.75 => ( ( divide_divide_real @ B @ C )
% 5.52/5.75 = A ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_eq_imp
% 5.52/5.75 thf(fact_2176_divide__eq__imp,axiom,
% 5.52/5.75 ! [C: rat,B: rat,A: rat] :
% 5.52/5.75 ( ( C != zero_zero_rat )
% 5.52/5.75 => ( ( B
% 5.52/5.75 = ( times_times_rat @ A @ C ) )
% 5.52/5.75 => ( ( divide_divide_rat @ B @ C )
% 5.52/5.75 = A ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % divide_eq_imp
% 5.52/5.75 thf(fact_2177_eq__divide__imp,axiom,
% 5.52/5.75 ! [C: complex,A: complex,B: complex] :
% 5.52/5.75 ( ( C != zero_zero_complex )
% 5.52/5.75 => ( ( ( times_times_complex @ A @ C )
% 5.52/5.75 = B )
% 5.52/5.75 => ( A
% 5.52/5.75 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % eq_divide_imp
% 5.52/5.75 thf(fact_2178_eq__divide__imp,axiom,
% 5.52/5.75 ! [C: real,A: real,B: real] :
% 5.52/5.75 ( ( C != zero_zero_real )
% 5.52/5.75 => ( ( ( times_times_real @ A @ C )
% 5.52/5.75 = B )
% 5.52/5.75 => ( A
% 5.52/5.75 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % eq_divide_imp
% 5.52/5.75 thf(fact_2179_eq__divide__imp,axiom,
% 5.52/5.75 ! [C: rat,A: rat,B: rat] :
% 5.52/5.75 ( ( C != zero_zero_rat )
% 5.52/5.75 => ( ( ( times_times_rat @ A @ C )
% 5.52/5.75 = B )
% 5.52/5.75 => ( A
% 5.52/5.75 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % eq_divide_imp
% 5.52/5.75 thf(fact_2180_nonzero__divide__eq__eq,axiom,
% 5.52/5.75 ! [C: complex,B: complex,A: complex] :
% 5.52/5.75 ( ( C != zero_zero_complex )
% 5.52/5.75 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.52/5.75 = A )
% 5.52/5.75 = ( B
% 5.52/5.75 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % nonzero_divide_eq_eq
% 5.52/5.75 thf(fact_2181_nonzero__divide__eq__eq,axiom,
% 5.52/5.75 ! [C: real,B: real,A: real] :
% 5.52/5.75 ( ( C != zero_zero_real )
% 5.52/5.75 => ( ( ( divide_divide_real @ B @ C )
% 5.52/5.75 = A )
% 5.52/5.75 = ( B
% 5.52/5.75 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % nonzero_divide_eq_eq
% 5.52/5.75 thf(fact_2182_nonzero__divide__eq__eq,axiom,
% 5.52/5.75 ! [C: rat,B: rat,A: rat] :
% 5.52/5.75 ( ( C != zero_zero_rat )
% 5.52/5.75 => ( ( ( divide_divide_rat @ B @ C )
% 5.52/5.75 = A )
% 5.52/5.75 = ( B
% 5.52/5.75 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % nonzero_divide_eq_eq
% 5.52/5.75 thf(fact_2183_nonzero__eq__divide__eq,axiom,
% 5.52/5.75 ! [C: complex,A: complex,B: complex] :
% 5.52/5.75 ( ( C != zero_zero_complex )
% 5.52/5.75 => ( ( A
% 5.52/5.75 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.52/5.75 = ( ( times_times_complex @ A @ C )
% 5.52/5.75 = B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % nonzero_eq_divide_eq
% 5.52/5.75 thf(fact_2184_nonzero__eq__divide__eq,axiom,
% 5.52/5.75 ! [C: real,A: real,B: real] :
% 5.52/5.75 ( ( C != zero_zero_real )
% 5.52/5.75 => ( ( A
% 5.52/5.75 = ( divide_divide_real @ B @ C ) )
% 5.52/5.75 = ( ( times_times_real @ A @ C )
% 5.52/5.75 = B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % nonzero_eq_divide_eq
% 5.52/5.75 thf(fact_2185_nonzero__eq__divide__eq,axiom,
% 5.52/5.75 ! [C: rat,A: rat,B: rat] :
% 5.52/5.75 ( ( C != zero_zero_rat )
% 5.52/5.75 => ( ( A
% 5.52/5.75 = ( divide_divide_rat @ B @ C ) )
% 5.52/5.75 = ( ( times_times_rat @ A @ C )
% 5.52/5.75 = B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % nonzero_eq_divide_eq
% 5.52/5.75 thf(fact_2186_right__inverse__eq,axiom,
% 5.52/5.75 ! [B: complex,A: complex] :
% 5.52/5.75 ( ( B != zero_zero_complex )
% 5.52/5.75 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.52/5.75 = one_one_complex )
% 5.52/5.75 = ( A = B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % right_inverse_eq
% 5.52/5.75 thf(fact_2187_right__inverse__eq,axiom,
% 5.52/5.75 ! [B: real,A: real] :
% 5.52/5.75 ( ( B != zero_zero_real )
% 5.52/5.75 => ( ( ( divide_divide_real @ A @ B )
% 5.52/5.75 = one_one_real )
% 5.52/5.75 = ( A = B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % right_inverse_eq
% 5.52/5.75 thf(fact_2188_right__inverse__eq,axiom,
% 5.52/5.75 ! [B: rat,A: rat] :
% 5.52/5.75 ( ( B != zero_zero_rat )
% 5.52/5.75 => ( ( ( divide_divide_rat @ A @ B )
% 5.52/5.75 = one_one_rat )
% 5.52/5.75 = ( A = B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % right_inverse_eq
% 5.52/5.75 thf(fact_2189_length__pos__if__in__set,axiom,
% 5.52/5.75 ! [X2: option_nat,Xs2: list_option_nat] :
% 5.52/5.75 ( ( member_option_nat @ X2 @ ( set_option_nat2 @ Xs2 ) )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ ( size_s6086282163384603972on_nat @ Xs2 ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % length_pos_if_in_set
% 5.52/5.75 thf(fact_2190_length__pos__if__in__set,axiom,
% 5.52/5.75 ! [X2: real,Xs2: list_real] :
% 5.52/5.75 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % length_pos_if_in_set
% 5.52/5.75 thf(fact_2191_length__pos__if__in__set,axiom,
% 5.52/5.75 ! [X2: set_nat_rat,Xs2: list_set_nat_rat] :
% 5.52/5.75 ( ( member_set_nat_rat @ X2 @ ( set_set_nat_rat2 @ Xs2 ) )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ ( size_s3959913991096427681at_rat @ Xs2 ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % length_pos_if_in_set
% 5.52/5.75 thf(fact_2192_length__pos__if__in__set,axiom,
% 5.52/5.75 ! [X2: int,Xs2: list_int] :
% 5.52/5.75 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % length_pos_if_in_set
% 5.52/5.75 thf(fact_2193_length__pos__if__in__set,axiom,
% 5.52/5.75 ! [X2: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.52/5.75 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % length_pos_if_in_set
% 5.52/5.75 thf(fact_2194_length__pos__if__in__set,axiom,
% 5.52/5.75 ! [X2: $o,Xs2: list_o] :
% 5.52/5.75 ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % length_pos_if_in_set
% 5.52/5.75 thf(fact_2195_length__pos__if__in__set,axiom,
% 5.52/5.75 ! [X2: nat,Xs2: list_nat] :
% 5.52/5.75 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % length_pos_if_in_set
% 5.52/5.75 thf(fact_2196_power__0,axiom,
% 5.52/5.75 ! [A: rat] :
% 5.52/5.75 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.52/5.75 = one_one_rat ) ).
% 5.52/5.75
% 5.52/5.75 % power_0
% 5.52/5.75 thf(fact_2197_power__0,axiom,
% 5.52/5.75 ! [A: nat] :
% 5.52/5.75 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.52/5.75 = one_one_nat ) ).
% 5.52/5.75
% 5.52/5.75 % power_0
% 5.52/5.75 thf(fact_2198_power__0,axiom,
% 5.52/5.75 ! [A: real] :
% 5.52/5.75 ( ( power_power_real @ A @ zero_zero_nat )
% 5.52/5.75 = one_one_real ) ).
% 5.52/5.75
% 5.52/5.75 % power_0
% 5.52/5.75 thf(fact_2199_power__0,axiom,
% 5.52/5.75 ! [A: int] :
% 5.52/5.75 ( ( power_power_int @ A @ zero_zero_nat )
% 5.52/5.75 = one_one_int ) ).
% 5.52/5.75
% 5.52/5.75 % power_0
% 5.52/5.75 thf(fact_2200_power__0,axiom,
% 5.52/5.75 ! [A: complex] :
% 5.52/5.75 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.52/5.75 = one_one_complex ) ).
% 5.52/5.75
% 5.52/5.75 % power_0
% 5.52/5.75 thf(fact_2201_less__Suc__eq__0__disj,axiom,
% 5.52/5.75 ! [M: nat,N: nat] :
% 5.52/5.75 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.52/5.75 = ( ( M = zero_zero_nat )
% 5.52/5.75 | ? [J3: nat] :
% 5.52/5.75 ( ( M
% 5.52/5.75 = ( suc @ J3 ) )
% 5.52/5.75 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % less_Suc_eq_0_disj
% 5.52/5.75 thf(fact_2202_gr0__implies__Suc,axiom,
% 5.52/5.75 ! [N: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.75 => ? [M4: nat] :
% 5.52/5.75 ( N
% 5.52/5.75 = ( suc @ M4 ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % gr0_implies_Suc
% 5.52/5.75 thf(fact_2203_All__less__Suc2,axiom,
% 5.52/5.75 ! [N: nat,P: nat > $o] :
% 5.52/5.75 ( ( ! [I4: nat] :
% 5.52/5.75 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.52/5.75 => ( P @ I4 ) ) )
% 5.52/5.75 = ( ( P @ zero_zero_nat )
% 5.52/5.75 & ! [I4: nat] :
% 5.52/5.75 ( ( ord_less_nat @ I4 @ N )
% 5.52/5.75 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % All_less_Suc2
% 5.52/5.75 thf(fact_2204_gr0__conv__Suc,axiom,
% 5.52/5.75 ! [N: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.75 = ( ? [M3: nat] :
% 5.52/5.75 ( N
% 5.52/5.75 = ( suc @ M3 ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % gr0_conv_Suc
% 5.52/5.75 thf(fact_2205_Ex__less__Suc2,axiom,
% 5.52/5.75 ! [N: nat,P: nat > $o] :
% 5.52/5.75 ( ( ? [I4: nat] :
% 5.52/5.75 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.52/5.75 & ( P @ I4 ) ) )
% 5.52/5.75 = ( ( P @ zero_zero_nat )
% 5.52/5.75 | ? [I4: nat] :
% 5.52/5.75 ( ( ord_less_nat @ I4 @ N )
% 5.52/5.75 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % Ex_less_Suc2
% 5.52/5.75 thf(fact_2206_add__is__1,axiom,
% 5.52/5.75 ! [M: nat,N: nat] :
% 5.52/5.75 ( ( ( plus_plus_nat @ M @ N )
% 5.52/5.75 = ( suc @ zero_zero_nat ) )
% 5.52/5.75 = ( ( ( M
% 5.52/5.75 = ( suc @ zero_zero_nat ) )
% 5.52/5.75 & ( N = zero_zero_nat ) )
% 5.52/5.75 | ( ( M = zero_zero_nat )
% 5.52/5.75 & ( N
% 5.52/5.75 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_is_1
% 5.52/5.75 thf(fact_2207_one__is__add,axiom,
% 5.52/5.75 ! [M: nat,N: nat] :
% 5.52/5.75 ( ( ( suc @ zero_zero_nat )
% 5.52/5.75 = ( plus_plus_nat @ M @ N ) )
% 5.52/5.75 = ( ( ( M
% 5.52/5.75 = ( suc @ zero_zero_nat ) )
% 5.52/5.75 & ( N = zero_zero_nat ) )
% 5.52/5.75 | ( ( M = zero_zero_nat )
% 5.52/5.75 & ( N
% 5.52/5.75 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % one_is_add
% 5.52/5.75 thf(fact_2208_option_Osize_I4_J,axiom,
% 5.52/5.75 ! [X23: product_prod_nat_nat] :
% 5.52/5.75 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X23 ) )
% 5.52/5.75 = ( suc @ zero_zero_nat ) ) ).
% 5.52/5.75
% 5.52/5.75 % option.size(4)
% 5.52/5.75 thf(fact_2209_option_Osize_I4_J,axiom,
% 5.52/5.75 ! [X23: nat] :
% 5.52/5.75 ( ( size_size_option_nat @ ( some_nat @ X23 ) )
% 5.52/5.75 = ( suc @ zero_zero_nat ) ) ).
% 5.52/5.75
% 5.52/5.75 % option.size(4)
% 5.52/5.75 thf(fact_2210_option_Osize_I4_J,axiom,
% 5.52/5.75 ! [X23: num] :
% 5.52/5.75 ( ( size_size_option_num @ ( some_num @ X23 ) )
% 5.52/5.75 = ( suc @ zero_zero_nat ) ) ).
% 5.52/5.75
% 5.52/5.75 % option.size(4)
% 5.52/5.75 thf(fact_2211_ex__least__nat__le,axiom,
% 5.52/5.75 ! [P: nat > $o,N: nat] :
% 5.52/5.75 ( ( P @ N )
% 5.52/5.75 => ( ~ ( P @ zero_zero_nat )
% 5.52/5.75 => ? [K3: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ K3 @ N )
% 5.52/5.75 & ! [I3: nat] :
% 5.52/5.75 ( ( ord_less_nat @ I3 @ K3 )
% 5.52/5.75 => ~ ( P @ I3 ) )
% 5.52/5.75 & ( P @ K3 ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % ex_least_nat_le
% 5.52/5.75 thf(fact_2212_One__nat__def,axiom,
% 5.52/5.75 ( one_one_nat
% 5.52/5.75 = ( suc @ zero_zero_nat ) ) ).
% 5.52/5.75
% 5.52/5.75 % One_nat_def
% 5.52/5.75 thf(fact_2213_less__imp__add__positive,axiom,
% 5.52/5.75 ! [I: nat,J: nat] :
% 5.52/5.75 ( ( ord_less_nat @ I @ J )
% 5.52/5.75 => ? [K3: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 5.52/5.75 & ( ( plus_plus_nat @ I @ K3 )
% 5.52/5.75 = J ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % less_imp_add_positive
% 5.52/5.75 thf(fact_2214_option_Osize_I3_J,axiom,
% 5.52/5.75 ( ( size_size_option_nat @ none_nat )
% 5.52/5.75 = ( suc @ zero_zero_nat ) ) ).
% 5.52/5.75
% 5.52/5.75 % option.size(3)
% 5.52/5.75 thf(fact_2215_option_Osize_I3_J,axiom,
% 5.52/5.75 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.52/5.75 = ( suc @ zero_zero_nat ) ) ).
% 5.52/5.75
% 5.52/5.75 % option.size(3)
% 5.52/5.75 thf(fact_2216_option_Osize_I3_J,axiom,
% 5.52/5.75 ( ( size_size_option_num @ none_num )
% 5.52/5.75 = ( suc @ zero_zero_nat ) ) ).
% 5.52/5.75
% 5.52/5.75 % option.size(3)
% 5.52/5.75 thf(fact_2217_diff__less,axiom,
% 5.52/5.75 ! [N: nat,M: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.75 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % diff_less
% 5.52/5.75 thf(fact_2218_nat__mult__less__cancel1,axiom,
% 5.52/5.75 ! [K: nat,M: nat,N: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.75 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.52/5.75 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % nat_mult_less_cancel1
% 5.52/5.75 thf(fact_2219_nat__mult__eq__cancel1,axiom,
% 5.52/5.75 ! [K: nat,M: nat,N: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.75 => ( ( ( times_times_nat @ K @ M )
% 5.52/5.75 = ( times_times_nat @ K @ N ) )
% 5.52/5.75 = ( M = N ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % nat_mult_eq_cancel1
% 5.52/5.75 thf(fact_2220_mult__less__mono1,axiom,
% 5.52/5.75 ! [I: nat,J: nat,K: nat] :
% 5.52/5.75 ( ( ord_less_nat @ I @ J )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.75 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_mono1
% 5.52/5.75 thf(fact_2221_mult__less__mono2,axiom,
% 5.52/5.75 ! [I: nat,J: nat,K: nat] :
% 5.52/5.75 ( ( ord_less_nat @ I @ J )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.75 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_mono2
% 5.52/5.75 thf(fact_2222_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.52/5.75 ! [M: nat,N: nat] :
% 5.52/5.75 ( ( ( divide_divide_nat @ M @ N )
% 5.52/5.75 = zero_zero_nat )
% 5.52/5.75 = ( ( ord_less_nat @ M @ N )
% 5.52/5.75 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % Euclidean_Division.div_eq_0_iff
% 5.52/5.75 thf(fact_2223_diff__add__0,axiom,
% 5.52/5.75 ! [N: nat,M: nat] :
% 5.52/5.75 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 5.52/5.75 = zero_zero_nat ) ).
% 5.52/5.75
% 5.52/5.75 % diff_add_0
% 5.52/5.75 thf(fact_2224_mult__eq__self__implies__10,axiom,
% 5.52/5.75 ! [M: nat,N: nat] :
% 5.52/5.75 ( ( M
% 5.52/5.75 = ( times_times_nat @ M @ N ) )
% 5.52/5.75 => ( ( N = one_one_nat )
% 5.52/5.75 | ( M = zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_eq_self_implies_10
% 5.52/5.75 thf(fact_2225_nat__power__less__imp__less,axiom,
% 5.52/5.75 ! [I: nat,M: nat,N: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ I )
% 5.52/5.75 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.52/5.75 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % nat_power_less_imp_less
% 5.52/5.75 thf(fact_2226_vebt__pred_Ocases,axiom,
% 5.52/5.75 ! [X2: produc9072475918466114483BT_nat] :
% 5.52/5.75 ( ! [Uu2: $o,Uv2: $o] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 5.52/5.75 => ( ! [A3: $o,Uw2: $o] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 5.52/5.75 => ( ! [A3: $o,B2: $o,Va3: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ ( suc @ ( suc @ Va3 ) ) ) )
% 5.52/5.75 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb2: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Vb2 ) )
% 5.52/5.75 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) @ Vf ) )
% 5.52/5.75 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj ) )
% 5.52/5.75 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % vebt_pred.cases
% 5.52/5.75 thf(fact_2227_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Ocases,axiom,
% 5.52/5.75 ! [X2: produc9072475918466114483BT_nat] :
% 5.52/5.75 ( ! [Uu2: $o,B2: $o] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B2 ) @ zero_zero_nat ) )
% 5.52/5.75 => ( ! [Uv2: $o,Uw2: $o,N2: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N2 ) ) )
% 5.52/5.75 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va2: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va2 ) )
% 5.52/5.75 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve ) )
% 5.52/5.75 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi ) )
% 5.52/5.75 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.cases
% 5.52/5.75 thf(fact_2228_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Ocases,axiom,
% 5.52/5.75 ! [X2: produc9072475918466114483BT_nat] :
% 5.52/5.75 ( ! [A3: $o,B2: $o,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X4 ) )
% 5.52/5.75 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ X4 ) )
% 5.52/5.75 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ X4 ) )
% 5.52/5.75 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ X4 ) )
% 5.52/5.75 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.cases
% 5.52/5.75 thf(fact_2229_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Ocases,axiom,
% 5.52/5.75 ! [X2: produc9072475918466114483BT_nat] :
% 5.52/5.75 ( ! [A3: $o,B2: $o,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X4 ) )
% 5.52/5.75 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X4 ) )
% 5.52/5.75 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X4 ) )
% 5.52/5.75 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X4 ) )
% 5.52/5.75 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.cases
% 5.52/5.75 thf(fact_2230_VEBT__internal_Omembermima_Ocases,axiom,
% 5.52/5.75 ! [X2: produc9072475918466114483BT_nat] :
% 5.52/5.75 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 5.52/5.75 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.52/5.75 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ X4 ) )
% 5.52/5.75 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ X4 ) )
% 5.52/5.75 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X4: nat] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ X4 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % VEBT_internal.membermima.cases
% 5.52/5.75 thf(fact_2231_vebt__insert_Osimps_I2_J,axiom,
% 5.52/5.75 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.52/5.75 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X2 )
% 5.52/5.75 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) ).
% 5.52/5.75
% 5.52/5.75 % vebt_insert.simps(2)
% 5.52/5.75 thf(fact_2232_vebt__pred_Osimps_I3_J,axiom,
% 5.52/5.75 ! [B: $o,A: $o,Va: nat] :
% 5.52/5.75 ( ( B
% 5.52/5.75 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.52/5.75 = ( some_nat @ one_one_nat ) ) )
% 5.52/5.75 & ( ~ B
% 5.52/5.75 => ( ( A
% 5.52/5.75 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.52/5.75 = ( some_nat @ zero_zero_nat ) ) )
% 5.52/5.75 & ( ~ A
% 5.52/5.75 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.52/5.75 = none_nat ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % vebt_pred.simps(3)
% 5.52/5.75 thf(fact_2233_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.52/5.75 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.52/5.75 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.52/5.75
% 5.52/5.75 % VEBT_internal.naive_member.simps(2)
% 5.52/5.75 thf(fact_2234_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Ocases,axiom,
% 5.52/5.75 ! [X2: vEBT_VEBT] :
% 5.52/5.75 ( ( X2
% 5.52/5.75 != ( vEBT_Leaf @ $false @ $false ) )
% 5.52/5.75 => ( ! [Uv2: $o] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.52/5.75 => ( ! [Uu2: $o] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.52/5.75 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.52/5.75 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.75 ( X2
% 5.52/5.75 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.cases
% 5.52/5.75 thf(fact_2235_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I1_J,axiom,
% 5.52/5.75 ! [A: $o,B: $o,X2: nat] :
% 5.52/5.75 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.52/5.75 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(1)
% 5.52/5.75 thf(fact_2236_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I2_J,axiom,
% 5.52/5.75 ! [Uv: $o,Uw: $o,N: nat] :
% 5.52/5.75 ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 5.52/5.75 = one_one_nat ) ).
% 5.52/5.75
% 5.52/5.75 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(2)
% 5.52/5.75 thf(fact_2237_vebt__succ_Osimps_I2_J,axiom,
% 5.52/5.75 ! [Uv: $o,Uw: $o,N: nat] :
% 5.52/5.75 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 5.52/5.75 = none_nat ) ).
% 5.52/5.75
% 5.52/5.75 % vebt_succ.simps(2)
% 5.52/5.75 thf(fact_2238_mult__le__cancel__left,axiom,
% 5.52/5.75 ! [C: real,A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.52/5.75 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_eq_real @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_cancel_left
% 5.52/5.75 thf(fact_2239_mult__le__cancel__left,axiom,
% 5.52/5.75 ! [C: rat,A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.52/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_eq_rat @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_cancel_left
% 5.52/5.75 thf(fact_2240_mult__le__cancel__left,axiom,
% 5.52/5.75 ! [C: int,A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.52/5.75 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_eq_int @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.52/5.75 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_cancel_left
% 5.52/5.75 thf(fact_2241_mult__le__cancel__right,axiom,
% 5.52/5.75 ! [A: real,C: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.52/5.75 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_eq_real @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_cancel_right
% 5.52/5.75 thf(fact_2242_mult__le__cancel__right,axiom,
% 5.52/5.75 ! [A: rat,C: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.52/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_eq_rat @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_cancel_right
% 5.52/5.75 thf(fact_2243_mult__le__cancel__right,axiom,
% 5.52/5.75 ! [A: int,C: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.52/5.75 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_eq_int @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.52/5.75 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_cancel_right
% 5.52/5.75 thf(fact_2244_mult__left__less__imp__less,axiom,
% 5.52/5.75 ! [C: real,A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_less_imp_less
% 5.52/5.75 thf(fact_2245_mult__left__less__imp__less,axiom,
% 5.52/5.75 ! [C: rat,A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_less_imp_less
% 5.52/5.75 thf(fact_2246_mult__left__less__imp__less,axiom,
% 5.52/5.75 ! [C: nat,A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_less_imp_less
% 5.52/5.75 thf(fact_2247_mult__left__less__imp__less,axiom,
% 5.52/5.75 ! [C: int,A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_int @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_less_imp_less
% 5.52/5.75 thf(fact_2248_mult__strict__mono,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real,D2: real] :
% 5.52/5.75 ( ( ord_less_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_real @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_mono
% 5.52/5.75 thf(fact_2249_mult__strict__mono,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.52/5.75 ( ( ord_less_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_rat @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_mono
% 5.52/5.75 thf(fact_2250_mult__strict__mono,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.52/5.75 ( ( ord_less_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_nat @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_mono
% 5.52/5.75 thf(fact_2251_mult__strict__mono,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int,D2: int] :
% 5.52/5.75 ( ( ord_less_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_int @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_mono
% 5.52/5.75 thf(fact_2252_mult__less__cancel__left,axiom,
% 5.52/5.75 ! [C: real,A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.52/5.75 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_left
% 5.52/5.75 thf(fact_2253_mult__less__cancel__left,axiom,
% 5.52/5.75 ! [C: rat,A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.52/5.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_left
% 5.52/5.75 thf(fact_2254_mult__less__cancel__left,axiom,
% 5.52/5.75 ! [C: int,A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.52/5.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_int @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.52/5.75 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_left
% 5.52/5.75 thf(fact_2255_mult__right__less__imp__less,axiom,
% 5.52/5.75 ! [A: real,C: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_less_imp_less
% 5.52/5.75 thf(fact_2256_mult__right__less__imp__less,axiom,
% 5.52/5.75 ! [A: rat,C: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_less_imp_less
% 5.52/5.75 thf(fact_2257_mult__right__less__imp__less,axiom,
% 5.52/5.75 ! [A: nat,C: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_less_imp_less
% 5.52/5.75 thf(fact_2258_mult__right__less__imp__less,axiom,
% 5.52/5.75 ! [A: int,C: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_int @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_less_imp_less
% 5.52/5.75 thf(fact_2259_mult__strict__mono_H,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real,D2: real] :
% 5.52/5.75 ( ( ord_less_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_real @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_mono'
% 5.52/5.75 thf(fact_2260_mult__strict__mono_H,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.52/5.75 ( ( ord_less_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_rat @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_mono'
% 5.52/5.75 thf(fact_2261_mult__strict__mono_H,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.52/5.75 ( ( ord_less_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_nat @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_mono'
% 5.52/5.75 thf(fact_2262_mult__strict__mono_H,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int,D2: int] :
% 5.52/5.75 ( ( ord_less_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_int @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_strict_mono'
% 5.52/5.75 thf(fact_2263_mult__less__cancel__right,axiom,
% 5.52/5.75 ! [A: real,C: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.52/5.75 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_right
% 5.52/5.75 thf(fact_2264_mult__less__cancel__right,axiom,
% 5.52/5.75 ! [A: rat,C: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.52/5.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_right
% 5.52/5.75 thf(fact_2265_mult__less__cancel__right,axiom,
% 5.52/5.75 ! [A: int,C: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.52/5.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_int @ A @ B ) )
% 5.52/5.75 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.52/5.75 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_cancel_right
% 5.52/5.75 thf(fact_2266_mult__le__cancel__left__neg,axiom,
% 5.52/5.75 ! [C: real,A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.52/5.75 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_cancel_left_neg
% 5.52/5.75 thf(fact_2267_mult__le__cancel__left__neg,axiom,
% 5.52/5.75 ! [C: rat,A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.52/5.75 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_cancel_left_neg
% 5.52/5.75 thf(fact_2268_mult__le__cancel__left__neg,axiom,
% 5.52/5.75 ! [C: int,A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ C @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.52/5.75 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_cancel_left_neg
% 5.52/5.75 thf(fact_2269_mult__le__cancel__left__pos,axiom,
% 5.52/5.75 ! [C: real,A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.52/5.75 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_cancel_left_pos
% 5.52/5.75 thf(fact_2270_mult__le__cancel__left__pos,axiom,
% 5.52/5.75 ! [C: rat,A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.52/5.75 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_cancel_left_pos
% 5.52/5.75 thf(fact_2271_mult__le__cancel__left__pos,axiom,
% 5.52/5.75 ! [C: int,A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.52/5.75 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_cancel_left_pos
% 5.52/5.75 thf(fact_2272_mult__left__le__imp__le,axiom,
% 5.52/5.75 ! [C: real,A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_le_imp_le
% 5.52/5.75 thf(fact_2273_mult__left__le__imp__le,axiom,
% 5.52/5.75 ! [C: rat,A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_le_imp_le
% 5.52/5.75 thf(fact_2274_mult__left__le__imp__le,axiom,
% 5.52/5.75 ! [C: nat,A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_le_imp_le
% 5.52/5.75 thf(fact_2275_mult__left__le__imp__le,axiom,
% 5.52/5.75 ! [C: int,A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_le_imp_le
% 5.52/5.75 thf(fact_2276_mult__right__le__imp__le,axiom,
% 5.52/5.75 ! [A: real,C: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_le_imp_le
% 5.52/5.75 thf(fact_2277_mult__right__le__imp__le,axiom,
% 5.52/5.75 ! [A: rat,C: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_le_imp_le
% 5.52/5.75 thf(fact_2278_mult__right__le__imp__le,axiom,
% 5.52/5.75 ! [A: nat,C: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_le_imp_le
% 5.52/5.75 thf(fact_2279_mult__right__le__imp__le,axiom,
% 5.52/5.75 ! [A: int,C: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_right_le_imp_le
% 5.52/5.75 thf(fact_2280_mult__le__less__imp__less,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real,D2: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_real @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_less_imp_less
% 5.52/5.75 thf(fact_2281_mult__le__less__imp__less,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_rat @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_less_imp_less
% 5.52/5.75 thf(fact_2282_mult__le__less__imp__less,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_nat @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_less_imp_less
% 5.52/5.75 thf(fact_2283_mult__le__less__imp__less,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int,D2: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_int @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_le_less_imp_less
% 5.52/5.75 thf(fact_2284_mult__less__le__imp__less,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real,D2: real] :
% 5.52/5.75 ( ( ord_less_real @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_real @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.75 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_le_imp_less
% 5.52/5.75 thf(fact_2285_mult__less__le__imp__less,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.52/5.75 ( ( ord_less_rat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_le_imp_less
% 5.52/5.75 thf(fact_2286_mult__less__le__imp__less,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.52/5.75 ( ( ord_less_nat @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.52/5.75 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_le_imp_less
% 5.52/5.75 thf(fact_2287_mult__less__le__imp__less,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int,D2: int] :
% 5.52/5.75 ( ( ord_less_int @ A @ B )
% 5.52/5.75 => ( ( ord_less_eq_int @ C @ D2 )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.75 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_less_le_imp_less
% 5.52/5.75 thf(fact_2288_add__neg__nonpos,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_neg_nonpos
% 5.52/5.75 thf(fact_2289_add__neg__nonpos,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_neg_nonpos
% 5.52/5.75 thf(fact_2290_add__neg__nonpos,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.52/5.75 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.52/5.75 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_neg_nonpos
% 5.52/5.75 thf(fact_2291_add__neg__nonpos,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ A @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.52/5.75 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_neg_nonpos
% 5.52/5.75 thf(fact_2292_add__nonneg__pos,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.75 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonneg_pos
% 5.52/5.75 thf(fact_2293_add__nonneg__pos,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.52/5.75 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonneg_pos
% 5.52/5.75 thf(fact_2294_add__nonneg__pos,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonneg_pos
% 5.52/5.75 thf(fact_2295_add__nonneg__pos,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.75 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonneg_pos
% 5.52/5.75 thf(fact_2296_add__nonpos__neg,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.75 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.52/5.75 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonpos_neg
% 5.52/5.75 thf(fact_2297_add__nonpos__neg,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.75 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.52/5.75 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonpos_neg
% 5.52/5.75 thf(fact_2298_add__nonpos__neg,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.52/5.75 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.52/5.75 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonpos_neg
% 5.52/5.75 thf(fact_2299_add__nonpos__neg,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.52/5.75 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_nonpos_neg
% 5.52/5.75 thf(fact_2300_add__pos__nonneg,axiom,
% 5.52/5.75 ! [A: real,B: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.75 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_pos_nonneg
% 5.52/5.75 thf(fact_2301_add__pos__nonneg,axiom,
% 5.52/5.75 ! [A: rat,B: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.75 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_pos_nonneg
% 5.52/5.75 thf(fact_2302_add__pos__nonneg,axiom,
% 5.52/5.75 ! [A: nat,B: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.52/5.75 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_pos_nonneg
% 5.52/5.75 thf(fact_2303_add__pos__nonneg,axiom,
% 5.52/5.75 ! [A: int,B: int] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.75 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_pos_nonneg
% 5.52/5.75 thf(fact_2304_add__strict__increasing,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_eq_real @ B @ C )
% 5.52/5.75 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_strict_increasing
% 5.52/5.75 thf(fact_2305_add__strict__increasing,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_eq_rat @ B @ C )
% 5.52/5.75 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_strict_increasing
% 5.52/5.75 thf(fact_2306_add__strict__increasing,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat] :
% 5.52/5.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_eq_nat @ B @ C )
% 5.52/5.75 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_strict_increasing
% 5.52/5.75 thf(fact_2307_add__strict__increasing,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int] :
% 5.52/5.75 ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_eq_int @ B @ C )
% 5.52/5.75 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_strict_increasing
% 5.52/5.75 thf(fact_2308_add__strict__increasing2,axiom,
% 5.52/5.75 ! [A: real,B: real,C: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.75 => ( ( ord_less_real @ B @ C )
% 5.52/5.75 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_strict_increasing2
% 5.52/5.75 thf(fact_2309_add__strict__increasing2,axiom,
% 5.52/5.75 ! [A: rat,B: rat,C: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.75 => ( ( ord_less_rat @ B @ C )
% 5.52/5.75 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_strict_increasing2
% 5.52/5.75 thf(fact_2310_add__strict__increasing2,axiom,
% 5.52/5.75 ! [A: nat,B: nat,C: nat] :
% 5.52/5.75 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.75 => ( ( ord_less_nat @ B @ C )
% 5.52/5.75 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_strict_increasing2
% 5.52/5.75 thf(fact_2311_add__strict__increasing2,axiom,
% 5.52/5.75 ! [A: int,B: int,C: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.75 => ( ( ord_less_int @ B @ C )
% 5.52/5.75 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % add_strict_increasing2
% 5.52/5.75 thf(fact_2312_field__le__epsilon,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ! [E2: real] :
% 5.52/5.75 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.52/5.75 => ( ord_less_eq_real @ X2 @ ( plus_plus_real @ Y2 @ E2 ) ) )
% 5.52/5.75 => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 5.52/5.75
% 5.52/5.75 % field_le_epsilon
% 5.52/5.75 thf(fact_2313_field__le__epsilon,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ! [E2: rat] :
% 5.52/5.75 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.52/5.75 => ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ Y2 @ E2 ) ) )
% 5.52/5.75 => ( ord_less_eq_rat @ X2 @ Y2 ) ) ).
% 5.52/5.75
% 5.52/5.75 % field_le_epsilon
% 5.52/5.75 thf(fact_2314_mult__left__le__one__le,axiom,
% 5.52/5.75 ! [X2: real,Y2: real] :
% 5.52/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.75 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.52/5.75 => ( ord_less_eq_real @ ( times_times_real @ Y2 @ X2 ) @ X2 ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_le_one_le
% 5.52/5.75 thf(fact_2315_mult__left__le__one__le,axiom,
% 5.52/5.75 ! [X2: rat,Y2: rat] :
% 5.52/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.52/5.75 => ( ( ord_less_eq_rat @ Y2 @ one_one_rat )
% 5.52/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ Y2 @ X2 ) @ X2 ) ) ) ) ).
% 5.52/5.75
% 5.52/5.75 % mult_left_le_one_le
% 5.52/5.75 thf(fact_2316_mult__left__le__one__le,axiom,
% 5.52/5.75 ! [X2: int,Y2: int] :
% 5.52/5.75 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.76 => ( ( ord_less_eq_int @ Y2 @ one_one_int )
% 5.52/5.76 => ( ord_less_eq_int @ ( times_times_int @ Y2 @ X2 ) @ X2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_left_le_one_le
% 5.52/5.76 thf(fact_2317_mult__right__le__one__le,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.76 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.52/5.76 => ( ord_less_eq_real @ ( times_times_real @ X2 @ Y2 ) @ X2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_right_le_one_le
% 5.52/5.76 thf(fact_2318_mult__right__le__one__le,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.52/5.76 => ( ( ord_less_eq_rat @ Y2 @ one_one_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Y2 ) @ X2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_right_le_one_le
% 5.52/5.76 thf(fact_2319_mult__right__le__one__le,axiom,
% 5.52/5.76 ! [X2: int,Y2: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.76 => ( ( ord_less_eq_int @ Y2 @ one_one_int )
% 5.52/5.76 => ( ord_less_eq_int @ ( times_times_int @ X2 @ Y2 ) @ X2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_right_le_one_le
% 5.52/5.76 thf(fact_2320_mult__le__one,axiom,
% 5.52/5.76 ! [A: real,B: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.76 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.52/5.76 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_one
% 5.52/5.76 thf(fact_2321_mult__le__one,axiom,
% 5.52/5.76 ! [A: rat,B: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.76 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_one
% 5.52/5.76 thf(fact_2322_mult__le__one,axiom,
% 5.52/5.76 ! [A: nat,B: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.52/5.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.52/5.76 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.52/5.76 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_one
% 5.52/5.76 thf(fact_2323_mult__le__one,axiom,
% 5.52/5.76 ! [A: int,B: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.76 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.52/5.76 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_one
% 5.52/5.76 thf(fact_2324_mult__left__le,axiom,
% 5.52/5.76 ! [C: real,A: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.76 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_left_le
% 5.52/5.76 thf(fact_2325_mult__left__le,axiom,
% 5.52/5.76 ! [C: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.76 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_left_le
% 5.52/5.76 thf(fact_2326_mult__left__le,axiom,
% 5.52/5.76 ! [C: nat,A: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.52/5.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.76 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_left_le
% 5.52/5.76 thf(fact_2327_mult__left__le,axiom,
% 5.52/5.76 ! [C: int,A: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.76 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_left_le
% 5.52/5.76 thf(fact_2328_div__positive,axiom,
% 5.52/5.76 ! [B: nat,A: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.76 => ( ( ord_less_eq_nat @ B @ A )
% 5.52/5.76 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_positive
% 5.52/5.76 thf(fact_2329_div__positive,axiom,
% 5.52/5.76 ! [B: int,A: int] :
% 5.52/5.76 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.76 => ( ( ord_less_eq_int @ B @ A )
% 5.52/5.76 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_positive
% 5.52/5.76 thf(fact_2330_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.52/5.76 ! [A: nat,B: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.76 => ( ( ord_less_nat @ A @ B )
% 5.52/5.76 => ( ( divide_divide_nat @ A @ B )
% 5.52/5.76 = zero_zero_nat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % unique_euclidean_semiring_numeral_class.div_less
% 5.52/5.76 thf(fact_2331_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.52/5.76 ! [A: int,B: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.76 => ( ( ord_less_int @ A @ B )
% 5.52/5.76 => ( ( divide_divide_int @ A @ B )
% 5.52/5.76 = zero_zero_int ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % unique_euclidean_semiring_numeral_class.div_less
% 5.52/5.76 thf(fact_2332_divide__nonpos__pos,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.52/5.76 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.76 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_nonpos_pos
% 5.52/5.76 thf(fact_2333_divide__nonpos__pos,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.52/5.76 => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.52/5.76 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_nonpos_pos
% 5.52/5.76 thf(fact_2334_divide__nonpos__neg,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.52/5.76 => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_nonpos_neg
% 5.52/5.76 thf(fact_2335_divide__nonpos__neg,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.52/5.76 => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_nonpos_neg
% 5.52/5.76 thf(fact_2336_divide__nonneg__pos,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.76 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_nonneg_pos
% 5.52/5.76 thf(fact_2337_divide__nonneg__pos,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.76 => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.52/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_nonneg_pos
% 5.52/5.76 thf(fact_2338_divide__nonneg__neg,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.76 => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_nonneg_neg
% 5.52/5.76 thf(fact_2339_divide__nonneg__neg,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.76 => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_nonneg_neg
% 5.52/5.76 thf(fact_2340_divide__le__cancel,axiom,
% 5.52/5.76 ! [A: real,C: real,B: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_eq_real @ A @ B ) )
% 5.52/5.76 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_le_cancel
% 5.52/5.76 thf(fact_2341_divide__le__cancel,axiom,
% 5.52/5.76 ! [A: rat,C: rat,B: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_eq_rat @ A @ B ) )
% 5.52/5.76 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_le_cancel
% 5.52/5.76 thf(fact_2342_frac__less2,axiom,
% 5.52/5.76 ! [X2: real,Y2: real,W: real,Z: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.76 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.52/5.76 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.52/5.76 => ( ( ord_less_real @ W @ Z )
% 5.52/5.76 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % frac_less2
% 5.52/5.76 thf(fact_2343_frac__less2,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat,W: rat,Z: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.52/5.76 => ( ( ord_less_eq_rat @ X2 @ Y2 )
% 5.52/5.76 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.52/5.76 => ( ( ord_less_rat @ W @ Z )
% 5.52/5.76 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % frac_less2
% 5.52/5.76 thf(fact_2344_frac__less,axiom,
% 5.52/5.76 ! [X2: real,Y2: real,W: real,Z: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.76 => ( ( ord_less_real @ X2 @ Y2 )
% 5.52/5.76 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.52/5.76 => ( ( ord_less_eq_real @ W @ Z )
% 5.52/5.76 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % frac_less
% 5.52/5.76 thf(fact_2345_frac__less,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat,W: rat,Z: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.76 => ( ( ord_less_rat @ X2 @ Y2 )
% 5.52/5.76 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.52/5.76 => ( ( ord_less_eq_rat @ W @ Z )
% 5.52/5.76 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % frac_less
% 5.52/5.76 thf(fact_2346_frac__le,axiom,
% 5.52/5.76 ! [Y2: real,X2: real,W: real,Z: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.76 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.52/5.76 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.52/5.76 => ( ( ord_less_eq_real @ W @ Z )
% 5.52/5.76 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % frac_le
% 5.52/5.76 thf(fact_2347_frac__le,axiom,
% 5.52/5.76 ! [Y2: rat,X2: rat,W: rat,Z: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.52/5.76 => ( ( ord_less_eq_rat @ X2 @ Y2 )
% 5.52/5.76 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.52/5.76 => ( ( ord_less_eq_rat @ W @ Z )
% 5.52/5.76 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % frac_le
% 5.52/5.76 thf(fact_2348_sum__squares__ge__zero,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_squares_ge_zero
% 5.52/5.76 thf(fact_2349_sum__squares__ge__zero,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y2 @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_squares_ge_zero
% 5.52/5.76 thf(fact_2350_sum__squares__ge__zero,axiom,
% 5.52/5.76 ! [X2: int,Y2: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y2 @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_squares_ge_zero
% 5.52/5.76 thf(fact_2351_sum__squares__le__zero__iff,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) ) @ zero_zero_real )
% 5.52/5.76 = ( ( X2 = zero_zero_real )
% 5.52/5.76 & ( Y2 = zero_zero_real ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_squares_le_zero_iff
% 5.52/5.76 thf(fact_2352_sum__squares__le__zero__iff,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y2 @ Y2 ) ) @ zero_zero_rat )
% 5.52/5.76 = ( ( X2 = zero_zero_rat )
% 5.52/5.76 & ( Y2 = zero_zero_rat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_squares_le_zero_iff
% 5.52/5.76 thf(fact_2353_sum__squares__le__zero__iff,axiom,
% 5.52/5.76 ! [X2: int,Y2: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y2 @ Y2 ) ) @ zero_zero_int )
% 5.52/5.76 = ( ( X2 = zero_zero_int )
% 5.52/5.76 & ( Y2 = zero_zero_int ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_squares_le_zero_iff
% 5.52/5.76 thf(fact_2354_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I2_J,axiom,
% 5.52/5.76 ! [Uv: $o,Uw: $o,N: nat] :
% 5.52/5.76 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 5.52/5.76 = one_one_nat ) ).
% 5.52/5.76
% 5.52/5.76 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(2)
% 5.52/5.76 thf(fact_2355_not__sum__squares__lt__zero,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) ) @ zero_zero_real ) ).
% 5.52/5.76
% 5.52/5.76 % not_sum_squares_lt_zero
% 5.52/5.76 thf(fact_2356_not__sum__squares__lt__zero,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y2 @ Y2 ) ) @ zero_zero_rat ) ).
% 5.52/5.76
% 5.52/5.76 % not_sum_squares_lt_zero
% 5.52/5.76 thf(fact_2357_not__sum__squares__lt__zero,axiom,
% 5.52/5.76 ! [X2: int,Y2: int] :
% 5.52/5.76 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y2 @ Y2 ) ) @ zero_zero_int ) ).
% 5.52/5.76
% 5.52/5.76 % not_sum_squares_lt_zero
% 5.52/5.76 thf(fact_2358_sum__squares__gt__zero__iff,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) ) )
% 5.52/5.76 = ( ( X2 != zero_zero_real )
% 5.52/5.76 | ( Y2 != zero_zero_real ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_squares_gt_zero_iff
% 5.52/5.76 thf(fact_2359_sum__squares__gt__zero__iff,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y2 @ Y2 ) ) )
% 5.52/5.76 = ( ( X2 != zero_zero_rat )
% 5.52/5.76 | ( Y2 != zero_zero_rat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_squares_gt_zero_iff
% 5.52/5.76 thf(fact_2360_sum__squares__gt__zero__iff,axiom,
% 5.52/5.76 ! [X2: int,Y2: int] :
% 5.52/5.76 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y2 @ Y2 ) ) )
% 5.52/5.76 = ( ( X2 != zero_zero_int )
% 5.52/5.76 | ( Y2 != zero_zero_int ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_squares_gt_zero_iff
% 5.52/5.76 thf(fact_2361_power__less__imp__less__base,axiom,
% 5.52/5.76 ! [A: real,N: nat,B: real] :
% 5.52/5.76 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.76 => ( ord_less_real @ A @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_less_imp_less_base
% 5.52/5.76 thf(fact_2362_power__less__imp__less__base,axiom,
% 5.52/5.76 ! [A: rat,N: nat,B: rat] :
% 5.52/5.76 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.76 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_less_imp_less_base
% 5.52/5.76 thf(fact_2363_power__less__imp__less__base,axiom,
% 5.52/5.76 ! [A: nat,N: nat,B: nat] :
% 5.52/5.76 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.52/5.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.52/5.76 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_less_imp_less_base
% 5.52/5.76 thf(fact_2364_power__less__imp__less__base,axiom,
% 5.52/5.76 ! [A: int,N: nat,B: int] :
% 5.52/5.76 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.76 => ( ord_less_int @ A @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_less_imp_less_base
% 5.52/5.76 thf(fact_2365_zero__less__two,axiom,
% 5.52/5.76 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.52/5.76
% 5.52/5.76 % zero_less_two
% 5.52/5.76 thf(fact_2366_zero__less__two,axiom,
% 5.52/5.76 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.52/5.76
% 5.52/5.76 % zero_less_two
% 5.52/5.76 thf(fact_2367_zero__less__two,axiom,
% 5.52/5.76 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.52/5.76
% 5.52/5.76 % zero_less_two
% 5.52/5.76 thf(fact_2368_zero__less__two,axiom,
% 5.52/5.76 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.52/5.76
% 5.52/5.76 % zero_less_two
% 5.52/5.76 thf(fact_2369_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.52/5.76 ! [C: nat,A: nat,B: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.76 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.52/5.76 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.52/5.76 thf(fact_2370_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.52/5.76 ! [C: int,A: int,B: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.76 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.52/5.76 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.52/5.76 thf(fact_2371_divide__strict__left__mono__neg,axiom,
% 5.52/5.76 ! [A: real,B: real,C: real] :
% 5.52/5.76 ( ( ord_less_real @ A @ B )
% 5.52/5.76 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.52/5.76 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_strict_left_mono_neg
% 5.52/5.76 thf(fact_2372_divide__strict__left__mono__neg,axiom,
% 5.52/5.76 ! [A: rat,B: rat,C: rat] :
% 5.52/5.76 ( ( ord_less_rat @ A @ B )
% 5.52/5.76 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.52/5.76 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_strict_left_mono_neg
% 5.52/5.76 thf(fact_2373_divide__strict__left__mono,axiom,
% 5.52/5.76 ! [B: real,A: real,C: real] :
% 5.52/5.76 ( ( ord_less_real @ B @ A )
% 5.52/5.76 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.52/5.76 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_strict_left_mono
% 5.52/5.76 thf(fact_2374_divide__strict__left__mono,axiom,
% 5.52/5.76 ! [B: rat,A: rat,C: rat] :
% 5.52/5.76 ( ( ord_less_rat @ B @ A )
% 5.52/5.76 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.52/5.76 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_strict_left_mono
% 5.52/5.76 thf(fact_2375_mult__imp__less__div__pos,axiom,
% 5.52/5.76 ! [Y2: real,Z: real,X2: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.76 => ( ( ord_less_real @ ( times_times_real @ Z @ Y2 ) @ X2 )
% 5.52/5.76 => ( ord_less_real @ Z @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_imp_less_div_pos
% 5.52/5.76 thf(fact_2376_mult__imp__less__div__pos,axiom,
% 5.52/5.76 ! [Y2: rat,Z: rat,X2: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.52/5.76 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y2 ) @ X2 )
% 5.52/5.76 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_imp_less_div_pos
% 5.52/5.76 thf(fact_2377_mult__imp__div__pos__less,axiom,
% 5.52/5.76 ! [Y2: real,X2: real,Z: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.76 => ( ( ord_less_real @ X2 @ ( times_times_real @ Z @ Y2 ) )
% 5.52/5.76 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_imp_div_pos_less
% 5.52/5.76 thf(fact_2378_mult__imp__div__pos__less,axiom,
% 5.52/5.76 ! [Y2: rat,X2: rat,Z: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.52/5.76 => ( ( ord_less_rat @ X2 @ ( times_times_rat @ Z @ Y2 ) )
% 5.52/5.76 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_imp_div_pos_less
% 5.52/5.76 thf(fact_2379_pos__less__divide__eq,axiom,
% 5.52/5.76 ! [C: real,A: real,B: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.52/5.76 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % pos_less_divide_eq
% 5.52/5.76 thf(fact_2380_pos__less__divide__eq,axiom,
% 5.52/5.76 ! [C: rat,A: rat,B: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.76 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % pos_less_divide_eq
% 5.52/5.76 thf(fact_2381_pos__divide__less__eq,axiom,
% 5.52/5.76 ! [C: real,B: real,A: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.52/5.76 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % pos_divide_less_eq
% 5.52/5.76 thf(fact_2382_pos__divide__less__eq,axiom,
% 5.52/5.76 ! [C: rat,B: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.52/5.76 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % pos_divide_less_eq
% 5.52/5.76 thf(fact_2383_neg__less__divide__eq,axiom,
% 5.52/5.76 ! [C: real,A: real,B: real] :
% 5.52/5.76 ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.52/5.76 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % neg_less_divide_eq
% 5.52/5.76 thf(fact_2384_neg__less__divide__eq,axiom,
% 5.52/5.76 ! [C: rat,A: rat,B: rat] :
% 5.52/5.76 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.76 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % neg_less_divide_eq
% 5.52/5.76 thf(fact_2385_neg__divide__less__eq,axiom,
% 5.52/5.76 ! [C: real,B: real,A: real] :
% 5.52/5.76 ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.52/5.76 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % neg_divide_less_eq
% 5.52/5.76 thf(fact_2386_neg__divide__less__eq,axiom,
% 5.52/5.76 ! [C: rat,B: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.52/5.76 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % neg_divide_less_eq
% 5.52/5.76 thf(fact_2387_less__divide__eq,axiom,
% 5.52/5.76 ! [A: real,B: real,C: real] :
% 5.52/5.76 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % less_divide_eq
% 5.52/5.76 thf(fact_2388_less__divide__eq,axiom,
% 5.52/5.76 ! [A: rat,B: rat,C: rat] :
% 5.52/5.76 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % less_divide_eq
% 5.52/5.76 thf(fact_2389_divide__less__eq,axiom,
% 5.52/5.76 ! [B: real,C: real,A: real] :
% 5.52/5.76 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_less_eq
% 5.52/5.76 thf(fact_2390_divide__less__eq,axiom,
% 5.52/5.76 ! [B: rat,C: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_less_eq
% 5.52/5.76 thf(fact_2391_less__divide__eq__1,axiom,
% 5.52/5.76 ! [B: real,A: real] :
% 5.52/5.76 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.76 & ( ord_less_real @ A @ B ) )
% 5.52/5.76 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.76 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % less_divide_eq_1
% 5.52/5.76 thf(fact_2392_less__divide__eq__1,axiom,
% 5.52/5.76 ! [B: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.76 & ( ord_less_rat @ A @ B ) )
% 5.52/5.76 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.76 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % less_divide_eq_1
% 5.52/5.76 thf(fact_2393_divide__less__eq__1,axiom,
% 5.52/5.76 ! [B: real,A: real] :
% 5.52/5.76 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.76 & ( ord_less_real @ B @ A ) )
% 5.52/5.76 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.76 & ( ord_less_real @ A @ B ) )
% 5.52/5.76 | ( A = zero_zero_real ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_less_eq_1
% 5.52/5.76 thf(fact_2394_divide__less__eq__1,axiom,
% 5.52/5.76 ! [B: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.76 & ( ord_less_rat @ B @ A ) )
% 5.52/5.76 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.76 & ( ord_less_rat @ A @ B ) )
% 5.52/5.76 | ( A = zero_zero_rat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_less_eq_1
% 5.52/5.76 thf(fact_2395_power__le__one,axiom,
% 5.52/5.76 ! [A: real,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.76 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.52/5.76 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_le_one
% 5.52/5.76 thf(fact_2396_power__le__one,axiom,
% 5.52/5.76 ! [A: rat,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.76 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_le_one
% 5.52/5.76 thf(fact_2397_power__le__one,axiom,
% 5.52/5.76 ! [A: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.76 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.52/5.76 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_le_one
% 5.52/5.76 thf(fact_2398_power__le__one,axiom,
% 5.52/5.76 ! [A: int,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.76 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.52/5.76 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_le_one
% 5.52/5.76 thf(fact_2399_divide__eq__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [B: complex,C: complex,W: num] :
% 5.52/5.76 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.52/5.76 = ( numera6690914467698888265omplex @ W ) )
% 5.52/5.76 = ( ( ( C != zero_zero_complex )
% 5.52/5.76 => ( B
% 5.52/5.76 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.52/5.76 & ( ( C = zero_zero_complex )
% 5.52/5.76 => ( ( numera6690914467698888265omplex @ W )
% 5.52/5.76 = zero_zero_complex ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_eq_eq_numeral(1)
% 5.52/5.76 thf(fact_2400_divide__eq__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [B: real,C: real,W: num] :
% 5.52/5.76 ( ( ( divide_divide_real @ B @ C )
% 5.52/5.76 = ( numeral_numeral_real @ W ) )
% 5.52/5.76 = ( ( ( C != zero_zero_real )
% 5.52/5.76 => ( B
% 5.52/5.76 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.52/5.76 & ( ( C = zero_zero_real )
% 5.52/5.76 => ( ( numeral_numeral_real @ W )
% 5.52/5.76 = zero_zero_real ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_eq_eq_numeral(1)
% 5.52/5.76 thf(fact_2401_divide__eq__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [B: rat,C: rat,W: num] :
% 5.52/5.76 ( ( ( divide_divide_rat @ B @ C )
% 5.52/5.76 = ( numeral_numeral_rat @ W ) )
% 5.52/5.76 = ( ( ( C != zero_zero_rat )
% 5.52/5.76 => ( B
% 5.52/5.76 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.52/5.76 & ( ( C = zero_zero_rat )
% 5.52/5.76 => ( ( numeral_numeral_rat @ W )
% 5.52/5.76 = zero_zero_rat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_eq_eq_numeral(1)
% 5.52/5.76 thf(fact_2402_eq__divide__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [W: num,B: complex,C: complex] :
% 5.52/5.76 ( ( ( numera6690914467698888265omplex @ W )
% 5.52/5.76 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.52/5.76 = ( ( ( C != zero_zero_complex )
% 5.52/5.76 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.52/5.76 = B ) )
% 5.52/5.76 & ( ( C = zero_zero_complex )
% 5.52/5.76 => ( ( numera6690914467698888265omplex @ W )
% 5.52/5.76 = zero_zero_complex ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % eq_divide_eq_numeral(1)
% 5.52/5.76 thf(fact_2403_eq__divide__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [W: num,B: real,C: real] :
% 5.52/5.76 ( ( ( numeral_numeral_real @ W )
% 5.52/5.76 = ( divide_divide_real @ B @ C ) )
% 5.52/5.76 = ( ( ( C != zero_zero_real )
% 5.52/5.76 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.52/5.76 = B ) )
% 5.52/5.76 & ( ( C = zero_zero_real )
% 5.52/5.76 => ( ( numeral_numeral_real @ W )
% 5.52/5.76 = zero_zero_real ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % eq_divide_eq_numeral(1)
% 5.52/5.76 thf(fact_2404_eq__divide__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [W: num,B: rat,C: rat] :
% 5.52/5.76 ( ( ( numeral_numeral_rat @ W )
% 5.52/5.76 = ( divide_divide_rat @ B @ C ) )
% 5.52/5.76 = ( ( ( C != zero_zero_rat )
% 5.52/5.76 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.52/5.76 = B ) )
% 5.52/5.76 & ( ( C = zero_zero_rat )
% 5.52/5.76 => ( ( numeral_numeral_rat @ W )
% 5.52/5.76 = zero_zero_rat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % eq_divide_eq_numeral(1)
% 5.52/5.76 thf(fact_2405_add__divide__eq__if__simps_I2_J,axiom,
% 5.52/5.76 ! [Z: complex,A: complex,B: complex] :
% 5.52/5.76 ( ( ( Z = zero_zero_complex )
% 5.52/5.76 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.52/5.76 = B ) )
% 5.52/5.76 & ( ( Z != zero_zero_complex )
% 5.52/5.76 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.52/5.76 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_divide_eq_if_simps(2)
% 5.52/5.76 thf(fact_2406_add__divide__eq__if__simps_I2_J,axiom,
% 5.52/5.76 ! [Z: real,A: real,B: real] :
% 5.52/5.76 ( ( ( Z = zero_zero_real )
% 5.52/5.76 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.52/5.76 = B ) )
% 5.52/5.76 & ( ( Z != zero_zero_real )
% 5.52/5.76 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.52/5.76 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_divide_eq_if_simps(2)
% 5.52/5.76 thf(fact_2407_add__divide__eq__if__simps_I2_J,axiom,
% 5.52/5.76 ! [Z: rat,A: rat,B: rat] :
% 5.52/5.76 ( ( ( Z = zero_zero_rat )
% 5.52/5.76 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.52/5.76 = B ) )
% 5.52/5.76 & ( ( Z != zero_zero_rat )
% 5.52/5.76 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.52/5.76 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_divide_eq_if_simps(2)
% 5.52/5.76 thf(fact_2408_add__divide__eq__if__simps_I1_J,axiom,
% 5.52/5.76 ! [Z: complex,A: complex,B: complex] :
% 5.52/5.76 ( ( ( Z = zero_zero_complex )
% 5.52/5.76 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.52/5.76 = A ) )
% 5.52/5.76 & ( ( Z != zero_zero_complex )
% 5.52/5.76 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.52/5.76 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_divide_eq_if_simps(1)
% 5.52/5.76 thf(fact_2409_add__divide__eq__if__simps_I1_J,axiom,
% 5.52/5.76 ! [Z: real,A: real,B: real] :
% 5.52/5.76 ( ( ( Z = zero_zero_real )
% 5.52/5.76 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.52/5.76 = A ) )
% 5.52/5.76 & ( ( Z != zero_zero_real )
% 5.52/5.76 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.52/5.76 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_divide_eq_if_simps(1)
% 5.52/5.76 thf(fact_2410_add__divide__eq__if__simps_I1_J,axiom,
% 5.52/5.76 ! [Z: rat,A: rat,B: rat] :
% 5.52/5.76 ( ( ( Z = zero_zero_rat )
% 5.52/5.76 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.52/5.76 = A ) )
% 5.52/5.76 & ( ( Z != zero_zero_rat )
% 5.52/5.76 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.52/5.76 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_divide_eq_if_simps(1)
% 5.52/5.76 thf(fact_2411_add__frac__eq,axiom,
% 5.52/5.76 ! [Y2: complex,Z: complex,X2: complex,W: complex] :
% 5.52/5.76 ( ( Y2 != zero_zero_complex )
% 5.52/5.76 => ( ( Z != zero_zero_complex )
% 5.52/5.76 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y2 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.52/5.76 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W @ Y2 ) ) @ ( times_times_complex @ Y2 @ Z ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_frac_eq
% 5.52/5.76 thf(fact_2412_add__frac__eq,axiom,
% 5.52/5.76 ! [Y2: real,Z: real,X2: real,W: real] :
% 5.52/5.76 ( ( Y2 != zero_zero_real )
% 5.52/5.76 => ( ( Z != zero_zero_real )
% 5.52/5.76 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 5.52/5.76 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_frac_eq
% 5.52/5.76 thf(fact_2413_add__frac__eq,axiom,
% 5.52/5.76 ! [Y2: rat,Z: rat,X2: rat,W: rat] :
% 5.52/5.76 ( ( Y2 != zero_zero_rat )
% 5.52/5.76 => ( ( Z != zero_zero_rat )
% 5.52/5.76 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.52/5.76 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_frac_eq
% 5.52/5.76 thf(fact_2414_add__frac__num,axiom,
% 5.52/5.76 ! [Y2: complex,X2: complex,Z: complex] :
% 5.52/5.76 ( ( Y2 != zero_zero_complex )
% 5.52/5.76 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y2 ) @ Z )
% 5.52/5.76 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_frac_num
% 5.52/5.76 thf(fact_2415_add__frac__num,axiom,
% 5.52/5.76 ! [Y2: real,X2: real,Z: real] :
% 5.52/5.76 ( ( Y2 != zero_zero_real )
% 5.52/5.76 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y2 ) @ Z )
% 5.52/5.76 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_frac_num
% 5.52/5.76 thf(fact_2416_add__frac__num,axiom,
% 5.52/5.76 ! [Y2: rat,X2: rat,Z: rat] :
% 5.52/5.76 ( ( Y2 != zero_zero_rat )
% 5.52/5.76 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ Z )
% 5.52/5.76 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_frac_num
% 5.52/5.76 thf(fact_2417_add__num__frac,axiom,
% 5.52/5.76 ! [Y2: complex,Z: complex,X2: complex] :
% 5.52/5.76 ( ( Y2 != zero_zero_complex )
% 5.52/5.76 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X2 @ Y2 ) )
% 5.52/5.76 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_num_frac
% 5.52/5.76 thf(fact_2418_add__num__frac,axiom,
% 5.52/5.76 ! [Y2: real,Z: real,X2: real] :
% 5.52/5.76 ( ( Y2 != zero_zero_real )
% 5.52/5.76 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.52/5.76 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_num_frac
% 5.52/5.76 thf(fact_2419_add__num__frac,axiom,
% 5.52/5.76 ! [Y2: rat,Z: rat,X2: rat] :
% 5.52/5.76 ( ( Y2 != zero_zero_rat )
% 5.52/5.76 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X2 @ Y2 ) )
% 5.52/5.76 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_num_frac
% 5.52/5.76 thf(fact_2420_add__divide__eq__iff,axiom,
% 5.52/5.76 ! [Z: complex,X2: complex,Y2: complex] :
% 5.52/5.76 ( ( Z != zero_zero_complex )
% 5.52/5.76 => ( ( plus_plus_complex @ X2 @ ( divide1717551699836669952omplex @ Y2 @ Z ) )
% 5.52/5.76 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_divide_eq_iff
% 5.52/5.76 thf(fact_2421_add__divide__eq__iff,axiom,
% 5.52/5.76 ! [Z: real,X2: real,Y2: real] :
% 5.52/5.76 ( ( Z != zero_zero_real )
% 5.52/5.76 => ( ( plus_plus_real @ X2 @ ( divide_divide_real @ Y2 @ Z ) )
% 5.52/5.76 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_divide_eq_iff
% 5.52/5.76 thf(fact_2422_add__divide__eq__iff,axiom,
% 5.52/5.76 ! [Z: rat,X2: rat,Y2: rat] :
% 5.52/5.76 ( ( Z != zero_zero_rat )
% 5.52/5.76 => ( ( plus_plus_rat @ X2 @ ( divide_divide_rat @ Y2 @ Z ) )
% 5.52/5.76 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_divide_eq_iff
% 5.52/5.76 thf(fact_2423_divide__add__eq__iff,axiom,
% 5.52/5.76 ! [Z: complex,X2: complex,Y2: complex] :
% 5.52/5.76 ( ( Z != zero_zero_complex )
% 5.52/5.76 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y2 )
% 5.52/5.76 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_add_eq_iff
% 5.52/5.76 thf(fact_2424_divide__add__eq__iff,axiom,
% 5.52/5.76 ! [Z: real,X2: real,Y2: real] :
% 5.52/5.76 ( ( Z != zero_zero_real )
% 5.52/5.76 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Z ) @ Y2 )
% 5.52/5.76 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_add_eq_iff
% 5.52/5.76 thf(fact_2425_divide__add__eq__iff,axiom,
% 5.52/5.76 ! [Z: rat,X2: rat,Y2: rat] :
% 5.52/5.76 ( ( Z != zero_zero_rat )
% 5.52/5.76 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y2 )
% 5.52/5.76 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_add_eq_iff
% 5.52/5.76 thf(fact_2426_power__le__imp__le__base,axiom,
% 5.52/5.76 ! [A: real,N: nat,B: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.76 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_le_imp_le_base
% 5.52/5.76 thf(fact_2427_power__le__imp__le__base,axiom,
% 5.52/5.76 ! [A: rat,N: nat,B: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.76 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_le_imp_le_base
% 5.52/5.76 thf(fact_2428_power__le__imp__le__base,axiom,
% 5.52/5.76 ! [A: nat,N: nat,B: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.52/5.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.52/5.76 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_le_imp_le_base
% 5.52/5.76 thf(fact_2429_power__le__imp__le__base,axiom,
% 5.52/5.76 ! [A: int,N: nat,B: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.76 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_le_imp_le_base
% 5.52/5.76 thf(fact_2430_power__inject__base,axiom,
% 5.52/5.76 ! [A: real,N: nat,B: real] :
% 5.52/5.76 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 5.52/5.76 = ( power_power_real @ B @ ( suc @ N ) ) )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.76 => ( A = B ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_inject_base
% 5.52/5.76 thf(fact_2431_power__inject__base,axiom,
% 5.52/5.76 ! [A: rat,N: nat,B: rat] :
% 5.52/5.76 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.52/5.76 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.76 => ( A = B ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_inject_base
% 5.52/5.76 thf(fact_2432_power__inject__base,axiom,
% 5.52/5.76 ! [A: nat,N: nat,B: nat] :
% 5.52/5.76 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.52/5.76 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.52/5.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.52/5.76 => ( A = B ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_inject_base
% 5.52/5.76 thf(fact_2433_power__inject__base,axiom,
% 5.52/5.76 ! [A: int,N: nat,B: int] :
% 5.52/5.76 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 5.52/5.76 = ( power_power_int @ B @ ( suc @ N ) ) )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.76 => ( A = B ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_inject_base
% 5.52/5.76 thf(fact_2434_div__add__self1,axiom,
% 5.52/5.76 ! [B: nat,A: nat] :
% 5.52/5.76 ( ( B != zero_zero_nat )
% 5.52/5.76 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.52/5.76 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_add_self1
% 5.52/5.76 thf(fact_2435_div__add__self1,axiom,
% 5.52/5.76 ! [B: int,A: int] :
% 5.52/5.76 ( ( B != zero_zero_int )
% 5.52/5.76 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.52/5.76 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_add_self1
% 5.52/5.76 thf(fact_2436_div__add__self2,axiom,
% 5.52/5.76 ! [B: nat,A: nat] :
% 5.52/5.76 ( ( B != zero_zero_nat )
% 5.52/5.76 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.52/5.76 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_add_self2
% 5.52/5.76 thf(fact_2437_div__add__self2,axiom,
% 5.52/5.76 ! [B: int,A: int] :
% 5.52/5.76 ( ( B != zero_zero_int )
% 5.52/5.76 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.52/5.76 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_add_self2
% 5.52/5.76 thf(fact_2438_divide__diff__eq__iff,axiom,
% 5.52/5.76 ! [Z: complex,X2: complex,Y2: complex] :
% 5.52/5.76 ( ( Z != zero_zero_complex )
% 5.52/5.76 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y2 )
% 5.52/5.76 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_diff_eq_iff
% 5.52/5.76 thf(fact_2439_divide__diff__eq__iff,axiom,
% 5.52/5.76 ! [Z: real,X2: real,Y2: real] :
% 5.52/5.76 ( ( Z != zero_zero_real )
% 5.52/5.76 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Z ) @ Y2 )
% 5.52/5.76 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_diff_eq_iff
% 5.52/5.76 thf(fact_2440_divide__diff__eq__iff,axiom,
% 5.52/5.76 ! [Z: rat,X2: rat,Y2: rat] :
% 5.52/5.76 ( ( Z != zero_zero_rat )
% 5.52/5.76 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y2 )
% 5.52/5.76 = ( divide_divide_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_diff_eq_iff
% 5.52/5.76 thf(fact_2441_diff__divide__eq__iff,axiom,
% 5.52/5.76 ! [Z: complex,X2: complex,Y2: complex] :
% 5.52/5.76 ( ( Z != zero_zero_complex )
% 5.52/5.76 => ( ( minus_minus_complex @ X2 @ ( divide1717551699836669952omplex @ Y2 @ Z ) )
% 5.52/5.76 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % diff_divide_eq_iff
% 5.52/5.76 thf(fact_2442_diff__divide__eq__iff,axiom,
% 5.52/5.76 ! [Z: real,X2: real,Y2: real] :
% 5.52/5.76 ( ( Z != zero_zero_real )
% 5.52/5.76 => ( ( minus_minus_real @ X2 @ ( divide_divide_real @ Y2 @ Z ) )
% 5.52/5.76 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % diff_divide_eq_iff
% 5.52/5.76 thf(fact_2443_diff__divide__eq__iff,axiom,
% 5.52/5.76 ! [Z: rat,X2: rat,Y2: rat] :
% 5.52/5.76 ( ( Z != zero_zero_rat )
% 5.52/5.76 => ( ( minus_minus_rat @ X2 @ ( divide_divide_rat @ Y2 @ Z ) )
% 5.52/5.76 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % diff_divide_eq_iff
% 5.52/5.76 thf(fact_2444_diff__frac__eq,axiom,
% 5.52/5.76 ! [Y2: complex,Z: complex,X2: complex,W: complex] :
% 5.52/5.76 ( ( Y2 != zero_zero_complex )
% 5.52/5.76 => ( ( Z != zero_zero_complex )
% 5.52/5.76 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Y2 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.52/5.76 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W @ Y2 ) ) @ ( times_times_complex @ Y2 @ Z ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % diff_frac_eq
% 5.52/5.76 thf(fact_2445_diff__frac__eq,axiom,
% 5.52/5.76 ! [Y2: real,Z: real,X2: real,W: real] :
% 5.52/5.76 ( ( Y2 != zero_zero_real )
% 5.52/5.76 => ( ( Z != zero_zero_real )
% 5.52/5.76 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 5.52/5.76 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % diff_frac_eq
% 5.52/5.76 thf(fact_2446_diff__frac__eq,axiom,
% 5.52/5.76 ! [Y2: rat,Z: rat,X2: rat,W: rat] :
% 5.52/5.76 ( ( Y2 != zero_zero_rat )
% 5.52/5.76 => ( ( Z != zero_zero_rat )
% 5.52/5.76 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.52/5.76 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % diff_frac_eq
% 5.52/5.76 thf(fact_2447_add__divide__eq__if__simps_I4_J,axiom,
% 5.52/5.76 ! [Z: complex,A: complex,B: complex] :
% 5.52/5.76 ( ( ( Z = zero_zero_complex )
% 5.52/5.76 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.52/5.76 = A ) )
% 5.52/5.76 & ( ( Z != zero_zero_complex )
% 5.52/5.76 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.52/5.76 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_divide_eq_if_simps(4)
% 5.52/5.76 thf(fact_2448_add__divide__eq__if__simps_I4_J,axiom,
% 5.52/5.76 ! [Z: real,A: real,B: real] :
% 5.52/5.76 ( ( ( Z = zero_zero_real )
% 5.52/5.76 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.52/5.76 = A ) )
% 5.52/5.76 & ( ( Z != zero_zero_real )
% 5.52/5.76 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.52/5.76 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_divide_eq_if_simps(4)
% 5.52/5.76 thf(fact_2449_add__divide__eq__if__simps_I4_J,axiom,
% 5.52/5.76 ! [Z: rat,A: rat,B: rat] :
% 5.52/5.76 ( ( ( Z = zero_zero_rat )
% 5.52/5.76 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.52/5.76 = A ) )
% 5.52/5.76 & ( ( Z != zero_zero_rat )
% 5.52/5.76 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.52/5.76 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_divide_eq_if_simps(4)
% 5.52/5.76 thf(fact_2450_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I1_J,axiom,
% 5.52/5.76 ! [A: $o,B: $o] :
% 5.52/5.76 ( ( vEBT_T_m_a_x_t @ ( vEBT_Leaf @ A @ B ) )
% 5.52/5.76 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(1)
% 5.52/5.76 thf(fact_2451_numeral__1__eq__Suc__0,axiom,
% 5.52/5.76 ( ( numeral_numeral_nat @ one )
% 5.52/5.76 = ( suc @ zero_zero_nat ) ) ).
% 5.52/5.76
% 5.52/5.76 % numeral_1_eq_Suc_0
% 5.52/5.76 thf(fact_2452_num_Osize_I5_J,axiom,
% 5.52/5.76 ! [X23: num] :
% 5.52/5.76 ( ( size_size_num @ ( bit0 @ X23 ) )
% 5.52/5.76 = ( plus_plus_nat @ ( size_size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % num.size(5)
% 5.52/5.76 thf(fact_2453_neq__if__length__neq,axiom,
% 5.52/5.76 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.52/5.76 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.52/5.76 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.52/5.76 => ( Xs2 != Ys ) ) ).
% 5.52/5.76
% 5.52/5.76 % neq_if_length_neq
% 5.52/5.76 thf(fact_2454_neq__if__length__neq,axiom,
% 5.52/5.76 ! [Xs2: list_o,Ys: list_o] :
% 5.52/5.76 ( ( ( size_size_list_o @ Xs2 )
% 5.52/5.76 != ( size_size_list_o @ Ys ) )
% 5.52/5.76 => ( Xs2 != Ys ) ) ).
% 5.52/5.76
% 5.52/5.76 % neq_if_length_neq
% 5.52/5.76 thf(fact_2455_neq__if__length__neq,axiom,
% 5.52/5.76 ! [Xs2: list_nat,Ys: list_nat] :
% 5.52/5.76 ( ( ( size_size_list_nat @ Xs2 )
% 5.52/5.76 != ( size_size_list_nat @ Ys ) )
% 5.52/5.76 => ( Xs2 != Ys ) ) ).
% 5.52/5.76
% 5.52/5.76 % neq_if_length_neq
% 5.52/5.76 thf(fact_2456_Ex__list__of__length,axiom,
% 5.52/5.76 ! [N: nat] :
% 5.52/5.76 ? [Xs3: list_VEBT_VEBT] :
% 5.52/5.76 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.52/5.76 = N ) ).
% 5.52/5.76
% 5.52/5.76 % Ex_list_of_length
% 5.52/5.76 thf(fact_2457_Ex__list__of__length,axiom,
% 5.52/5.76 ! [N: nat] :
% 5.52/5.76 ? [Xs3: list_o] :
% 5.52/5.76 ( ( size_size_list_o @ Xs3 )
% 5.52/5.76 = N ) ).
% 5.52/5.76
% 5.52/5.76 % Ex_list_of_length
% 5.52/5.76 thf(fact_2458_Ex__list__of__length,axiom,
% 5.52/5.76 ! [N: nat] :
% 5.52/5.76 ? [Xs3: list_nat] :
% 5.52/5.76 ( ( size_size_list_nat @ Xs3 )
% 5.52/5.76 = N ) ).
% 5.52/5.76
% 5.52/5.76 % Ex_list_of_length
% 5.52/5.76 thf(fact_2459_ex__least__nat__less,axiom,
% 5.52/5.76 ! [P: nat > $o,N: nat] :
% 5.52/5.76 ( ( P @ N )
% 5.52/5.76 => ( ~ ( P @ zero_zero_nat )
% 5.52/5.76 => ? [K3: nat] :
% 5.52/5.76 ( ( ord_less_nat @ K3 @ N )
% 5.52/5.76 & ! [I3: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ I3 @ K3 )
% 5.52/5.76 => ~ ( P @ I3 ) )
% 5.52/5.76 & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % ex_least_nat_less
% 5.52/5.76 thf(fact_2460_nat__induct__non__zero,axiom,
% 5.52/5.76 ! [N: nat,P: nat > $o] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ( P @ one_one_nat )
% 5.52/5.76 => ( ! [N2: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.52/5.76 => ( ( P @ N2 )
% 5.52/5.76 => ( P @ ( suc @ N2 ) ) ) )
% 5.52/5.76 => ( P @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % nat_induct_non_zero
% 5.52/5.76 thf(fact_2461_num_Osize_I6_J,axiom,
% 5.52/5.76 ! [X32: num] :
% 5.52/5.76 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.52/5.76 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % num.size(6)
% 5.52/5.76 thf(fact_2462_diff__Suc__less,axiom,
% 5.52/5.76 ! [N: nat,I: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 5.52/5.76
% 5.52/5.76 % diff_Suc_less
% 5.52/5.76 thf(fact_2463_one__less__mult,axiom,
% 5.52/5.76 ! [N: nat,M: nat] :
% 5.52/5.76 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.52/5.76 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.52/5.76 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % one_less_mult
% 5.52/5.76 thf(fact_2464_n__less__m__mult__n,axiom,
% 5.52/5.76 ! [N: nat,M: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.52/5.76 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % n_less_m_mult_n
% 5.52/5.76 thf(fact_2465_n__less__n__mult__m,axiom,
% 5.52/5.76 ! [N: nat,M: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.52/5.76 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % n_less_n_mult_m
% 5.52/5.76 thf(fact_2466_nat__mult__le__cancel1,axiom,
% 5.52/5.76 ! [K: nat,M: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.76 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.52/5.76 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % nat_mult_le_cancel1
% 5.52/5.76 thf(fact_2467_nat__diff__split,axiom,
% 5.52/5.76 ! [P: nat > $o,A: nat,B: nat] :
% 5.52/5.76 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.52/5.76 = ( ( ( ord_less_nat @ A @ B )
% 5.52/5.76 => ( P @ zero_zero_nat ) )
% 5.52/5.76 & ! [D: nat] :
% 5.52/5.76 ( ( A
% 5.52/5.76 = ( plus_plus_nat @ B @ D ) )
% 5.52/5.76 => ( P @ D ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % nat_diff_split
% 5.52/5.76 thf(fact_2468_nat__diff__split__asm,axiom,
% 5.52/5.76 ! [P: nat > $o,A: nat,B: nat] :
% 5.52/5.76 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.52/5.76 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.52/5.76 & ~ ( P @ zero_zero_nat ) )
% 5.52/5.76 | ? [D: nat] :
% 5.52/5.76 ( ( A
% 5.52/5.76 = ( plus_plus_nat @ B @ D ) )
% 5.52/5.76 & ~ ( P @ D ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % nat_diff_split_asm
% 5.52/5.76 thf(fact_2469_div__greater__zero__iff,axiom,
% 5.52/5.76 ! [M: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 5.52/5.76 = ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.76 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_greater_zero_iff
% 5.52/5.76 thf(fact_2470_div__le__mono2,axiom,
% 5.52/5.76 ! [M: nat,N: nat,K: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.76 => ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.76 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_le_mono2
% 5.52/5.76 thf(fact_2471_power__gt__expt,axiom,
% 5.52/5.76 ! [N: nat,K: nat] :
% 5.52/5.76 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.52/5.76 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_gt_expt
% 5.52/5.76 thf(fact_2472_nat__one__le__power,axiom,
% 5.52/5.76 ! [I: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 5.52/5.76 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % nat_one_le_power
% 5.52/5.76 thf(fact_2473_div__eq__dividend__iff,axiom,
% 5.52/5.76 ! [M: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.76 => ( ( ( divide_divide_nat @ M @ N )
% 5.52/5.76 = M )
% 5.52/5.76 = ( N = one_one_nat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_eq_dividend_iff
% 5.52/5.76 thf(fact_2474_div__less__dividend,axiom,
% 5.52/5.76 ! [N: nat,M: nat] :
% 5.52/5.76 ( ( ord_less_nat @ one_one_nat @ N )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.76 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_less_dividend
% 5.52/5.76 thf(fact_2475_div__less__iff__less__mult,axiom,
% 5.52/5.76 ! [Q2: nat,M: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.52/5.76 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 5.52/5.76 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_less_iff_less_mult
% 5.52/5.76 thf(fact_2476_nat__mult__div__cancel1,axiom,
% 5.52/5.76 ! [K: nat,M: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.76 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.52/5.76 = ( divide_divide_nat @ M @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % nat_mult_div_cancel1
% 5.52/5.76 thf(fact_2477_vebt__insert_Osimps_I3_J,axiom,
% 5.52/5.76 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.52/5.76 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X2 )
% 5.52/5.76 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) ).
% 5.52/5.76
% 5.52/5.76 % vebt_insert.simps(3)
% 5.52/5.76 thf(fact_2478_vebt__member_Osimps_I3_J,axiom,
% 5.52/5.76 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.52/5.76 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 ) ).
% 5.52/5.76
% 5.52/5.76 % vebt_member.simps(3)
% 5.52/5.76 thf(fact_2479_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Oelims,axiom,
% 5.52/5.76 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.52/5.76 ( ( ( vEBT_T_m_i_n_t @ X2 )
% 5.52/5.76 = Y2 )
% 5.52/5.76 => ( ! [A3: $o] :
% 5.52/5.76 ( ? [B2: $o] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.76 => ( Y2
% 5.52/5.76 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ A3 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.52/5.76 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.76 => ( Y2 != one_one_nat ) )
% 5.52/5.76 => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.76 => ( Y2 != one_one_nat ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.elims
% 5.52/5.76 thf(fact_2480_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.52/5.76 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.52/5.76 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.52/5.76
% 5.52/5.76 % VEBT_internal.membermima.simps(2)
% 5.52/5.76 thf(fact_2481_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Ocases,axiom,
% 5.52/5.76 ! [X2: vEBT_VEBT] :
% 5.52/5.76 ( ! [A3: $o,B2: $o] :
% 5.52/5.76 ( X2
% 5.52/5.76 != ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.76 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.76 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.cases
% 5.52/5.76 thf(fact_2482_mult__le__cancel__left1,axiom,
% 5.52/5.76 ! [C: real,B: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.52/5.76 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_cancel_left1
% 5.52/5.76 thf(fact_2483_mult__le__cancel__left1,axiom,
% 5.52/5.76 ! [C: rat,B: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.52/5.76 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_cancel_left1
% 5.52/5.76 thf(fact_2484_mult__le__cancel__left1,axiom,
% 5.52/5.76 ! [C: int,B: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.52/5.76 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.76 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.52/5.76 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.52/5.76 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_cancel_left1
% 5.52/5.76 thf(fact_2485_mult__le__cancel__left2,axiom,
% 5.52/5.76 ! [C: real,A: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.52/5.76 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_cancel_left2
% 5.52/5.76 thf(fact_2486_mult__le__cancel__left2,axiom,
% 5.52/5.76 ! [C: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.52/5.76 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_cancel_left2
% 5.52/5.76 thf(fact_2487_mult__le__cancel__left2,axiom,
% 5.52/5.76 ! [C: int,A: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.52/5.76 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.76 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.52/5.76 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.52/5.76 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_cancel_left2
% 5.52/5.76 thf(fact_2488_mult__le__cancel__right1,axiom,
% 5.52/5.76 ! [C: real,B: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.52/5.76 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_cancel_right1
% 5.52/5.76 thf(fact_2489_mult__le__cancel__right1,axiom,
% 5.52/5.76 ! [C: rat,B: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.52/5.76 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_cancel_right1
% 5.52/5.76 thf(fact_2490_mult__le__cancel__right1,axiom,
% 5.52/5.76 ! [C: int,B: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.76 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.52/5.76 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.52/5.76 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_cancel_right1
% 5.52/5.76 thf(fact_2491_mult__le__cancel__right2,axiom,
% 5.52/5.76 ! [A: real,C: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.52/5.76 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_cancel_right2
% 5.52/5.76 thf(fact_2492_mult__le__cancel__right2,axiom,
% 5.52/5.76 ! [A: rat,C: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.52/5.76 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_cancel_right2
% 5.52/5.76 thf(fact_2493_mult__le__cancel__right2,axiom,
% 5.52/5.76 ! [A: int,C: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.52/5.76 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.52/5.76 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.52/5.76 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.52/5.76 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_le_cancel_right2
% 5.52/5.76 thf(fact_2494_mult__less__cancel__left1,axiom,
% 5.52/5.76 ! [C: real,B: real] :
% 5.52/5.76 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.52/5.76 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_real @ one_one_real @ B ) )
% 5.52/5.76 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_less_cancel_left1
% 5.52/5.76 thf(fact_2495_mult__less__cancel__left1,axiom,
% 5.52/5.76 ! [C: rat,B: rat] :
% 5.52/5.76 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.52/5.76 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.52/5.76 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_less_cancel_left1
% 5.52/5.76 thf(fact_2496_mult__less__cancel__left1,axiom,
% 5.52/5.76 ! [C: int,B: int] :
% 5.52/5.76 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.52/5.76 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.76 => ( ord_less_int @ one_one_int @ B ) )
% 5.52/5.76 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.52/5.76 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_less_cancel_left1
% 5.52/5.76 thf(fact_2497_mult__less__cancel__left2,axiom,
% 5.52/5.76 ! [C: real,A: real] :
% 5.52/5.76 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.52/5.76 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_real @ A @ one_one_real ) )
% 5.52/5.76 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_less_cancel_left2
% 5.52/5.76 thf(fact_2498_mult__less__cancel__left2,axiom,
% 5.52/5.76 ! [C: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.52/5.76 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.52/5.76 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_less_cancel_left2
% 5.52/5.76 thf(fact_2499_mult__less__cancel__left2,axiom,
% 5.52/5.76 ! [C: int,A: int] :
% 5.52/5.76 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.52/5.76 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.76 => ( ord_less_int @ A @ one_one_int ) )
% 5.52/5.76 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.52/5.76 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_less_cancel_left2
% 5.52/5.76 thf(fact_2500_mult__less__cancel__right1,axiom,
% 5.52/5.76 ! [C: real,B: real] :
% 5.52/5.76 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_real @ one_one_real @ B ) )
% 5.52/5.76 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_less_cancel_right1
% 5.52/5.76 thf(fact_2501_mult__less__cancel__right1,axiom,
% 5.52/5.76 ! [C: rat,B: rat] :
% 5.52/5.76 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.52/5.76 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_less_cancel_right1
% 5.52/5.76 thf(fact_2502_mult__less__cancel__right1,axiom,
% 5.52/5.76 ! [C: int,B: int] :
% 5.52/5.76 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.76 => ( ord_less_int @ one_one_int @ B ) )
% 5.52/5.76 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.52/5.76 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_less_cancel_right1
% 5.52/5.76 thf(fact_2503_mult__less__cancel__right2,axiom,
% 5.52/5.76 ! [A: real,C: real] :
% 5.52/5.76 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.52/5.76 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_real @ A @ one_one_real ) )
% 5.52/5.76 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_less_cancel_right2
% 5.52/5.76 thf(fact_2504_mult__less__cancel__right2,axiom,
% 5.52/5.76 ! [A: rat,C: rat] :
% 5.52/5.76 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.52/5.76 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.52/5.76 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_less_cancel_right2
% 5.52/5.76 thf(fact_2505_mult__less__cancel__right2,axiom,
% 5.52/5.76 ! [A: int,C: int] :
% 5.52/5.76 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.52/5.76 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.76 => ( ord_less_int @ A @ one_one_int ) )
% 5.52/5.76 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.52/5.76 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_less_cancel_right2
% 5.52/5.76 thf(fact_2506_field__le__mult__one__interval,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ! [Z3: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 5.52/5.76 => ( ( ord_less_real @ Z3 @ one_one_real )
% 5.52/5.76 => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X2 ) @ Y2 ) ) )
% 5.52/5.76 => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 5.52/5.76
% 5.52/5.76 % field_le_mult_one_interval
% 5.52/5.76 thf(fact_2507_field__le__mult__one__interval,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ! [Z3: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 5.52/5.76 => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X2 ) @ Y2 ) ) )
% 5.52/5.76 => ( ord_less_eq_rat @ X2 @ Y2 ) ) ).
% 5.52/5.76
% 5.52/5.76 % field_le_mult_one_interval
% 5.52/5.76 thf(fact_2508_divide__le__eq,axiom,
% 5.52/5.76 ! [B: real,C: real,A: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_le_eq
% 5.52/5.76 thf(fact_2509_divide__le__eq,axiom,
% 5.52/5.76 ! [B: rat,C: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_le_eq
% 5.52/5.76 thf(fact_2510_le__divide__eq,axiom,
% 5.52/5.76 ! [A: real,B: real,C: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % le_divide_eq
% 5.52/5.76 thf(fact_2511_le__divide__eq,axiom,
% 5.52/5.76 ! [A: rat,B: rat,C: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % le_divide_eq
% 5.52/5.76 thf(fact_2512_divide__left__mono,axiom,
% 5.52/5.76 ! [B: real,A: real,C: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ B @ A )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.52/5.76 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_left_mono
% 5.52/5.76 thf(fact_2513_divide__left__mono,axiom,
% 5.52/5.76 ! [B: rat,A: rat,C: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ B @ A )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.52/5.76 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_left_mono
% 5.52/5.76 thf(fact_2514_neg__divide__le__eq,axiom,
% 5.52/5.76 ! [C: real,B: real,A: real] :
% 5.52/5.76 ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.52/5.76 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % neg_divide_le_eq
% 5.52/5.76 thf(fact_2515_neg__divide__le__eq,axiom,
% 5.52/5.76 ! [C: rat,B: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.52/5.76 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % neg_divide_le_eq
% 5.52/5.76 thf(fact_2516_neg__le__divide__eq,axiom,
% 5.52/5.76 ! [C: real,A: real,B: real] :
% 5.52/5.76 ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.52/5.76 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % neg_le_divide_eq
% 5.52/5.76 thf(fact_2517_neg__le__divide__eq,axiom,
% 5.52/5.76 ! [C: rat,A: rat,B: rat] :
% 5.52/5.76 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.76 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % neg_le_divide_eq
% 5.52/5.76 thf(fact_2518_pos__divide__le__eq,axiom,
% 5.52/5.76 ! [C: real,B: real,A: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.52/5.76 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % pos_divide_le_eq
% 5.52/5.76 thf(fact_2519_pos__divide__le__eq,axiom,
% 5.52/5.76 ! [C: rat,B: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.52/5.76 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % pos_divide_le_eq
% 5.52/5.76 thf(fact_2520_pos__le__divide__eq,axiom,
% 5.52/5.76 ! [C: real,A: real,B: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.52/5.76 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % pos_le_divide_eq
% 5.52/5.76 thf(fact_2521_pos__le__divide__eq,axiom,
% 5.52/5.76 ! [C: rat,A: rat,B: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.76 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % pos_le_divide_eq
% 5.52/5.76 thf(fact_2522_mult__imp__div__pos__le,axiom,
% 5.52/5.76 ! [Y2: real,X2: real,Z: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.76 => ( ( ord_less_eq_real @ X2 @ ( times_times_real @ Z @ Y2 ) )
% 5.52/5.76 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_imp_div_pos_le
% 5.52/5.76 thf(fact_2523_mult__imp__div__pos__le,axiom,
% 5.52/5.76 ! [Y2: rat,X2: rat,Z: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.52/5.76 => ( ( ord_less_eq_rat @ X2 @ ( times_times_rat @ Z @ Y2 ) )
% 5.52/5.76 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_imp_div_pos_le
% 5.52/5.76 thf(fact_2524_mult__imp__le__div__pos,axiom,
% 5.52/5.76 ! [Y2: real,Z: real,X2: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.76 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y2 ) @ X2 )
% 5.52/5.76 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_imp_le_div_pos
% 5.52/5.76 thf(fact_2525_mult__imp__le__div__pos,axiom,
% 5.52/5.76 ! [Y2: rat,Z: rat,X2: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.52/5.76 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y2 ) @ X2 )
% 5.52/5.76 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_imp_le_div_pos
% 5.52/5.76 thf(fact_2526_divide__left__mono__neg,axiom,
% 5.52/5.76 ! [A: real,B: real,C: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.76 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.52/5.76 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_left_mono_neg
% 5.52/5.76 thf(fact_2527_divide__left__mono__neg,axiom,
% 5.52/5.76 ! [A: rat,B: rat,C: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.76 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.52/5.76 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_left_mono_neg
% 5.52/5.76 thf(fact_2528_divide__le__eq__1,axiom,
% 5.52/5.76 ! [B: real,A: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.76 & ( ord_less_eq_real @ B @ A ) )
% 5.52/5.76 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.76 & ( ord_less_eq_real @ A @ B ) )
% 5.52/5.76 | ( A = zero_zero_real ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_le_eq_1
% 5.52/5.76 thf(fact_2529_divide__le__eq__1,axiom,
% 5.52/5.76 ! [B: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.76 & ( ord_less_eq_rat @ B @ A ) )
% 5.52/5.76 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.76 & ( ord_less_eq_rat @ A @ B ) )
% 5.52/5.76 | ( A = zero_zero_rat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_le_eq_1
% 5.52/5.76 thf(fact_2530_le__divide__eq__1,axiom,
% 5.52/5.76 ! [B: real,A: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.76 & ( ord_less_eq_real @ A @ B ) )
% 5.52/5.76 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.76 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % le_divide_eq_1
% 5.52/5.76 thf(fact_2531_le__divide__eq__1,axiom,
% 5.52/5.76 ! [B: rat,A: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.76 & ( ord_less_eq_rat @ A @ B ) )
% 5.52/5.76 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.76 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % le_divide_eq_1
% 5.52/5.76 thf(fact_2532_convex__bound__le,axiom,
% 5.52/5.76 ! [X2: real,A: real,Y2: real,U: real,V: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ X2 @ A )
% 5.52/5.76 => ( ( ord_less_eq_real @ Y2 @ A )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.52/5.76 => ( ( ( plus_plus_real @ U @ V )
% 5.52/5.76 = one_one_real )
% 5.52/5.76 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % convex_bound_le
% 5.52/5.76 thf(fact_2533_convex__bound__le,axiom,
% 5.52/5.76 ! [X2: rat,A: rat,Y2: rat,U: rat,V: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ X2 @ A )
% 5.52/5.76 => ( ( ord_less_eq_rat @ Y2 @ A )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.52/5.76 => ( ( ( plus_plus_rat @ U @ V )
% 5.52/5.76 = one_one_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % convex_bound_le
% 5.52/5.76 thf(fact_2534_convex__bound__le,axiom,
% 5.52/5.76 ! [X2: int,A: int,Y2: int,U: int,V: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ X2 @ A )
% 5.52/5.76 => ( ( ord_less_eq_int @ Y2 @ A )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.52/5.76 => ( ( ( plus_plus_int @ U @ V )
% 5.52/5.76 = one_one_int )
% 5.52/5.76 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % convex_bound_le
% 5.52/5.76 thf(fact_2535_vebt__maxt_Oelims,axiom,
% 5.52/5.76 ! [X2: vEBT_VEBT,Y2: option_nat] :
% 5.52/5.76 ( ( ( vEBT_vebt_maxt @ X2 )
% 5.52/5.76 = Y2 )
% 5.52/5.76 => ( ! [A3: $o,B2: $o] :
% 5.52/5.76 ( ( X2
% 5.52/5.76 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.76 => ~ ( ( B2
% 5.52/5.76 => ( Y2
% 5.52/5.76 = ( some_nat @ one_one_nat ) ) )
% 5.52/5.76 & ( ~ B2
% 5.52/5.76 => ( ( A3
% 5.52/5.76 => ( Y2
% 5.52/5.76 = ( some_nat @ zero_zero_nat ) ) )
% 5.52/5.76 & ( ~ A3
% 5.52/5.76 => ( Y2 = none_nat ) ) ) ) ) )
% 5.52/5.76 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.76 => ( Y2 != none_nat ) )
% 5.52/5.76 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.52/5.76 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.76 => ( Y2
% 5.52/5.76 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % vebt_maxt.elims
% 5.52/5.76 thf(fact_2536_divide__less__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [B: real,C: real,W: num] :
% 5.52/5.76 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_less_eq_numeral(1)
% 5.52/5.76 thf(fact_2537_divide__less__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [B: rat,C: rat,W: num] :
% 5.52/5.76 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_less_eq_numeral(1)
% 5.52/5.76 thf(fact_2538_less__divide__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [W: num,B: real,C: real] :
% 5.52/5.76 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % less_divide_eq_numeral(1)
% 5.52/5.76 thf(fact_2539_less__divide__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [W: num,B: rat,C: rat] :
% 5.52/5.76 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % less_divide_eq_numeral(1)
% 5.52/5.76 thf(fact_2540_frac__le__eq,axiom,
% 5.52/5.76 ! [Y2: real,Z: real,X2: real,W: real] :
% 5.52/5.76 ( ( Y2 != zero_zero_real )
% 5.52/5.76 => ( ( Z != zero_zero_real )
% 5.52/5.76 => ( ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 5.52/5.76 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % frac_le_eq
% 5.52/5.76 thf(fact_2541_frac__le__eq,axiom,
% 5.52/5.76 ! [Y2: rat,Z: rat,X2: rat,W: rat] :
% 5.52/5.76 ( ( Y2 != zero_zero_rat )
% 5.52/5.76 => ( ( Z != zero_zero_rat )
% 5.52/5.76 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.52/5.76 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % frac_le_eq
% 5.52/5.76 thf(fact_2542_vebt__mint_Oelims,axiom,
% 5.52/5.76 ! [X2: vEBT_VEBT,Y2: option_nat] :
% 5.52/5.76 ( ( ( vEBT_vebt_mint @ X2 )
% 5.52/5.76 = Y2 )
% 5.52/5.76 => ( ! [A3: $o,B2: $o] :
% 5.52/5.76 ( ( X2
% 5.52/5.76 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.76 => ~ ( ( A3
% 5.52/5.76 => ( Y2
% 5.52/5.76 = ( some_nat @ zero_zero_nat ) ) )
% 5.52/5.76 & ( ~ A3
% 5.52/5.76 => ( ( B2
% 5.52/5.76 => ( Y2
% 5.52/5.76 = ( some_nat @ one_one_nat ) ) )
% 5.52/5.76 & ( ~ B2
% 5.52/5.76 => ( Y2 = none_nat ) ) ) ) ) )
% 5.52/5.76 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.76 => ( Y2 != none_nat ) )
% 5.52/5.76 => ~ ! [Mi2: nat] :
% 5.52/5.76 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.76 => ( Y2
% 5.52/5.76 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % vebt_mint.elims
% 5.52/5.76 thf(fact_2543_power__Suc__less,axiom,
% 5.52/5.76 ! [A: real,N: nat] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.76 => ( ( ord_less_real @ A @ one_one_real )
% 5.52/5.76 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_Suc_less
% 5.52/5.76 thf(fact_2544_power__Suc__less,axiom,
% 5.52/5.76 ! [A: rat,N: nat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.76 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.52/5.76 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_Suc_less
% 5.52/5.76 thf(fact_2545_power__Suc__less,axiom,
% 5.52/5.76 ! [A: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.76 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.52/5.76 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_Suc_less
% 5.52/5.76 thf(fact_2546_power__Suc__less,axiom,
% 5.52/5.76 ! [A: int,N: nat] :
% 5.52/5.76 ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.76 => ( ( ord_less_int @ A @ one_one_int )
% 5.52/5.76 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_Suc_less
% 5.52/5.76 thf(fact_2547_frac__less__eq,axiom,
% 5.52/5.76 ! [Y2: real,Z: real,X2: real,W: real] :
% 5.52/5.76 ( ( Y2 != zero_zero_real )
% 5.52/5.76 => ( ( Z != zero_zero_real )
% 5.52/5.76 => ( ( ord_less_real @ ( divide_divide_real @ X2 @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 5.52/5.76 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % frac_less_eq
% 5.52/5.76 thf(fact_2548_frac__less__eq,axiom,
% 5.52/5.76 ! [Y2: rat,Z: rat,X2: rat,W: rat] :
% 5.52/5.76 ( ( Y2 != zero_zero_rat )
% 5.52/5.76 => ( ( Z != zero_zero_rat )
% 5.52/5.76 => ( ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.52/5.76 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % frac_less_eq
% 5.52/5.76 thf(fact_2549_power__Suc__le__self,axiom,
% 5.52/5.76 ! [A: real,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.76 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.52/5.76 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_Suc_le_self
% 5.52/5.76 thf(fact_2550_power__Suc__le__self,axiom,
% 5.52/5.76 ! [A: rat,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.76 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_Suc_le_self
% 5.52/5.76 thf(fact_2551_power__Suc__le__self,axiom,
% 5.52/5.76 ! [A: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.76 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.52/5.76 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_Suc_le_self
% 5.52/5.76 thf(fact_2552_power__Suc__le__self,axiom,
% 5.52/5.76 ! [A: int,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.76 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.52/5.76 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_Suc_le_self
% 5.52/5.76 thf(fact_2553_power__Suc__less__one,axiom,
% 5.52/5.76 ! [A: real,N: nat] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.76 => ( ( ord_less_real @ A @ one_one_real )
% 5.52/5.76 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_Suc_less_one
% 5.52/5.76 thf(fact_2554_power__Suc__less__one,axiom,
% 5.52/5.76 ! [A: rat,N: nat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.76 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.52/5.76 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_Suc_less_one
% 5.52/5.76 thf(fact_2555_power__Suc__less__one,axiom,
% 5.52/5.76 ! [A: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.76 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.52/5.76 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_Suc_less_one
% 5.52/5.76 thf(fact_2556_power__Suc__less__one,axiom,
% 5.52/5.76 ! [A: int,N: nat] :
% 5.52/5.76 ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.76 => ( ( ord_less_int @ A @ one_one_int )
% 5.52/5.76 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_Suc_less_one
% 5.52/5.76 thf(fact_2557_power__strict__decreasing,axiom,
% 5.52/5.76 ! [N: nat,N4: nat,A: real] :
% 5.52/5.76 ( ( ord_less_nat @ N @ N4 )
% 5.52/5.76 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.76 => ( ( ord_less_real @ A @ one_one_real )
% 5.52/5.76 => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_strict_decreasing
% 5.52/5.76 thf(fact_2558_power__strict__decreasing,axiom,
% 5.52/5.76 ! [N: nat,N4: nat,A: rat] :
% 5.52/5.76 ( ( ord_less_nat @ N @ N4 )
% 5.52/5.76 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.76 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.52/5.76 => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_strict_decreasing
% 5.52/5.76 thf(fact_2559_power__strict__decreasing,axiom,
% 5.52/5.76 ! [N: nat,N4: nat,A: nat] :
% 5.52/5.76 ( ( ord_less_nat @ N @ N4 )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.52/5.76 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.52/5.76 => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_strict_decreasing
% 5.52/5.76 thf(fact_2560_power__strict__decreasing,axiom,
% 5.52/5.76 ! [N: nat,N4: nat,A: int] :
% 5.52/5.76 ( ( ord_less_nat @ N @ N4 )
% 5.52/5.76 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.76 => ( ( ord_less_int @ A @ one_one_int )
% 5.52/5.76 => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_strict_decreasing
% 5.52/5.76 thf(fact_2561_power__decreasing,axiom,
% 5.52/5.76 ! [N: nat,N4: nat,A: real] :
% 5.52/5.76 ( ( ord_less_eq_nat @ N @ N4 )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.76 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.52/5.76 => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_decreasing
% 5.52/5.76 thf(fact_2562_power__decreasing,axiom,
% 5.52/5.76 ! [N: nat,N4: nat,A: rat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ N @ N4 )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.76 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_decreasing
% 5.52/5.76 thf(fact_2563_power__decreasing,axiom,
% 5.52/5.76 ! [N: nat,N4: nat,A: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ N @ N4 )
% 5.52/5.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.76 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.52/5.76 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_decreasing
% 5.52/5.76 thf(fact_2564_power__decreasing,axiom,
% 5.52/5.76 ! [N: nat,N4: nat,A: int] :
% 5.52/5.76 ( ( ord_less_eq_nat @ N @ N4 )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.76 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.52/5.76 => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_decreasing
% 5.52/5.76 thf(fact_2565_zero__power2,axiom,
% 5.52/5.76 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.76 = zero_zero_rat ) ).
% 5.52/5.76
% 5.52/5.76 % zero_power2
% 5.52/5.76 thf(fact_2566_zero__power2,axiom,
% 5.52/5.76 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.76 = zero_zero_nat ) ).
% 5.52/5.76
% 5.52/5.76 % zero_power2
% 5.52/5.76 thf(fact_2567_zero__power2,axiom,
% 5.52/5.76 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.76 = zero_zero_real ) ).
% 5.52/5.76
% 5.52/5.76 % zero_power2
% 5.52/5.76 thf(fact_2568_zero__power2,axiom,
% 5.52/5.76 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.76 = zero_zero_int ) ).
% 5.52/5.76
% 5.52/5.76 % zero_power2
% 5.52/5.76 thf(fact_2569_zero__power2,axiom,
% 5.52/5.76 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.76 = zero_zero_complex ) ).
% 5.52/5.76
% 5.52/5.76 % zero_power2
% 5.52/5.76 thf(fact_2570_self__le__power,axiom,
% 5.52/5.76 ! [A: real,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % self_le_power
% 5.52/5.76 thf(fact_2571_self__le__power,axiom,
% 5.52/5.76 ! [A: rat,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % self_le_power
% 5.52/5.76 thf(fact_2572_self__le__power,axiom,
% 5.52/5.76 ! [A: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % self_le_power
% 5.52/5.76 thf(fact_2573_self__le__power,axiom,
% 5.52/5.76 ! [A: int,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % self_le_power
% 5.52/5.76 thf(fact_2574_one__less__power,axiom,
% 5.52/5.76 ! [A: real,N: nat] :
% 5.52/5.76 ( ( ord_less_real @ one_one_real @ A )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % one_less_power
% 5.52/5.76 thf(fact_2575_one__less__power,axiom,
% 5.52/5.76 ! [A: rat,N: nat] :
% 5.52/5.76 ( ( ord_less_rat @ one_one_rat @ A )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % one_less_power
% 5.52/5.76 thf(fact_2576_one__less__power,axiom,
% 5.52/5.76 ! [A: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ one_one_nat @ A )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % one_less_power
% 5.52/5.76 thf(fact_2577_one__less__power,axiom,
% 5.52/5.76 ! [A: int,N: nat] :
% 5.52/5.76 ( ( ord_less_int @ one_one_int @ A )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % one_less_power
% 5.52/5.76 thf(fact_2578_numeral__2__eq__2,axiom,
% 5.52/5.76 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.52/5.76 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % numeral_2_eq_2
% 5.52/5.76 thf(fact_2579_pos2,axiom,
% 5.52/5.76 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.52/5.76
% 5.52/5.76 % pos2
% 5.52/5.76 thf(fact_2580_power__diff,axiom,
% 5.52/5.76 ! [A: complex,N: nat,M: nat] :
% 5.52/5.76 ( ( A != zero_zero_complex )
% 5.52/5.76 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.76 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.76 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_diff
% 5.52/5.76 thf(fact_2581_power__diff,axiom,
% 5.52/5.76 ! [A: real,N: nat,M: nat] :
% 5.52/5.76 ( ( A != zero_zero_real )
% 5.52/5.76 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.76 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.76 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_diff
% 5.52/5.76 thf(fact_2582_power__diff,axiom,
% 5.52/5.76 ! [A: rat,N: nat,M: nat] :
% 5.52/5.76 ( ( A != zero_zero_rat )
% 5.52/5.76 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.76 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.76 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_diff
% 5.52/5.76 thf(fact_2583_power__diff,axiom,
% 5.52/5.76 ! [A: nat,N: nat,M: nat] :
% 5.52/5.76 ( ( A != zero_zero_nat )
% 5.52/5.76 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.76 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.76 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_diff
% 5.52/5.76 thf(fact_2584_power__diff,axiom,
% 5.52/5.76 ! [A: int,N: nat,M: nat] :
% 5.52/5.76 ( ( A != zero_zero_int )
% 5.52/5.76 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.76 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.76 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_diff
% 5.52/5.76 thf(fact_2585_numeral__3__eq__3,axiom,
% 5.52/5.76 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.52/5.76 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % numeral_3_eq_3
% 5.52/5.76 thf(fact_2586_Suc__pred_H,axiom,
% 5.52/5.76 ! [N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( N
% 5.52/5.76 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % Suc_pred'
% 5.52/5.76 thf(fact_2587_Suc__diff__eq__diff__pred,axiom,
% 5.52/5.76 ! [N: nat,M: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.52/5.76 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % Suc_diff_eq_diff_pred
% 5.52/5.76 thf(fact_2588_div__if,axiom,
% 5.52/5.76 ( divide_divide_nat
% 5.52/5.76 = ( ^ [M3: nat,N3: nat] :
% 5.52/5.76 ( if_nat
% 5.52/5.76 @ ( ( ord_less_nat @ M3 @ N3 )
% 5.52/5.76 | ( N3 = zero_zero_nat ) )
% 5.52/5.76 @ zero_zero_nat
% 5.52/5.76 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N3 ) @ N3 ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_if
% 5.52/5.76 thf(fact_2589_div__geq,axiom,
% 5.52/5.76 ! [N: nat,M: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ~ ( ord_less_nat @ M @ N )
% 5.52/5.76 => ( ( divide_divide_nat @ M @ N )
% 5.52/5.76 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_geq
% 5.52/5.76 thf(fact_2590_add__eq__if,axiom,
% 5.52/5.76 ( plus_plus_nat
% 5.52/5.76 = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N3 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % add_eq_if
% 5.52/5.76 thf(fact_2591_less__eq__div__iff__mult__less__eq,axiom,
% 5.52/5.76 ! [Q2: nat,M: nat,N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.52/5.76 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 5.52/5.76 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % less_eq_div_iff_mult_less_eq
% 5.52/5.76 thf(fact_2592_split__div,axiom,
% 5.52/5.76 ! [P: nat > $o,M: nat,N: nat] :
% 5.52/5.76 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.52/5.76 = ( ( ( N = zero_zero_nat )
% 5.52/5.76 => ( P @ zero_zero_nat ) )
% 5.52/5.76 & ( ( N != zero_zero_nat )
% 5.52/5.76 => ! [I4: nat,J3: nat] :
% 5.52/5.76 ( ( ord_less_nat @ J3 @ N )
% 5.52/5.76 => ( ( M
% 5.52/5.76 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.52/5.76 => ( P @ I4 ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % split_div
% 5.52/5.76 thf(fact_2593_dividend__less__div__times,axiom,
% 5.52/5.76 ! [N: nat,M: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % dividend_less_div_times
% 5.52/5.76 thf(fact_2594_dividend__less__times__div,axiom,
% 5.52/5.76 ! [N: nat,M: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % dividend_less_times_div
% 5.52/5.76 thf(fact_2595_mult__eq__if,axiom,
% 5.52/5.76 ( times_times_nat
% 5.52/5.76 = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N3 @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % mult_eq_if
% 5.52/5.76 thf(fact_2596_vebt__member_Osimps_I4_J,axiom,
% 5.52/5.76 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.52/5.76 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 ) ).
% 5.52/5.76
% 5.52/5.76 % vebt_member.simps(4)
% 5.52/5.76 thf(fact_2597_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I4_J,axiom,
% 5.52/5.76 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve2: nat] :
% 5.52/5.76 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve2 )
% 5.52/5.76 = one_one_nat ) ).
% 5.52/5.76
% 5.52/5.76 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(4)
% 5.52/5.76 thf(fact_2598_vebt__succ_Osimps_I4_J,axiom,
% 5.52/5.76 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve2: nat] :
% 5.52/5.76 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve2 )
% 5.52/5.76 = none_nat ) ).
% 5.52/5.76
% 5.52/5.76 % vebt_succ.simps(4)
% 5.52/5.76 thf(fact_2599_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.52/5.76 ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X2: nat] :
% 5.52/5.76 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X2 )
% 5.52/5.76 = ( ( X2 = Mi )
% 5.52/5.76 | ( X2 = Ma ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % VEBT_internal.membermima.simps(3)
% 5.52/5.76 thf(fact_2600_vebt__pred_Osimps_I5_J,axiom,
% 5.52/5.76 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 5.52/5.76 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve2 ) @ Vf2 )
% 5.52/5.76 = none_nat ) ).
% 5.52/5.76
% 5.52/5.76 % vebt_pred.simps(5)
% 5.52/5.76 thf(fact_2601_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I4_J,axiom,
% 5.52/5.76 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve2: nat] :
% 5.52/5.76 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve2 )
% 5.52/5.76 = one_one_nat ) ).
% 5.52/5.76
% 5.52/5.76 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(4)
% 5.52/5.76 thf(fact_2602_convex__bound__lt,axiom,
% 5.52/5.76 ! [X2: real,A: real,Y2: real,U: real,V: real] :
% 5.52/5.76 ( ( ord_less_real @ X2 @ A )
% 5.52/5.76 => ( ( ord_less_real @ Y2 @ A )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.52/5.76 => ( ( ( plus_plus_real @ U @ V )
% 5.52/5.76 = one_one_real )
% 5.52/5.76 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % convex_bound_lt
% 5.52/5.76 thf(fact_2603_convex__bound__lt,axiom,
% 5.52/5.76 ! [X2: rat,A: rat,Y2: rat,U: rat,V: rat] :
% 5.52/5.76 ( ( ord_less_rat @ X2 @ A )
% 5.52/5.76 => ( ( ord_less_rat @ Y2 @ A )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.52/5.76 => ( ( ( plus_plus_rat @ U @ V )
% 5.52/5.76 = one_one_rat )
% 5.52/5.76 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % convex_bound_lt
% 5.52/5.76 thf(fact_2604_convex__bound__lt,axiom,
% 5.52/5.76 ! [X2: int,A: int,Y2: int,U: int,V: int] :
% 5.52/5.76 ( ( ord_less_int @ X2 @ A )
% 5.52/5.76 => ( ( ord_less_int @ Y2 @ A )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.52/5.76 => ( ( ( plus_plus_int @ U @ V )
% 5.52/5.76 = one_one_int )
% 5.52/5.76 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % convex_bound_lt
% 5.52/5.76 thf(fact_2605_divide__le__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [B: real,C: real,W: num] :
% 5.52/5.76 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_le_eq_numeral(1)
% 5.52/5.76 thf(fact_2606_divide__le__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [B: rat,C: rat,W: num] :
% 5.52/5.76 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % divide_le_eq_numeral(1)
% 5.52/5.76 thf(fact_2607_le__divide__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [W: num,B: real,C: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.76 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.76 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % le_divide_eq_numeral(1)
% 5.52/5.76 thf(fact_2608_le__divide__eq__numeral_I1_J,axiom,
% 5.52/5.76 ! [W: num,B: rat,C: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.76 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.52/5.76 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % le_divide_eq_numeral(1)
% 5.52/5.76 thf(fact_2609_half__gt__zero,axiom,
% 5.52/5.76 ! [A: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.76 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % half_gt_zero
% 5.52/5.76 thf(fact_2610_half__gt__zero,axiom,
% 5.52/5.76 ! [A: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.76 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % half_gt_zero
% 5.52/5.76 thf(fact_2611_half__gt__zero__iff,axiom,
% 5.52/5.76 ! [A: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.76 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.52/5.76
% 5.52/5.76 % half_gt_zero_iff
% 5.52/5.76 thf(fact_2612_half__gt__zero__iff,axiom,
% 5.52/5.76 ! [A: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.52/5.76
% 5.52/5.76 % half_gt_zero_iff
% 5.52/5.76 thf(fact_2613_scaling__mono,axiom,
% 5.52/5.76 ! [U: real,V: real,R: real,S: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ U @ V )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ R )
% 5.52/5.76 => ( ( ord_less_eq_real @ R @ S )
% 5.52/5.76 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % scaling_mono
% 5.52/5.76 thf(fact_2614_scaling__mono,axiom,
% 5.52/5.76 ! [U: rat,V: rat,R: rat,S: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ U @ V )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 5.52/5.76 => ( ( ord_less_eq_rat @ R @ S )
% 5.52/5.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % scaling_mono
% 5.52/5.76 thf(fact_2615_zero__le__power2,axiom,
% 5.52/5.76 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % zero_le_power2
% 5.52/5.76 thf(fact_2616_zero__le__power2,axiom,
% 5.52/5.76 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % zero_le_power2
% 5.52/5.76 thf(fact_2617_zero__le__power2,axiom,
% 5.52/5.76 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % zero_le_power2
% 5.52/5.76 thf(fact_2618_power2__eq__imp__eq,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.76 = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.76 => ( X2 = Y2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power2_eq_imp_eq
% 5.52/5.76 thf(fact_2619_power2__eq__imp__eq,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.76 = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.52/5.76 => ( X2 = Y2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power2_eq_imp_eq
% 5.52/5.76 thf(fact_2620_power2__eq__imp__eq,axiom,
% 5.52/5.76 ! [X2: nat,Y2: nat] :
% 5.52/5.76 ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.76 = ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.52/5.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.52/5.76 => ( X2 = Y2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power2_eq_imp_eq
% 5.52/5.76 thf(fact_2621_power2__eq__imp__eq,axiom,
% 5.52/5.76 ! [X2: int,Y2: int] :
% 5.52/5.76 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.76 = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.76 => ( X2 = Y2 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power2_eq_imp_eq
% 5.52/5.76 thf(fact_2622_power2__le__imp__le,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.76 => ( ord_less_eq_real @ X2 @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power2_le_imp_le
% 5.52/5.76 thf(fact_2623_power2__le__imp__le,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.52/5.76 => ( ord_less_eq_rat @ X2 @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power2_le_imp_le
% 5.52/5.76 thf(fact_2624_power2__le__imp__le,axiom,
% 5.52/5.76 ! [X2: nat,Y2: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.52/5.76 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power2_le_imp_le
% 5.52/5.76 thf(fact_2625_power2__le__imp__le,axiom,
% 5.52/5.76 ! [X2: int,Y2: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.76 => ( ord_less_eq_int @ X2 @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power2_le_imp_le
% 5.52/5.76 thf(fact_2626_power2__less__0,axiom,
% 5.52/5.76 ! [A: real] :
% 5.52/5.76 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.52/5.76
% 5.52/5.76 % power2_less_0
% 5.52/5.76 thf(fact_2627_power2__less__0,axiom,
% 5.52/5.76 ! [A: rat] :
% 5.52/5.76 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.52/5.76
% 5.52/5.76 % power2_less_0
% 5.52/5.76 thf(fact_2628_power2__less__0,axiom,
% 5.52/5.76 ! [A: int] :
% 5.52/5.76 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.52/5.76
% 5.52/5.76 % power2_less_0
% 5.52/5.76 thf(fact_2629_exp__add__not__zero__imp__left,axiom,
% 5.52/5.76 ! [M: nat,N: nat] :
% 5.52/5.76 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.52/5.76 != zero_zero_nat )
% 5.52/5.76 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.52/5.76 != zero_zero_nat ) ) ).
% 5.52/5.76
% 5.52/5.76 % exp_add_not_zero_imp_left
% 5.52/5.76 thf(fact_2630_exp__add__not__zero__imp__left,axiom,
% 5.52/5.76 ! [M: nat,N: nat] :
% 5.52/5.76 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.52/5.76 != zero_zero_int )
% 5.52/5.76 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.52/5.76 != zero_zero_int ) ) ).
% 5.52/5.76
% 5.52/5.76 % exp_add_not_zero_imp_left
% 5.52/5.76 thf(fact_2631_exp__add__not__zero__imp__right,axiom,
% 5.52/5.76 ! [M: nat,N: nat] :
% 5.52/5.76 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.52/5.76 != zero_zero_nat )
% 5.52/5.76 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.76 != zero_zero_nat ) ) ).
% 5.52/5.76
% 5.52/5.76 % exp_add_not_zero_imp_right
% 5.52/5.76 thf(fact_2632_exp__add__not__zero__imp__right,axiom,
% 5.52/5.76 ! [M: nat,N: nat] :
% 5.52/5.76 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.52/5.76 != zero_zero_int )
% 5.52/5.76 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.52/5.76 != zero_zero_int ) ) ).
% 5.52/5.76
% 5.52/5.76 % exp_add_not_zero_imp_right
% 5.52/5.76 thf(fact_2633_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.52/5.76 ! [N: nat,M: nat] :
% 5.52/5.76 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.76 != zero_zero_nat )
% 5.52/5.76 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.52/5.76 != zero_zero_nat ) ) ).
% 5.52/5.76
% 5.52/5.76 % exp_not_zero_imp_exp_diff_not_zero
% 5.52/5.76 thf(fact_2634_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.52/5.76 ! [N: nat,M: nat] :
% 5.52/5.76 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.52/5.76 != zero_zero_int )
% 5.52/5.76 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.52/5.76 != zero_zero_int ) ) ).
% 5.52/5.76
% 5.52/5.76 % exp_not_zero_imp_exp_diff_not_zero
% 5.52/5.76 thf(fact_2635_power__diff__power__eq,axiom,
% 5.52/5.76 ! [A: nat,N: nat,M: nat] :
% 5.52/5.76 ( ( A != zero_zero_nat )
% 5.52/5.76 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.76 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.52/5.76 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.52/5.76 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.52/5.76 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.52/5.76 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_diff_power_eq
% 5.52/5.76 thf(fact_2636_power__diff__power__eq,axiom,
% 5.52/5.76 ! [A: int,N: nat,M: nat] :
% 5.52/5.76 ( ( A != zero_zero_int )
% 5.52/5.76 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.76 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.52/5.76 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.52/5.76 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.52/5.76 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.52/5.76 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_diff_power_eq
% 5.52/5.76 thf(fact_2637_less__2__cases,axiom,
% 5.52/5.76 ! [N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.76 => ( ( N = zero_zero_nat )
% 5.52/5.76 | ( N
% 5.52/5.76 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % less_2_cases
% 5.52/5.76 thf(fact_2638_less__2__cases__iff,axiom,
% 5.52/5.76 ! [N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.76 = ( ( N = zero_zero_nat )
% 5.52/5.76 | ( N
% 5.52/5.76 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % less_2_cases_iff
% 5.52/5.76 thf(fact_2639_nat__induct2,axiom,
% 5.52/5.76 ! [P: nat > $o,N: nat] :
% 5.52/5.76 ( ( P @ zero_zero_nat )
% 5.52/5.76 => ( ( P @ one_one_nat )
% 5.52/5.76 => ( ! [N2: nat] :
% 5.52/5.76 ( ( P @ N2 )
% 5.52/5.76 => ( P @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.76 => ( P @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % nat_induct2
% 5.52/5.76 thf(fact_2640_power__eq__if,axiom,
% 5.52/5.76 ( power_power_complex
% 5.52/5.76 = ( ^ [P4: complex,M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P4 @ ( power_power_complex @ P4 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_eq_if
% 5.52/5.76 thf(fact_2641_power__eq__if,axiom,
% 5.52/5.76 ( power_power_real
% 5.52/5.76 = ( ^ [P4: real,M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P4 @ ( power_power_real @ P4 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_eq_if
% 5.52/5.76 thf(fact_2642_power__eq__if,axiom,
% 5.52/5.76 ( power_power_rat
% 5.52/5.76 = ( ^ [P4: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P4 @ ( power_power_rat @ P4 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_eq_if
% 5.52/5.76 thf(fact_2643_power__eq__if,axiom,
% 5.52/5.76 ( power_power_nat
% 5.52/5.76 = ( ^ [P4: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P4 @ ( power_power_nat @ P4 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_eq_if
% 5.52/5.76 thf(fact_2644_power__eq__if,axiom,
% 5.52/5.76 ( power_power_int
% 5.52/5.76 = ( ^ [P4: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P4 @ ( power_power_int @ P4 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_eq_if
% 5.52/5.76 thf(fact_2645_power__minus__mult,axiom,
% 5.52/5.76 ! [N: nat,A: complex] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.52/5.76 = ( power_power_complex @ A @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_minus_mult
% 5.52/5.76 thf(fact_2646_power__minus__mult,axiom,
% 5.52/5.76 ! [N: nat,A: real] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.52/5.76 = ( power_power_real @ A @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_minus_mult
% 5.52/5.76 thf(fact_2647_power__minus__mult,axiom,
% 5.52/5.76 ! [N: nat,A: rat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.52/5.76 = ( power_power_rat @ A @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_minus_mult
% 5.52/5.76 thf(fact_2648_power__minus__mult,axiom,
% 5.52/5.76 ! [N: nat,A: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.52/5.76 = ( power_power_nat @ A @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_minus_mult
% 5.52/5.76 thf(fact_2649_power__minus__mult,axiom,
% 5.52/5.76 ! [N: nat,A: int] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.52/5.76 = ( power_power_int @ A @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power_minus_mult
% 5.52/5.76 thf(fact_2650_le__div__geq,axiom,
% 5.52/5.76 ! [N: nat,M: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.76 => ( ( divide_divide_nat @ M @ N )
% 5.52/5.76 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % le_div_geq
% 5.52/5.76 thf(fact_2651_split__div_H,axiom,
% 5.52/5.76 ! [P: nat > $o,M: nat,N: nat] :
% 5.52/5.76 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.52/5.76 = ( ( ( N = zero_zero_nat )
% 5.52/5.76 & ( P @ zero_zero_nat ) )
% 5.52/5.76 | ? [Q4: nat] :
% 5.52/5.76 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M )
% 5.52/5.76 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 5.52/5.76 & ( P @ Q4 ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % split_div'
% 5.52/5.76 thf(fact_2652_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I5_J,axiom,
% 5.52/5.76 ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.52/5.76 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 5.52/5.76 = one_one_nat ) ).
% 5.52/5.76
% 5.52/5.76 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(5)
% 5.52/5.76 thf(fact_2653_vebt__succ_Osimps_I5_J,axiom,
% 5.52/5.76 ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.52/5.76 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 5.52/5.76 = none_nat ) ).
% 5.52/5.76
% 5.52/5.76 % vebt_succ.simps(5)
% 5.52/5.76 thf(fact_2654_vebt__pred_Osimps_I6_J,axiom,
% 5.52/5.76 ! [V: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.52/5.76 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 5.52/5.76 = none_nat ) ).
% 5.52/5.76
% 5.52/5.76 % vebt_pred.simps(6)
% 5.52/5.76 thf(fact_2655_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I5_J,axiom,
% 5.52/5.76 ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.52/5.76 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 5.52/5.76 = one_one_nat ) ).
% 5.52/5.76
% 5.52/5.76 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(5)
% 5.52/5.76 thf(fact_2656_power2__less__imp__less,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.76 => ( ord_less_real @ X2 @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power2_less_imp_less
% 5.52/5.76 thf(fact_2657_power2__less__imp__less,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.52/5.76 => ( ord_less_rat @ X2 @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power2_less_imp_less
% 5.52/5.76 thf(fact_2658_power2__less__imp__less,axiom,
% 5.52/5.76 ! [X2: nat,Y2: nat] :
% 5.52/5.76 ( ( ord_less_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.52/5.76 => ( ord_less_nat @ X2 @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power2_less_imp_less
% 5.52/5.76 thf(fact_2659_power2__less__imp__less,axiom,
% 5.52/5.76 ! [X2: int,Y2: int] :
% 5.52/5.76 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.76 => ( ord_less_int @ X2 @ Y2 ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % power2_less_imp_less
% 5.52/5.76 thf(fact_2660_sum__power2__ge__zero,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_power2_ge_zero
% 5.52/5.76 thf(fact_2661_sum__power2__ge__zero,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_power2_ge_zero
% 5.52/5.76 thf(fact_2662_sum__power2__ge__zero,axiom,
% 5.52/5.76 ! [X2: int,Y2: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_power2_ge_zero
% 5.52/5.76 thf(fact_2663_sum__power2__le__zero__iff,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.52/5.76 = ( ( X2 = zero_zero_real )
% 5.52/5.76 & ( Y2 = zero_zero_real ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_power2_le_zero_iff
% 5.52/5.76 thf(fact_2664_sum__power2__le__zero__iff,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.52/5.76 = ( ( X2 = zero_zero_rat )
% 5.52/5.76 & ( Y2 = zero_zero_rat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_power2_le_zero_iff
% 5.52/5.76 thf(fact_2665_sum__power2__le__zero__iff,axiom,
% 5.52/5.76 ! [X2: int,Y2: int] :
% 5.52/5.76 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.52/5.76 = ( ( X2 = zero_zero_int )
% 5.52/5.76 & ( Y2 = zero_zero_int ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_power2_le_zero_iff
% 5.52/5.76 thf(fact_2666_not__sum__power2__lt__zero,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.52/5.76
% 5.52/5.76 % not_sum_power2_lt_zero
% 5.52/5.76 thf(fact_2667_not__sum__power2__lt__zero,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.52/5.76
% 5.52/5.76 % not_sum_power2_lt_zero
% 5.52/5.76 thf(fact_2668_not__sum__power2__lt__zero,axiom,
% 5.52/5.76 ! [X2: int,Y2: int] :
% 5.52/5.76 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.52/5.76
% 5.52/5.76 % not_sum_power2_lt_zero
% 5.52/5.76 thf(fact_2669_sum__power2__gt__zero__iff,axiom,
% 5.52/5.76 ! [X2: real,Y2: real] :
% 5.52/5.76 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.76 = ( ( X2 != zero_zero_real )
% 5.52/5.76 | ( Y2 != zero_zero_real ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_power2_gt_zero_iff
% 5.52/5.76 thf(fact_2670_sum__power2__gt__zero__iff,axiom,
% 5.52/5.76 ! [X2: rat,Y2: rat] :
% 5.52/5.76 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.76 = ( ( X2 != zero_zero_rat )
% 5.52/5.76 | ( Y2 != zero_zero_rat ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_power2_gt_zero_iff
% 5.52/5.76 thf(fact_2671_sum__power2__gt__zero__iff,axiom,
% 5.52/5.76 ! [X2: int,Y2: int] :
% 5.52/5.76 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.76 = ( ( X2 != zero_zero_int )
% 5.52/5.76 | ( Y2 != zero_zero_int ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % sum_power2_gt_zero_iff
% 5.52/5.76 thf(fact_2672_zero__le__even__power_H,axiom,
% 5.52/5.76 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % zero_le_even_power'
% 5.52/5.76 thf(fact_2673_zero__le__even__power_H,axiom,
% 5.52/5.76 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % zero_le_even_power'
% 5.52/5.76 thf(fact_2674_zero__le__even__power_H,axiom,
% 5.52/5.76 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % zero_le_even_power'
% 5.52/5.76 thf(fact_2675_nat__bit__induct,axiom,
% 5.52/5.76 ! [P: nat > $o,N: nat] :
% 5.52/5.76 ( ( P @ zero_zero_nat )
% 5.52/5.76 => ( ! [N2: nat] :
% 5.52/5.76 ( ( P @ N2 )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.52/5.76 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.52/5.76 => ( ! [N2: nat] :
% 5.52/5.76 ( ( P @ N2 )
% 5.52/5.76 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.52/5.76 => ( P @ N ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % nat_bit_induct
% 5.52/5.76 thf(fact_2676_div__2__gt__zero,axiom,
% 5.52/5.76 ! [N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.52/5.76 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % div_2_gt_zero
% 5.52/5.76 thf(fact_2677_Suc__n__div__2__gt__zero,axiom,
% 5.52/5.76 ! [N: nat] :
% 5.52/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % Suc_n_div_2_gt_zero
% 5.52/5.76 thf(fact_2678_length__induct,axiom,
% 5.52/5.76 ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 5.52/5.76 ( ! [Xs3: list_VEBT_VEBT] :
% 5.52/5.76 ( ! [Ys2: list_VEBT_VEBT] :
% 5.52/5.76 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.52/5.76 => ( P @ Ys2 ) )
% 5.52/5.76 => ( P @ Xs3 ) )
% 5.52/5.76 => ( P @ Xs2 ) ) ).
% 5.52/5.76
% 5.52/5.76 % length_induct
% 5.52/5.76 thf(fact_2679_length__induct,axiom,
% 5.52/5.76 ! [P: list_o > $o,Xs2: list_o] :
% 5.52/5.76 ( ! [Xs3: list_o] :
% 5.52/5.76 ( ! [Ys2: list_o] :
% 5.52/5.76 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 5.52/5.76 => ( P @ Ys2 ) )
% 5.52/5.76 => ( P @ Xs3 ) )
% 5.52/5.76 => ( P @ Xs2 ) ) ).
% 5.52/5.76
% 5.52/5.76 % length_induct
% 5.52/5.76 thf(fact_2680_length__induct,axiom,
% 5.52/5.76 ! [P: list_nat > $o,Xs2: list_nat] :
% 5.52/5.76 ( ! [Xs3: list_nat] :
% 5.52/5.76 ( ! [Ys2: list_nat] :
% 5.52/5.76 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 5.52/5.76 => ( P @ Ys2 ) )
% 5.52/5.76 => ( P @ Xs3 ) )
% 5.52/5.76 => ( P @ Xs2 ) ) ).
% 5.52/5.76
% 5.52/5.76 % length_induct
% 5.52/5.76 thf(fact_2681_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.52/5.76 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.52/5.76 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.52/5.76 = Y2 )
% 5.52/5.76 => ( ! [A3: $o,B2: $o] :
% 5.52/5.76 ( ( X2
% 5.52/5.76 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.76 => ( Y2
% 5.52/5.76 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.76 => A3 )
% 5.52/5.76 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.76 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.76 => B2 )
% 5.52/5.76 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.52/5.76 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.52/5.76 => Y2 )
% 5.52/5.76 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.52/5.76 ( ? [S2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) )
% 5.52/5.76 => ( Y2
% 5.52/5.76 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.76 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.76 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % VEBT_internal.naive_member.elims(1)
% 5.52/5.76 thf(fact_2682_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.52/5.76 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.76 ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.52/5.76 => ( ! [A3: $o,B2: $o] :
% 5.52/5.76 ( ( X2
% 5.52/5.76 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.76 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.76 => A3 )
% 5.52/5.76 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.76 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.76 => B2 )
% 5.52/5.76 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.52/5.76 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.52/5.76 ( ? [S2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) )
% 5.52/5.76 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.76 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.76 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % VEBT_internal.naive_member.elims(2)
% 5.52/5.76 thf(fact_2683_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.52/5.76 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.76 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.52/5.76 => ( ! [A3: $o,B2: $o] :
% 5.52/5.76 ( ( X2
% 5.52/5.76 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.76 => ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.76 => A3 )
% 5.52/5.76 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.76 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.76 => B2 )
% 5.52/5.76 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.52/5.76 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.52/5.76 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.52/5.76 ( ? [S2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) )
% 5.52/5.76 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.76 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.76 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % VEBT_internal.naive_member.elims(3)
% 5.52/5.76 thf(fact_2684_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I3_J,axiom,
% 5.52/5.76 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.52/5.76 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 )
% 5.52/5.76 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(3)
% 5.52/5.76 thf(fact_2685_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Oelims,axiom,
% 5.52/5.76 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.52/5.76 ( ( ( vEBT_T_m_a_x_t @ X2 )
% 5.52/5.76 = Y2 )
% 5.52/5.76 => ( ! [A3: $o,B2: $o] :
% 5.52/5.76 ( ( X2
% 5.52/5.76 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.76 => ( Y2
% 5.52/5.76 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B2 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.52/5.76 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.76 => ( Y2 != one_one_nat ) )
% 5.52/5.76 => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.76 => ( Y2 != one_one_nat ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.elims
% 5.52/5.76 thf(fact_2686_odd__0__le__power__imp__0__le,axiom,
% 5.52/5.76 ! [A: real,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.52/5.76 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.52/5.76
% 5.52/5.76 % odd_0_le_power_imp_0_le
% 5.52/5.76 thf(fact_2687_odd__0__le__power__imp__0__le,axiom,
% 5.52/5.76 ! [A: rat,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.52/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.52/5.76
% 5.52/5.76 % odd_0_le_power_imp_0_le
% 5.52/5.76 thf(fact_2688_odd__0__le__power__imp__0__le,axiom,
% 5.52/5.76 ! [A: int,N: nat] :
% 5.52/5.76 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.52/5.76 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.52/5.76
% 5.52/5.76 % odd_0_le_power_imp_0_le
% 5.52/5.76 thf(fact_2689_odd__power__less__zero,axiom,
% 5.52/5.76 ! [A: real,N: nat] :
% 5.52/5.76 ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.76 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.52/5.76
% 5.52/5.76 % odd_power_less_zero
% 5.52/5.76 thf(fact_2690_odd__power__less__zero,axiom,
% 5.52/5.76 ! [A: rat,N: nat] :
% 5.52/5.76 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.76 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.52/5.76
% 5.52/5.76 % odd_power_less_zero
% 5.52/5.76 thf(fact_2691_odd__power__less__zero,axiom,
% 5.52/5.76 ! [A: int,N: nat] :
% 5.52/5.76 ( ( ord_less_int @ A @ zero_zero_int )
% 5.52/5.76 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.52/5.76
% 5.52/5.76 % odd_power_less_zero
% 5.52/5.76 thf(fact_2692_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.52/5.76 ! [X2: nat,N: nat,M: nat] :
% 5.52/5.76 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.76 => ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % VEBT_internal.exp_split_high_low(1)
% 5.52/5.76 thf(fact_2693_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.52/5.76 ! [X2: nat,N: nat,M: nat] :
% 5.52/5.76 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.76 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.76 => ( ord_less_nat @ ( vEBT_VEBT_low @ X2 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % VEBT_internal.exp_split_high_low(2)
% 5.52/5.76 thf(fact_2694_vebt__member_Oelims_I2_J,axiom,
% 5.52/5.76 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.76 ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.52/5.76 => ( ! [A3: $o,B2: $o] :
% 5.52/5.76 ( ( X2
% 5.52/5.76 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.76 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.76 => A3 )
% 5.52/5.76 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.76 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.76 => B2 )
% 5.52/5.76 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.52/5.76 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.52/5.76 ( ? [Summary2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.76 => ~ ( ( Xa2 != Mi2 )
% 5.52/5.76 => ( ( Xa2 != Ma2 )
% 5.52/5.76 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.76 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.76 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.76 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.76 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.76 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.76 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % vebt_member.elims(2)
% 5.52/5.76 thf(fact_2695_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.52/5.76 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.52/5.76 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.52/5.76 = Y2 )
% 5.52/5.76 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.52/5.76 => Y2 )
% 5.52/5.76 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.52/5.76 => Y2 )
% 5.52/5.76 => ( ! [Mi2: nat,Ma2: nat] :
% 5.52/5.76 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.52/5.76 => ( Y2
% 5.52/5.76 = ( ~ ( ( Xa2 = Mi2 )
% 5.52/5.76 | ( Xa2 = Ma2 ) ) ) ) )
% 5.52/5.76 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.52/5.76 ( ? [Vc2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.52/5.76 => ( Y2
% 5.52/5.76 = ( ~ ( ( Xa2 = Mi2 )
% 5.52/5.76 | ( Xa2 = Ma2 )
% 5.52/5.76 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.76 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.76 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 5.52/5.76 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.52/5.76 ( ? [Vd2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.52/5.76 => ( Y2
% 5.52/5.76 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.76 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.76 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.76
% 5.52/5.76 % VEBT_internal.membermima.elims(1)
% 5.52/5.76 thf(fact_2696_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.52/5.76 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.76 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.52/5.76 => ( ! [Uu2: $o,Uv2: $o] :
% 5.52/5.76 ( X2
% 5.52/5.76 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.52/5.76 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.52/5.76 => ( ! [Mi2: nat,Ma2: nat] :
% 5.52/5.76 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.52/5.76 => ( ( Xa2 = Mi2 )
% 5.52/5.76 | ( Xa2 = Ma2 ) ) )
% 5.52/5.76 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.52/5.76 ( ? [Vc2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.52/5.76 => ( ( Xa2 = Mi2 )
% 5.52/5.76 | ( Xa2 = Ma2 )
% 5.52/5.76 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.76 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.76 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.52/5.76 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.52/5.76 ( ? [Vd2: vEBT_VEBT] :
% 5.52/5.76 ( X2
% 5.52/5.76 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.52/5.77 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % VEBT_internal.membermima.elims(3)
% 5.52/5.77 thf(fact_2697_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I4_J,axiom,
% 5.52/5.77 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 )
% 5.52/5.77 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(4)
% 5.52/5.77 thf(fact_2698_vebt__member_Oelims_I3_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.77 ( ~ ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => A3 )
% 5.52/5.77 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.77 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.77 => B2 )
% 5.52/5.77 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.52/5.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.52/5.77 ( ? [Summary2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( Xa2 != Mi2 )
% 5.52/5.77 => ( ( Xa2 != Ma2 )
% 5.52/5.77 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.77 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % vebt_member.elims(3)
% 5.52/5.77 thf(fact_2699_vebt__member_Oelims_I1_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.52/5.77 ( ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => A3 )
% 5.52/5.77 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.77 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.77 => B2 )
% 5.52/5.77 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.52/5.77 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.77 => Y2 )
% 5.52/5.77 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.52/5.77 => Y2 )
% 5.52/5.77 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.52/5.77 => Y2 )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.52/5.77 ( ? [Summary2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( ~ ( ( Xa2 != Mi2 )
% 5.52/5.77 => ( ( Xa2 != Ma2 )
% 5.52/5.77 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.77 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % vebt_member.elims(1)
% 5.52/5.77 thf(fact_2700_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I4_J,axiom,
% 5.52/5.77 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X2 )
% 5.52/5.77 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(4)
% 5.52/5.77 thf(fact_2701_insersimp,axiom,
% 5.52/5.77 ! [T: vEBT_VEBT,N: nat,Y2: nat] :
% 5.52/5.77 ( ( vEBT_invar_vebt @ T @ N )
% 5.52/5.77 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 5.52/5.77 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ Y2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % insersimp
% 5.52/5.77 thf(fact_2702_arith__geo__mean,axiom,
% 5.52/5.77 ! [U: real,X2: real,Y2: real] :
% 5.52/5.77 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.77 = ( times_times_real @ X2 @ Y2 ) )
% 5.52/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.77 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % arith_geo_mean
% 5.52/5.77 thf(fact_2703_arith__geo__mean,axiom,
% 5.52/5.77 ! [U: rat,X2: rat,Y2: rat] :
% 5.52/5.77 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.77 = ( times_times_rat @ X2 @ Y2 ) )
% 5.52/5.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.52/5.77 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % arith_geo_mean
% 5.52/5.77 thf(fact_2704_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Oelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.52/5.77 ( ( ( vEBT_T_m_e_m_b_e_r @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( ? [A3: $o,B2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( Y2
% 5.52/5.77 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.52/5.77 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ( Y2
% 5.52/5.77 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.77 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.52/5.77 => ( Y2
% 5.52/5.77 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.77 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.52/5.77 => ( Y2
% 5.52/5.77 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.52/5.77 ( ? [Summary2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( Y2
% 5.52/5.77 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.elims
% 5.52/5.77 thf(fact_2705_invar__vebt_Ocases,axiom,
% 5.52/5.77 ! [A1: vEBT_VEBT,A22: nat] :
% 5.52/5.77 ( ( vEBT_invar_vebt @ A1 @ A22 )
% 5.52/5.77 => ( ( ? [A3: $o,B2: $o] :
% 5.52/5.77 ( A1
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( A22
% 5.52/5.77 != ( suc @ zero_zero_nat ) ) )
% 5.52/5.77 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.52/5.77 ( ( A1
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( A22 = Deg2 )
% 5.52/5.77 => ( ! [X6: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_invar_vebt @ X6 @ N2 ) )
% 5.52/5.77 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.52/5.77 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.52/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.52/5.77 => ( ( M4 = N2 )
% 5.52/5.77 => ( ( Deg2
% 5.52/5.77 = ( plus_plus_nat @ N2 @ M4 ) )
% 5.52/5.77 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.52/5.77 => ~ ! [X6: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.77 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.52/5.77 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.52/5.77 ( ( A1
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( A22 = Deg2 )
% 5.52/5.77 => ( ! [X6: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_invar_vebt @ X6 @ N2 ) )
% 5.52/5.77 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.52/5.77 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.52/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.52/5.77 => ( ( M4
% 5.52/5.77 = ( suc @ N2 ) )
% 5.52/5.77 => ( ( Deg2
% 5.52/5.77 = ( plus_plus_nat @ N2 @ M4 ) )
% 5.52/5.77 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.52/5.77 => ~ ! [X6: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.77 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.52/5.77 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.52/5.77 ( ( A1
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( A22 = Deg2 )
% 5.52/5.77 => ( ! [X6: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_invar_vebt @ X6 @ N2 ) )
% 5.52/5.77 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.52/5.77 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.52/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.52/5.77 => ( ( M4 = N2 )
% 5.52/5.77 => ( ( Deg2
% 5.52/5.77 = ( plus_plus_nat @ N2 @ M4 ) )
% 5.52/5.77 => ( ! [I3: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.52/5.77 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X7 ) )
% 5.52/5.77 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.52/5.77 => ( ( ( Mi2 = Ma2 )
% 5.52/5.77 => ! [X6: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.77 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) )
% 5.52/5.77 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.52/5.77 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.77 => ~ ( ( Mi2 != Ma2 )
% 5.52/5.77 => ! [I3: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.52/5.77 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 5.52/5.77 = I3 )
% 5.52/5.77 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 5.52/5.77 & ! [X6: nat] :
% 5.52/5.77 ( ( ( ( vEBT_VEBT_high @ X6 @ N2 )
% 5.52/5.77 = I3 )
% 5.52/5.77 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X6 @ N2 ) ) )
% 5.52/5.77 => ( ( ord_less_nat @ Mi2 @ X6 )
% 5.52/5.77 & ( ord_less_eq_nat @ X6 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.52/5.77 => ~ ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.52/5.77 ( ( A1
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( A22 = Deg2 )
% 5.52/5.77 => ( ! [X6: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_invar_vebt @ X6 @ N2 ) )
% 5.52/5.77 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.52/5.77 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.52/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.52/5.77 => ( ( M4
% 5.52/5.77 = ( suc @ N2 ) )
% 5.52/5.77 => ( ( Deg2
% 5.52/5.77 = ( plus_plus_nat @ N2 @ M4 ) )
% 5.52/5.77 => ( ! [I3: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.52/5.77 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X7 ) )
% 5.52/5.77 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.52/5.77 => ( ( ( Mi2 = Ma2 )
% 5.52/5.77 => ! [X6: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.77 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) )
% 5.52/5.77 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.52/5.77 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.77 => ~ ( ( Mi2 != Ma2 )
% 5.52/5.77 => ! [I3: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.52/5.77 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 5.52/5.77 = I3 )
% 5.52/5.77 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 5.52/5.77 & ! [X6: nat] :
% 5.52/5.77 ( ( ( ( vEBT_VEBT_high @ X6 @ N2 )
% 5.52/5.77 = I3 )
% 5.52/5.77 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X6 @ N2 ) ) )
% 5.52/5.77 => ( ( ord_less_nat @ Mi2 @ X6 )
% 5.52/5.77 & ( ord_less_eq_nat @ X6 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % invar_vebt.cases
% 5.52/5.77 thf(fact_2706_invar__vebt_Osimps,axiom,
% 5.52/5.77 ( vEBT_invar_vebt
% 5.52/5.77 = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 5.52/5.77 ( ( ? [A4: $o,B3: $o] :
% 5.52/5.77 ( A12
% 5.52/5.77 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.52/5.77 & ( A23
% 5.52/5.77 = ( suc @ zero_zero_nat ) ) )
% 5.52/5.77 | ? [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT] :
% 5.52/5.77 ( ( A12
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList3 @ Summary3 ) )
% 5.52/5.77 & ! [X: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.52/5.77 => ( vEBT_invar_vebt @ X @ N3 ) )
% 5.52/5.77 & ( vEBT_invar_vebt @ Summary3 @ N3 )
% 5.52/5.77 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.52/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 5.52/5.77 & ( A23
% 5.52/5.77 = ( plus_plus_nat @ N3 @ N3 ) )
% 5.52/5.77 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X7 )
% 5.52/5.77 & ! [X: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.52/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.77 | ? [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT] :
% 5.52/5.77 ( ( A12
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList3 @ Summary3 ) )
% 5.52/5.77 & ! [X: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.52/5.77 => ( vEBT_invar_vebt @ X @ N3 ) )
% 5.52/5.77 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N3 ) )
% 5.52/5.77 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.52/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 5.52/5.77 & ( A23
% 5.52/5.77 = ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) )
% 5.52/5.77 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X7 )
% 5.52/5.77 & ! [X: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.52/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.77 | ? [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.52/5.77 ( ( A12
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList3 @ Summary3 ) )
% 5.52/5.77 & ! [X: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.52/5.77 => ( vEBT_invar_vebt @ X @ N3 ) )
% 5.52/5.77 & ( vEBT_invar_vebt @ Summary3 @ N3 )
% 5.52/5.77 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.52/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 5.52/5.77 & ( A23
% 5.52/5.77 = ( plus_plus_nat @ N3 @ N3 ) )
% 5.52/5.77 & ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 5.52/5.77 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X7 ) )
% 5.52/5.77 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 5.52/5.77 & ( ( Mi3 = Ma3 )
% 5.52/5.77 => ! [X: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.52/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.77 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.52/5.77 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.52/5.77 & ( ( Mi3 != Ma3 )
% 5.52/5.77 => ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 5.52/5.77 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 5.52/5.77 = I4 )
% 5.52/5.77 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 5.52/5.77 & ! [X: nat] :
% 5.52/5.77 ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 5.52/5.77 = I4 )
% 5.52/5.77 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 5.52/5.77 => ( ( ord_less_nat @ Mi3 @ X )
% 5.52/5.77 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) )
% 5.52/5.77 | ? [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.52/5.77 ( ( A12
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList3 @ Summary3 ) )
% 5.52/5.77 & ! [X: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.52/5.77 => ( vEBT_invar_vebt @ X @ N3 ) )
% 5.52/5.77 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N3 ) )
% 5.52/5.77 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.52/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 5.52/5.77 & ( A23
% 5.52/5.77 = ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) )
% 5.52/5.77 & ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 5.52/5.77 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X7 ) )
% 5.52/5.77 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 5.52/5.77 & ( ( Mi3 = Ma3 )
% 5.52/5.77 => ! [X: vEBT_VEBT] :
% 5.52/5.77 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.52/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.77 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.52/5.77 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.52/5.77 & ( ( Mi3 != Ma3 )
% 5.52/5.77 => ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 5.52/5.77 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 5.52/5.77 = I4 )
% 5.52/5.77 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 5.52/5.77 & ! [X: nat] :
% 5.52/5.77 ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 5.52/5.77 = I4 )
% 5.52/5.77 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 5.52/5.77 => ( ( ord_less_nat @ Mi3 @ X )
% 5.52/5.77 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % invar_vebt.simps
% 5.52/5.77 thf(fact_2707_nth__equalityI,axiom,
% 5.52/5.77 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.52/5.77 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.52/5.77 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.52/5.77 => ( ! [I2: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.52/5.77 => ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 5.52/5.77 = ( nth_VEBT_VEBT @ Ys @ I2 ) ) )
% 5.52/5.77 => ( Xs2 = Ys ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % nth_equalityI
% 5.52/5.77 thf(fact_2708_nth__equalityI,axiom,
% 5.52/5.77 ! [Xs2: list_o,Ys: list_o] :
% 5.52/5.77 ( ( ( size_size_list_o @ Xs2 )
% 5.52/5.77 = ( size_size_list_o @ Ys ) )
% 5.52/5.77 => ( ! [I2: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.52/5.77 => ( ( nth_o @ Xs2 @ I2 )
% 5.52/5.77 = ( nth_o @ Ys @ I2 ) ) )
% 5.52/5.77 => ( Xs2 = Ys ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % nth_equalityI
% 5.52/5.77 thf(fact_2709_nth__equalityI,axiom,
% 5.52/5.77 ! [Xs2: list_nat,Ys: list_nat] :
% 5.52/5.77 ( ( ( size_size_list_nat @ Xs2 )
% 5.52/5.77 = ( size_size_list_nat @ Ys ) )
% 5.52/5.77 => ( ! [I2: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.52/5.77 => ( ( nth_nat @ Xs2 @ I2 )
% 5.52/5.77 = ( nth_nat @ Ys @ I2 ) ) )
% 5.52/5.77 => ( Xs2 = Ys ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % nth_equalityI
% 5.52/5.77 thf(fact_2710_Skolem__list__nth,axiom,
% 5.52/5.77 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.52/5.77 ( ( ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ K )
% 5.52/5.77 => ? [X7: vEBT_VEBT] : ( P @ I4 @ X7 ) ) )
% 5.52/5.77 = ( ? [Xs: list_VEBT_VEBT] :
% 5.52/5.77 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.52/5.77 = K )
% 5.52/5.77 & ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ K )
% 5.52/5.77 => ( P @ I4 @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % Skolem_list_nth
% 5.52/5.77 thf(fact_2711_Skolem__list__nth,axiom,
% 5.52/5.77 ! [K: nat,P: nat > $o > $o] :
% 5.52/5.77 ( ( ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ K )
% 5.52/5.77 => ? [X7: $o] : ( P @ I4 @ X7 ) ) )
% 5.52/5.77 = ( ? [Xs: list_o] :
% 5.52/5.77 ( ( ( size_size_list_o @ Xs )
% 5.52/5.77 = K )
% 5.52/5.77 & ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ K )
% 5.52/5.77 => ( P @ I4 @ ( nth_o @ Xs @ I4 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % Skolem_list_nth
% 5.52/5.77 thf(fact_2712_Skolem__list__nth,axiom,
% 5.52/5.77 ! [K: nat,P: nat > nat > $o] :
% 5.52/5.77 ( ( ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ K )
% 5.52/5.77 => ? [X7: nat] : ( P @ I4 @ X7 ) ) )
% 5.52/5.77 = ( ? [Xs: list_nat] :
% 5.52/5.77 ( ( ( size_size_list_nat @ Xs )
% 5.52/5.77 = K )
% 5.52/5.77 & ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ K )
% 5.52/5.77 => ( P @ I4 @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % Skolem_list_nth
% 5.52/5.77 thf(fact_2713_list__eq__iff__nth__eq,axiom,
% 5.52/5.77 ( ( ^ [Y5: list_VEBT_VEBT,Z4: list_VEBT_VEBT] : ( Y5 = Z4 ) )
% 5.52/5.77 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.52/5.77 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.52/5.77 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.52/5.77 & ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.52/5.77 => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 5.52/5.77 = ( nth_VEBT_VEBT @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % list_eq_iff_nth_eq
% 5.52/5.77 thf(fact_2714_list__eq__iff__nth__eq,axiom,
% 5.52/5.77 ( ( ^ [Y5: list_o,Z4: list_o] : ( Y5 = Z4 ) )
% 5.52/5.77 = ( ^ [Xs: list_o,Ys3: list_o] :
% 5.52/5.77 ( ( ( size_size_list_o @ Xs )
% 5.52/5.77 = ( size_size_list_o @ Ys3 ) )
% 5.52/5.77 & ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.52/5.77 => ( ( nth_o @ Xs @ I4 )
% 5.52/5.77 = ( nth_o @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % list_eq_iff_nth_eq
% 5.52/5.77 thf(fact_2715_list__eq__iff__nth__eq,axiom,
% 5.52/5.77 ( ( ^ [Y5: list_nat,Z4: list_nat] : ( Y5 = Z4 ) )
% 5.52/5.77 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 5.52/5.77 ( ( ( size_size_list_nat @ Xs )
% 5.52/5.77 = ( size_size_list_nat @ Ys3 ) )
% 5.52/5.77 & ! [I4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.52/5.77 => ( ( nth_nat @ Xs @ I4 )
% 5.52/5.77 = ( nth_nat @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % list_eq_iff_nth_eq
% 5.52/5.77 thf(fact_2716_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Oelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.52/5.77 ( ( ( vEBT_T_s_u_c_c2 @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( ? [Uu2: $o,B2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 5.52/5.77 => ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => ( Y2 != one_one_nat ) ) )
% 5.52/5.77 => ( ( ? [Uv2: $o,Uw2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ( ? [N2: nat] :
% 5.52/5.77 ( Xa2
% 5.52/5.77 = ( suc @ N2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) ) )
% 5.52/5.77 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( Y2 = one_one_nat ) )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 @ ( if_nat
% 5.52/5.77 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 != none_nat )
% 5.52/5.77 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.52/5.77 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.elims
% 5.52/5.77 thf(fact_2717_vebt__succ_Oelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 5.52/5.77 ( ( ( vEBT_vebt_succ @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ! [Uu2: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 5.52/5.77 => ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => ~ ( ( B2
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( some_nat @ one_one_nat ) ) )
% 5.52/5.77 & ( ~ B2
% 5.52/5.77 => ( Y2 = none_nat ) ) ) ) )
% 5.52/5.77 => ( ( ? [Uv2: $o,Uw2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ( ? [N2: nat] :
% 5.52/5.77 ( Xa2
% 5.52/5.77 = ( suc @ N2 ) )
% 5.52/5.77 => ( Y2 != none_nat ) ) )
% 5.52/5.77 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.77 => ( Y2 != none_nat ) )
% 5.52/5.77 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.52/5.77 => ( Y2 != none_nat ) )
% 5.52/5.77 => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.52/5.77 => ( Y2 != none_nat ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( some_nat @ Mi2 ) ) )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 @ ( if_option_nat
% 5.52/5.77 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 != none_nat )
% 5.52/5.77 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.52/5.77 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 @ ( if_option_nat
% 5.52/5.77 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.77 = none_nat )
% 5.52/5.77 @ none_nat
% 5.52/5.77 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.52/5.77 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % vebt_succ.elims
% 5.52/5.77 thf(fact_2718_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Oelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.52/5.77 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( ? [A3: $o,B2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.52/5.77 ( ? [Summary2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( Y2
% 5.52/5.77 != ( plus_plus_nat @ one_one_nat
% 5.52/5.77 @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 5.52/5.77 @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 5.52/5.77 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 5.52/5.77 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 5.52/5.77 @ ( if_nat
% 5.52/5.77 @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 5.52/5.77 & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 5.52/5.77 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.52/5.77 @ zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.elims
% 5.52/5.77 thf(fact_2719_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I5_J,axiom,
% 5.52/5.77 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.52/5.77 = ( plus_plus_nat @ one_one_nat
% 5.52/5.77 @ ( if_nat @ ( X2 = Mi ) @ zero_zero_nat
% 5.52/5.77 @ ( if_nat @ ( X2 = Ma ) @ zero_zero_nat
% 5.52/5.77 @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ zero_zero_nat
% 5.52/5.77 @ ( if_nat @ ( ord_less_nat @ Ma @ X2 ) @ zero_zero_nat
% 5.52/5.77 @ ( if_nat
% 5.52/5.77 @ ( ( ord_less_nat @ Mi @ X2 )
% 5.52/5.77 & ( ord_less_nat @ X2 @ Ma ) )
% 5.52/5.77 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.52/5.77 @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(5)
% 5.52/5.77 thf(fact_2720_inrange,axiom,
% 5.52/5.77 ! [T: vEBT_VEBT,N: nat] :
% 5.52/5.77 ( ( vEBT_invar_vebt @ T @ N )
% 5.52/5.77 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % inrange
% 5.52/5.77 thf(fact_2721_set__bit__0,axiom,
% 5.52/5.77 ! [A: int] :
% 5.52/5.77 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.52/5.77 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % set_bit_0
% 5.52/5.77 thf(fact_2722_set__bit__0,axiom,
% 5.52/5.77 ! [A: nat] :
% 5.52/5.77 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.52/5.77 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % set_bit_0
% 5.52/5.77 thf(fact_2723_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Opelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.52/5.77 ( ( ( vEBT_T_s_u_c_c @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [Uu2: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 5.52/5.77 => ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B2 ) @ zero_zero_nat ) ) ) ) )
% 5.52/5.77 => ( ! [Uv2: $o,Uw2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ! [N2: nat] :
% 5.52/5.77 ( ( Xa2
% 5.52/5.77 = ( suc @ N2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N2 ) ) ) ) ) )
% 5.52/5.77 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( plus_plus_nat @ one_one_nat
% 5.52/5.77 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat
% 5.52/5.77 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 5.52/5.77 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.52/5.77 @ ( if_nat
% 5.52/5.77 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 != none_nat )
% 5.52/5.77 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 5.52/5.77 @ ( if_nat
% 5.52/5.77 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.77 = none_nat )
% 5.52/5.77 @ one_one_nat
% 5.52/5.77 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.52/5.77 @ one_one_nat ) ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.pelims
% 5.52/5.77 thf(fact_2724_vebt__succ_Opelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 5.52/5.77 ( ( ( vEBT_vebt_succ @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [Uu2: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 5.52/5.77 => ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => ( ( ( B2
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( some_nat @ one_one_nat ) ) )
% 5.52/5.77 & ( ~ B2
% 5.52/5.77 => ( Y2 = none_nat ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B2 ) @ zero_zero_nat ) ) ) ) )
% 5.52/5.77 => ( ! [Uv2: $o,Uw2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ! [N2: nat] :
% 5.52/5.77 ( ( Xa2
% 5.52/5.77 = ( suc @ N2 ) )
% 5.52/5.77 => ( ( Y2 = none_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N2 ) ) ) ) ) )
% 5.52/5.77 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.77 => ( ( Y2 = none_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.52/5.77 => ( ( Y2 = none_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.52/5.77 => ( ( Y2 = none_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( some_nat @ Mi2 ) ) )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 @ ( if_option_nat
% 5.52/5.77 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 != none_nat )
% 5.52/5.77 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.52/5.77 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 @ ( if_option_nat
% 5.52/5.77 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.77 = none_nat )
% 5.52/5.77 @ none_nat
% 5.52/5.77 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.52/5.77 @ none_nat ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % vebt_succ.pelims
% 5.52/5.77 thf(fact_2725_vebt__pred_Opelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 5.52/5.77 ( ( ( vEBT_vebt_pred @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [Uu2: $o,Uv2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.52/5.77 => ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => ( ( Y2 = none_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.52/5.77 => ( ! [A3: $o,Uw2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.52/5.77 => ( ( Xa2
% 5.52/5.77 = ( suc @ zero_zero_nat ) )
% 5.52/5.77 => ( ( ( A3
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( some_nat @ zero_zero_nat ) ) )
% 5.52/5.77 & ( ~ A3
% 5.52/5.77 => ( Y2 = none_nat ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ! [Va3: nat] :
% 5.52/5.77 ( ( Xa2
% 5.52/5.77 = ( suc @ ( suc @ Va3 ) ) )
% 5.52/5.77 => ( ( ( B2
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( some_nat @ one_one_nat ) ) )
% 5.52/5.77 & ( ~ B2
% 5.52/5.77 => ( ( A3
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( some_nat @ zero_zero_nat ) ) )
% 5.52/5.77 & ( ~ A3
% 5.52/5.77 => ( Y2 = none_nat ) ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) )
% 5.52/5.77 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.52/5.77 => ( ( Y2 = none_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) )
% 5.52/5.77 => ( ( Y2 = none_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.52/5.77 => ( ( Y2 = none_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( some_nat @ Ma2 ) ) )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 @ ( if_option_nat
% 5.52/5.77 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 != none_nat )
% 5.52/5.77 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.52/5.77 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 @ ( if_option_nat
% 5.52/5.77 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.77 = none_nat )
% 5.52/5.77 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.52/5.77 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.52/5.77 @ none_nat ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % vebt_pred.pelims
% 5.52/5.77 thf(fact_2726_double__eq__0__iff,axiom,
% 5.52/5.77 ! [A: real] :
% 5.52/5.77 ( ( ( plus_plus_real @ A @ A )
% 5.52/5.77 = zero_zero_real )
% 5.52/5.77 = ( A = zero_zero_real ) ) ).
% 5.52/5.77
% 5.52/5.77 % double_eq_0_iff
% 5.52/5.77 thf(fact_2727_double__eq__0__iff,axiom,
% 5.52/5.77 ! [A: rat] :
% 5.52/5.77 ( ( ( plus_plus_rat @ A @ A )
% 5.52/5.77 = zero_zero_rat )
% 5.52/5.77 = ( A = zero_zero_rat ) ) ).
% 5.52/5.77
% 5.52/5.77 % double_eq_0_iff
% 5.52/5.77 thf(fact_2728_double__eq__0__iff,axiom,
% 5.52/5.77 ! [A: int] :
% 5.52/5.77 ( ( ( plus_plus_int @ A @ A )
% 5.52/5.77 = zero_zero_int )
% 5.52/5.77 = ( A = zero_zero_int ) ) ).
% 5.52/5.77
% 5.52/5.77 % double_eq_0_iff
% 5.52/5.77 thf(fact_2729_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Opelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.52/5.77 ( ( ( vEBT_T_s_u_c_c2 @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [Uu2: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 5.52/5.77 => ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B2 ) @ zero_zero_nat ) ) ) ) )
% 5.52/5.77 => ( ! [Uv2: $o,Uw2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ! [N2: nat] :
% 5.52/5.77 ( ( Xa2
% 5.52/5.77 = ( suc @ N2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N2 ) ) ) ) ) )
% 5.52/5.77 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( Y2 = one_one_nat ) )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( Y2
% 5.52/5.77 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 @ ( if_nat
% 5.52/5.77 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 != none_nat )
% 5.52/5.77 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.52/5.77 @ one_one_nat ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.pelims
% 5.52/5.77 thf(fact_2730_not__min__Null__member,axiom,
% 5.52/5.77 ! [T: vEBT_VEBT] :
% 5.52/5.77 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.52/5.77 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 5.52/5.77
% 5.52/5.77 % not_min_Null_member
% 5.52/5.77 thf(fact_2731_min__Null__member,axiom,
% 5.52/5.77 ! [T: vEBT_VEBT,X2: nat] :
% 5.52/5.77 ( ( vEBT_VEBT_minNull @ T )
% 5.52/5.77 => ~ ( vEBT_vebt_member @ T @ X2 ) ) ).
% 5.52/5.77
% 5.52/5.77 % min_Null_member
% 5.52/5.77 thf(fact_2732_minNullmin,axiom,
% 5.52/5.77 ! [T: vEBT_VEBT] :
% 5.52/5.77 ( ( vEBT_VEBT_minNull @ T )
% 5.52/5.77 => ( ( vEBT_vebt_mint @ T )
% 5.52/5.77 = none_nat ) ) ).
% 5.52/5.77
% 5.52/5.77 % minNullmin
% 5.52/5.77 thf(fact_2733_minminNull,axiom,
% 5.52/5.77 ! [T: vEBT_VEBT] :
% 5.52/5.77 ( ( ( vEBT_vebt_mint @ T )
% 5.52/5.77 = none_nat )
% 5.52/5.77 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.52/5.77
% 5.52/5.77 % minminNull
% 5.52/5.77 thf(fact_2734_div__neg__neg__trivial,axiom,
% 5.52/5.77 ! [K: int,L: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.52/5.77 => ( ( ord_less_int @ L @ K )
% 5.52/5.77 => ( ( divide_divide_int @ K @ L )
% 5.52/5.77 = zero_zero_int ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % div_neg_neg_trivial
% 5.52/5.77 thf(fact_2735_div__pos__pos__trivial,axiom,
% 5.52/5.77 ! [K: int,L: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.77 => ( ( ord_less_int @ K @ L )
% 5.52/5.77 => ( ( divide_divide_int @ K @ L )
% 5.52/5.77 = zero_zero_int ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % div_pos_pos_trivial
% 5.52/5.77 thf(fact_2736_i0__less,axiom,
% 5.52/5.77 ! [N: extended_enat] :
% 5.52/5.77 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.52/5.77 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 5.52/5.77
% 5.52/5.77 % i0_less
% 5.52/5.77 thf(fact_2737_idiff__0__right,axiom,
% 5.52/5.77 ! [N: extended_enat] :
% 5.52/5.77 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.52/5.77 = N ) ).
% 5.52/5.77
% 5.52/5.77 % idiff_0_right
% 5.52/5.77 thf(fact_2738_idiff__0,axiom,
% 5.52/5.77 ! [N: extended_enat] :
% 5.52/5.77 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.52/5.77 = zero_z5237406670263579293d_enat ) ).
% 5.52/5.77
% 5.52/5.77 % idiff_0
% 5.52/5.77 thf(fact_2739_not__real__square__gt__zero,axiom,
% 5.52/5.77 ! [X2: real] :
% 5.52/5.77 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X2 @ X2 ) ) )
% 5.52/5.77 = ( X2 = zero_zero_real ) ) ).
% 5.52/5.77
% 5.52/5.77 % not_real_square_gt_zero
% 5.52/5.77 thf(fact_2740_half__nonnegative__int__iff,axiom,
% 5.52/5.77 ! [K: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.52/5.77 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.52/5.77
% 5.52/5.77 % half_nonnegative_int_iff
% 5.52/5.77 thf(fact_2741_half__negative__int__iff,axiom,
% 5.52/5.77 ! [K: int] :
% 5.52/5.77 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.52/5.77 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.52/5.77
% 5.52/5.77 % half_negative_int_iff
% 5.52/5.77 thf(fact_2742_div__pos__geq,axiom,
% 5.52/5.77 ! [L: int,K: int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ L )
% 5.52/5.77 => ( ( ord_less_eq_int @ L @ K )
% 5.52/5.77 => ( ( divide_divide_int @ K @ L )
% 5.52/5.77 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % div_pos_geq
% 5.52/5.77 thf(fact_2743_zdiv__zmult2__eq,axiom,
% 5.52/5.77 ! [C: int,A: int,B: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.77 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.52/5.77 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % zdiv_zmult2_eq
% 5.52/5.77 thf(fact_2744_split__zdiv,axiom,
% 5.52/5.77 ! [P: int > $o,N: int,K: int] :
% 5.52/5.77 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.52/5.77 = ( ( ( K = zero_zero_int )
% 5.52/5.77 => ( P @ zero_zero_int ) )
% 5.52/5.77 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.52/5.77 => ! [I4: int,J3: int] :
% 5.52/5.77 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.52/5.77 & ( ord_less_int @ J3 @ K )
% 5.52/5.77 & ( N
% 5.52/5.77 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.52/5.77 => ( P @ I4 ) ) )
% 5.52/5.77 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.52/5.77 => ! [I4: int,J3: int] :
% 5.52/5.77 ( ( ( ord_less_int @ K @ J3 )
% 5.52/5.77 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.52/5.77 & ( N
% 5.52/5.77 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.52/5.77 => ( P @ I4 ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % split_zdiv
% 5.52/5.77 thf(fact_2745_zdiv__mono1,axiom,
% 5.52/5.77 ! [A: int,A5: int,B: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ A @ A5 )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.77 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A5 @ B ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % zdiv_mono1
% 5.52/5.77 thf(fact_2746_zdiv__mono2,axiom,
% 5.52/5.77 ! [A: int,B5: int,B: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.52/5.77 => ( ( ord_less_eq_int @ B5 @ B )
% 5.52/5.77 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B5 ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % zdiv_mono2
% 5.52/5.77 thf(fact_2747_zdiv__eq__0__iff,axiom,
% 5.52/5.77 ! [I: int,K: int] :
% 5.52/5.77 ( ( ( divide_divide_int @ I @ K )
% 5.52/5.77 = zero_zero_int )
% 5.52/5.77 = ( ( K = zero_zero_int )
% 5.52/5.77 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.52/5.77 & ( ord_less_int @ I @ K ) )
% 5.52/5.77 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.52/5.77 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % zdiv_eq_0_iff
% 5.52/5.77 thf(fact_2748_int__div__neg__eq,axiom,
% 5.52/5.77 ! [A: int,B: int,Q2: int,R: int] :
% 5.52/5.77 ( ( A
% 5.52/5.77 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.52/5.77 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 5.52/5.77 => ( ( ord_less_int @ B @ R )
% 5.52/5.77 => ( ( divide_divide_int @ A @ B )
% 5.52/5.77 = Q2 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % int_div_neg_eq
% 5.52/5.77 thf(fact_2749_int__div__pos__eq,axiom,
% 5.52/5.77 ! [A: int,B: int,Q2: int,R: int] :
% 5.52/5.77 ( ( A
% 5.52/5.77 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.52/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.52/5.77 => ( ( ord_less_int @ R @ B )
% 5.52/5.77 => ( ( divide_divide_int @ A @ B )
% 5.52/5.77 = Q2 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % int_div_pos_eq
% 5.52/5.77 thf(fact_2750_zdiv__mono1__neg,axiom,
% 5.52/5.77 ! [A: int,A5: int,B: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ A @ A5 )
% 5.52/5.77 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.52/5.77 => ( ord_less_eq_int @ ( divide_divide_int @ A5 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % zdiv_mono1_neg
% 5.52/5.77 thf(fact_2751_zdiv__mono2__neg,axiom,
% 5.52/5.77 ! [A: int,B5: int,B: int] :
% 5.52/5.77 ( ( ord_less_int @ A @ zero_zero_int )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.52/5.77 => ( ( ord_less_eq_int @ B5 @ B )
% 5.52/5.77 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B5 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % zdiv_mono2_neg
% 5.52/5.77 thf(fact_2752_div__int__pos__iff,axiom,
% 5.52/5.77 ! [K: int,L: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 5.52/5.77 = ( ( K = zero_zero_int )
% 5.52/5.77 | ( L = zero_zero_int )
% 5.52/5.77 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.77 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 5.52/5.77 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.52/5.77 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % div_int_pos_iff
% 5.52/5.77 thf(fact_2753_div__positive__int,axiom,
% 5.52/5.77 ! [L: int,K: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ L @ K )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ L )
% 5.52/5.77 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % div_positive_int
% 5.52/5.77 thf(fact_2754_div__neg__pos__less0,axiom,
% 5.52/5.77 ! [A: int,B: int] :
% 5.52/5.77 ( ( ord_less_int @ A @ zero_zero_int )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.77 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % div_neg_pos_less0
% 5.52/5.77 thf(fact_2755_int__div__less__self,axiom,
% 5.52/5.77 ! [X2: int,K: int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.52/5.77 => ( ( ord_less_int @ one_one_int @ K )
% 5.52/5.77 => ( ord_less_int @ ( divide_divide_int @ X2 @ K ) @ X2 ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % int_div_less_self
% 5.52/5.77 thf(fact_2756_div__nonneg__neg__le0,axiom,
% 5.52/5.77 ! [A: int,B: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.77 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.52/5.77 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % div_nonneg_neg_le0
% 5.52/5.77 thf(fact_2757_div__nonpos__pos__le0,axiom,
% 5.52/5.77 ! [A: int,B: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.77 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % div_nonpos_pos_le0
% 5.52/5.77 thf(fact_2758_neg__imp__zdiv__neg__iff,axiom,
% 5.52/5.77 ! [B: int,A: int] :
% 5.52/5.77 ( ( ord_less_int @ B @ zero_zero_int )
% 5.52/5.77 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.52/5.77 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % neg_imp_zdiv_neg_iff
% 5.52/5.77 thf(fact_2759_pos__imp__zdiv__neg__iff,axiom,
% 5.52/5.77 ! [B: int,A: int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.77 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.52/5.77 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pos_imp_zdiv_neg_iff
% 5.52/5.77 thf(fact_2760_pos__imp__zdiv__pos__iff,axiom,
% 5.52/5.77 ! [K: int,I: int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ K )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 5.52/5.77 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pos_imp_zdiv_pos_iff
% 5.52/5.77 thf(fact_2761_neg__imp__zdiv__nonneg__iff,axiom,
% 5.52/5.77 ! [B: int,A: int] :
% 5.52/5.77 ( ( ord_less_int @ B @ zero_zero_int )
% 5.52/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.52/5.77 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % neg_imp_zdiv_nonneg_iff
% 5.52/5.77 thf(fact_2762_pos__imp__zdiv__nonneg__iff,axiom,
% 5.52/5.77 ! [B: int,A: int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.52/5.77 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pos_imp_zdiv_nonneg_iff
% 5.52/5.77 thf(fact_2763_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.52/5.77 ! [A: int,B: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.52/5.77 = ( ( ord_less_eq_int @ B @ A )
% 5.52/5.77 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % nonneg1_imp_zdiv_pos_iff
% 5.52/5.77 thf(fact_2764_enat__0__less__mult__iff,axiom,
% 5.52/5.77 ! [M: extended_enat,N: extended_enat] :
% 5.52/5.77 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 5.52/5.77 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.52/5.77 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % enat_0_less_mult_iff
% 5.52/5.77 thf(fact_2765_not__iless0,axiom,
% 5.52/5.77 ! [N: extended_enat] :
% 5.52/5.77 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 5.52/5.77
% 5.52/5.77 % not_iless0
% 5.52/5.77 thf(fact_2766_iadd__is__0,axiom,
% 5.52/5.77 ! [M: extended_enat,N: extended_enat] :
% 5.52/5.77 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.52/5.77 = zero_z5237406670263579293d_enat )
% 5.52/5.77 = ( ( M = zero_z5237406670263579293d_enat )
% 5.52/5.77 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % iadd_is_0
% 5.52/5.77 thf(fact_2767_ile0__eq,axiom,
% 5.52/5.77 ! [N: extended_enat] :
% 5.52/5.77 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.52/5.77 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.52/5.77
% 5.52/5.77 % ile0_eq
% 5.52/5.77 thf(fact_2768_i0__lb,axiom,
% 5.52/5.77 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 5.52/5.77
% 5.52/5.77 % i0_lb
% 5.52/5.77 thf(fact_2769_all__nat__less,axiom,
% 5.52/5.77 ! [N: nat,P: nat > $o] :
% 5.52/5.77 ( ( ! [M3: nat] :
% 5.52/5.77 ( ( ord_less_eq_nat @ M3 @ N )
% 5.52/5.77 => ( P @ M3 ) ) )
% 5.52/5.77 = ( ! [X: nat] :
% 5.52/5.77 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.52/5.77 => ( P @ X ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % all_nat_less
% 5.52/5.77 thf(fact_2770_ex__nat__less,axiom,
% 5.52/5.77 ! [N: nat,P: nat > $o] :
% 5.52/5.77 ( ( ? [M3: nat] :
% 5.52/5.77 ( ( ord_less_eq_nat @ M3 @ N )
% 5.52/5.77 & ( P @ M3 ) ) )
% 5.52/5.77 = ( ? [X: nat] :
% 5.52/5.77 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.52/5.77 & ( P @ X ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % ex_nat_less
% 5.52/5.77 thf(fact_2771_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.52/5.77 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.52/5.77 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 5.52/5.77
% 5.52/5.77 % VEBT_internal.minNull.simps(5)
% 5.52/5.77 thf(fact_2772_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.52/5.77 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 5.52/5.77
% 5.52/5.77 % VEBT_internal.minNull.simps(4)
% 5.52/5.77 thf(fact_2773_not__exp__less__eq__0__int,axiom,
% 5.52/5.77 ! [N: nat] :
% 5.52/5.77 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.52/5.77
% 5.52/5.77 % not_exp_less_eq_0_int
% 5.52/5.77 thf(fact_2774_realpow__pos__nth2,axiom,
% 5.52/5.77 ! [A: real,N: nat] :
% 5.52/5.77 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.77 => ? [R3: real] :
% 5.52/5.77 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.52/5.77 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 5.52/5.77 = A ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % realpow_pos_nth2
% 5.52/5.77 thf(fact_2775_real__arch__pow__inv,axiom,
% 5.52/5.77 ! [Y2: real,X2: real] :
% 5.52/5.77 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.77 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.52/5.77 => ? [N2: nat] : ( ord_less_real @ ( power_power_real @ X2 @ N2 ) @ Y2 ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % real_arch_pow_inv
% 5.52/5.77 thf(fact_2776_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I1_J,axiom,
% 5.52/5.77 ! [A: $o,B: $o,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(1)
% 5.52/5.77 thf(fact_2777_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT] :
% 5.52/5.77 ( ~ ( vEBT_VEBT_minNull @ X2 )
% 5.52/5.77 => ( ! [Uv2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.52/5.77 => ( ! [Uu2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.52/5.77 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % VEBT_internal.minNull.elims(3)
% 5.52/5.77 thf(fact_2778_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT] :
% 5.52/5.77 ( ( vEBT_VEBT_minNull @ X2 )
% 5.52/5.77 => ( ( X2
% 5.52/5.77 != ( vEBT_Leaf @ $false @ $false ) )
% 5.52/5.77 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % VEBT_internal.minNull.elims(2)
% 5.52/5.77 thf(fact_2779_realpow__pos__nth,axiom,
% 5.52/5.77 ! [N: nat,A: real] :
% 5.52/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.77 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.77 => ? [R3: real] :
% 5.52/5.77 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.52/5.77 & ( ( power_power_real @ R3 @ N )
% 5.52/5.77 = A ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % realpow_pos_nth
% 5.52/5.77 thf(fact_2780_realpow__pos__nth__unique,axiom,
% 5.52/5.77 ! [N: nat,A: real] :
% 5.52/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.77 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.77 => ? [X4: real] :
% 5.52/5.77 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.52/5.77 & ( ( power_power_real @ X4 @ N )
% 5.52/5.77 = A )
% 5.52/5.77 & ! [Y4: real] :
% 5.52/5.77 ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.52/5.77 & ( ( power_power_real @ Y4 @ N )
% 5.52/5.77 = A ) )
% 5.52/5.77 => ( Y4 = X4 ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % realpow_pos_nth_unique
% 5.52/5.77 thf(fact_2781_neg__zdiv__mult__2,axiom,
% 5.52/5.77 ! [A: int,B: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.77 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.77 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % neg_zdiv_mult_2
% 5.52/5.77 thf(fact_2782_pos__zdiv__mult__2,axiom,
% 5.52/5.77 ! [A: int,B: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.77 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.77 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pos_zdiv_mult_2
% 5.52/5.77 thf(fact_2783_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Y2: $o] :
% 5.52/5.77 ( ( ( vEBT_VEBT_minNull @ X2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ $false @ $false ) )
% 5.52/5.77 => ~ Y2 )
% 5.52/5.77 => ( ( ? [Uv2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.52/5.77 => Y2 )
% 5.52/5.77 => ( ( ? [Uu2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.52/5.77 => Y2 )
% 5.52/5.77 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.52/5.77 => ~ Y2 )
% 5.52/5.77 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.52/5.77 => Y2 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % VEBT_internal.minNull.elims(1)
% 5.52/5.77 thf(fact_2784_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I2_J,axiom,
% 5.52/5.77 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X2 )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(2)
% 5.52/5.77 thf(fact_2785_int__power__div__base,axiom,
% 5.52/5.77 ! [M: nat,K: int] :
% 5.52/5.77 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.52/5.77 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.52/5.77 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % int_power_div_base
% 5.52/5.77 thf(fact_2786_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I3_J,axiom,
% 5.52/5.77 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(3)
% 5.52/5.77 thf(fact_2787_insertsimp,axiom,
% 5.52/5.77 ! [T: vEBT_VEBT,N: nat,L: nat] :
% 5.52/5.77 ( ( vEBT_invar_vebt @ T @ N )
% 5.52/5.77 => ( ( vEBT_VEBT_minNull @ T )
% 5.52/5.77 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ L ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % insertsimp
% 5.52/5.77 thf(fact_2788_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J,axiom,
% 5.52/5.77 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(4)
% 5.52/5.77 thf(fact_2789_member__bound__height_H,axiom,
% 5.52/5.77 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.52/5.77 ( ( vEBT_invar_vebt @ T @ N )
% 5.52/5.77 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ T @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % member_bound_height'
% 5.52/5.77 thf(fact_2790_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Opelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.52/5.77 ( ( ( vEBT_T_m_e_m_b_e_r @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.pelims
% 5.52/5.77 thf(fact_2791_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Opelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.52/5.77 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( plus_plus_nat @ one_one_nat
% 5.52/5.77 @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 5.52/5.77 @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 5.52/5.77 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 5.52/5.77 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 5.52/5.77 @ ( if_nat
% 5.52/5.77 @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 5.52/5.77 & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 5.52/5.77 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.52/5.77 @ zero_zero_nat ) ) ) ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.pelims
% 5.52/5.77 thf(fact_2792_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Oelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.52/5.77 ( ( ( vEBT_T_i_n_s_e_r_t @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( ? [A3: $o,B2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( Y2
% 5.52/5.77 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.52/5.77 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( Y2
% 5.52/5.77 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( Y2
% 5.52/5.77 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.52/5.77 @ ( if_nat
% 5.52/5.77 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 & ~ ( ( Xa2 = Mi2 )
% 5.52/5.77 | ( Xa2 = Ma2 ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.52/5.77 @ one_one_nat ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.elims
% 5.52/5.77 thf(fact_2793_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I5_J,axiom,
% 5.52/5.77 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.52/5.77 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.52/5.77 @ ( if_nat
% 5.52/5.77 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.52/5.77 & ~ ( ( X2 = Mi )
% 5.52/5.77 | ( X2 = Ma ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.52/5.77 @ one_one_nat ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(5)
% 5.52/5.77 thf(fact_2794_vebt__member_Opelims_I3_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.77 ( ~ ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.52/5.77 => ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => A3 )
% 5.52/5.77 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.77 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.77 => B2 )
% 5.52/5.77 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.52/5.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.52/5.77 => ( ( Xa2 != Mi2 )
% 5.52/5.77 => ( ( Xa2 != Ma2 )
% 5.52/5.77 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.77 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % vebt_member.pelims(3)
% 5.52/5.77 thf(fact_2795_vebt__member_Opelims_I1_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.52/5.77 ( ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => A3 )
% 5.52/5.77 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.77 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.77 => B2 )
% 5.52/5.77 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ( ~ Y2
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.52/5.77 => ( ~ Y2
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.52/5.77 => ( ~ Y2
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( ( Xa2 != Mi2 )
% 5.52/5.77 => ( ( Xa2 != Ma2 )
% 5.52/5.77 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.77 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % vebt_member.pelims(1)
% 5.52/5.77 thf(fact_2796_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.77 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.52/5.77 => ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => A3 )
% 5.52/5.77 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.77 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.77 => B2 )
% 5.52/5.77 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.52/5.77 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.52/5.77 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) @ Xa2 ) )
% 5.52/5.77 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % VEBT_internal.naive_member.pelims(3)
% 5.52/5.77 thf(fact_2797_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.77 ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.52/5.77 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => A3 )
% 5.52/5.77 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.77 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.77 => B2 )
% 5.52/5.77 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.52/5.77 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) @ Xa2 ) )
% 5.52/5.77 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % VEBT_internal.naive_member.pelims(2)
% 5.52/5.77 thf(fact_2798_set__bit__nonnegative__int__iff,axiom,
% 5.52/5.77 ! [N: nat,K: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 5.52/5.77 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.52/5.77
% 5.52/5.77 % set_bit_nonnegative_int_iff
% 5.52/5.77 thf(fact_2799_set__bit__negative__int__iff,axiom,
% 5.52/5.77 ! [N: nat,K: int] :
% 5.52/5.77 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 5.52/5.77 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.52/5.77
% 5.52/5.77 % set_bit_negative_int_iff
% 5.52/5.77 thf(fact_2800_zle__add1__eq__le,axiom,
% 5.52/5.77 ! [W: int,Z: int] :
% 5.52/5.77 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.52/5.77 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.52/5.77
% 5.52/5.77 % zle_add1_eq_le
% 5.52/5.77 thf(fact_2801_zle__diff1__eq,axiom,
% 5.52/5.77 ! [W: int,Z: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.52/5.77 = ( ord_less_int @ W @ Z ) ) ).
% 5.52/5.77
% 5.52/5.77 % zle_diff1_eq
% 5.52/5.77 thf(fact_2802_pos__zmult__eq__1__iff,axiom,
% 5.52/5.77 ! [M: int,N: int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ M )
% 5.52/5.77 => ( ( ( times_times_int @ M @ N )
% 5.52/5.77 = one_one_int )
% 5.52/5.77 = ( ( M = one_one_int )
% 5.52/5.77 & ( N = one_one_int ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pos_zmult_eq_1_iff
% 5.52/5.77 thf(fact_2803_zmult__zless__mono2,axiom,
% 5.52/5.77 ! [I: int,J: int,K: int] :
% 5.52/5.77 ( ( ord_less_int @ I @ J )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.52/5.77 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % zmult_zless_mono2
% 5.52/5.77 thf(fact_2804_int__one__le__iff__zero__less,axiom,
% 5.52/5.77 ! [Z: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.52/5.77 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.52/5.77
% 5.52/5.77 % int_one_le_iff_zero_less
% 5.52/5.77 thf(fact_2805_less__int__code_I1_J,axiom,
% 5.52/5.77 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.52/5.77
% 5.52/5.77 % less_int_code(1)
% 5.52/5.77 thf(fact_2806_zero__one__enat__neq_I1_J,axiom,
% 5.52/5.77 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.52/5.77
% 5.52/5.77 % zero_one_enat_neq(1)
% 5.52/5.77 thf(fact_2807_imult__is__0,axiom,
% 5.52/5.77 ! [M: extended_enat,N: extended_enat] :
% 5.52/5.77 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 5.52/5.77 = zero_z5237406670263579293d_enat )
% 5.52/5.77 = ( ( M = zero_z5237406670263579293d_enat )
% 5.52/5.77 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % imult_is_0
% 5.52/5.77 thf(fact_2808_le__imp__0__less,axiom,
% 5.52/5.77 ! [Z: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.52/5.77 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % le_imp_0_less
% 5.52/5.77 thf(fact_2809_odd__less__0__iff,axiom,
% 5.52/5.77 ! [Z: int] :
% 5.52/5.77 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.52/5.77 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.52/5.77
% 5.52/5.77 % odd_less_0_iff
% 5.52/5.77 thf(fact_2810_unique__quotient__lemma__neg,axiom,
% 5.52/5.77 ! [B: int,Q5: int,R4: int,Q2: int,R: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.52/5.77 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 5.52/5.77 => ( ( ord_less_int @ B @ R )
% 5.52/5.77 => ( ( ord_less_int @ B @ R4 )
% 5.52/5.77 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % unique_quotient_lemma_neg
% 5.52/5.77 thf(fact_2811_unique__quotient__lemma,axiom,
% 5.52/5.77 ! [B: int,Q5: int,R4: int,Q2: int,R: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.52/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.52/5.77 => ( ( ord_less_int @ R4 @ B )
% 5.52/5.77 => ( ( ord_less_int @ R @ B )
% 5.52/5.77 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % unique_quotient_lemma
% 5.52/5.77 thf(fact_2812_zdiv__mono2__neg__lemma,axiom,
% 5.52/5.77 ! [B: int,Q2: int,R: int,B5: int,Q5: int,R4: int] :
% 5.52/5.77 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 5.52/5.77 = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 5.52/5.77 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) @ zero_zero_int )
% 5.52/5.77 => ( ( ord_less_int @ R @ B )
% 5.52/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.52/5.77 => ( ( ord_less_eq_int @ B5 @ B )
% 5.52/5.77 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % zdiv_mono2_neg_lemma
% 5.52/5.77 thf(fact_2813_zdiv__mono2__lemma,axiom,
% 5.52/5.77 ! [B: int,Q2: int,R: int,B5: int,Q5: int,R4: int] :
% 5.52/5.77 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 5.52/5.77 = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 5.52/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 5.52/5.77 => ( ( ord_less_int @ R4 @ B5 )
% 5.52/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.52/5.77 => ( ( ord_less_eq_int @ B5 @ B )
% 5.52/5.77 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % zdiv_mono2_lemma
% 5.52/5.77 thf(fact_2814_q__pos__lemma,axiom,
% 5.52/5.77 ! [B5: int,Q5: int,R4: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 5.52/5.77 => ( ( ord_less_int @ R4 @ B5 )
% 5.52/5.77 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.52/5.77 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % q_pos_lemma
% 5.52/5.77 thf(fact_2815_zless__imp__add1__zle,axiom,
% 5.52/5.77 ! [W: int,Z: int] :
% 5.52/5.77 ( ( ord_less_int @ W @ Z )
% 5.52/5.77 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 5.52/5.77
% 5.52/5.77 % zless_imp_add1_zle
% 5.52/5.77 thf(fact_2816_int__less__induct,axiom,
% 5.52/5.77 ! [I: int,K: int,P: int > $o] :
% 5.52/5.77 ( ( ord_less_int @ I @ K )
% 5.52/5.77 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.52/5.77 => ( ! [I2: int] :
% 5.52/5.77 ( ( ord_less_int @ I2 @ K )
% 5.52/5.77 => ( ( P @ I2 )
% 5.52/5.77 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.52/5.77 => ( P @ I ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % int_less_induct
% 5.52/5.77 thf(fact_2817_zless__add1__eq,axiom,
% 5.52/5.77 ! [W: int,Z: int] :
% 5.52/5.77 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.52/5.77 = ( ( ord_less_int @ W @ Z )
% 5.52/5.77 | ( W = Z ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % zless_add1_eq
% 5.52/5.77 thf(fact_2818_int__gr__induct,axiom,
% 5.52/5.77 ! [K: int,I: int,P: int > $o] :
% 5.52/5.77 ( ( ord_less_int @ K @ I )
% 5.52/5.77 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.52/5.77 => ( ! [I2: int] :
% 5.52/5.77 ( ( ord_less_int @ K @ I2 )
% 5.52/5.77 => ( ( P @ I2 )
% 5.52/5.77 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 5.52/5.77 => ( P @ I ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % int_gr_induct
% 5.52/5.77 thf(fact_2819_add1__zle__eq,axiom,
% 5.52/5.77 ! [W: int,Z: int] :
% 5.52/5.77 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 5.52/5.77 = ( ord_less_int @ W @ Z ) ) ).
% 5.52/5.77
% 5.52/5.77 % add1_zle_eq
% 5.52/5.77 thf(fact_2820_set__bit__greater__eq,axiom,
% 5.52/5.77 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 5.52/5.77
% 5.52/5.77 % set_bit_greater_eq
% 5.52/5.77 thf(fact_2821_minNull__bound,axiom,
% 5.52/5.77 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_N_u_l_l @ T ) @ one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % minNull_bound
% 5.52/5.77 thf(fact_2822_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I3_J,axiom,
% 5.52/5.77 ! [Uu: $o] :
% 5.52/5.77 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ Uu @ $true ) )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(3)
% 5.52/5.77 thf(fact_2823_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I2_J,axiom,
% 5.52/5.77 ! [Uv: $o] :
% 5.52/5.77 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $true @ Uv ) )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(2)
% 5.52/5.77 thf(fact_2824_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I1_J,axiom,
% 5.52/5.77 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $false @ $false ) )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(1)
% 5.52/5.77 thf(fact_2825_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I5_J,axiom,
% 5.52/5.77 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.52/5.77 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(5)
% 5.52/5.77 thf(fact_2826_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I4_J,axiom,
% 5.52/5.77 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.52/5.77 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(4)
% 5.52/5.77 thf(fact_2827_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Oelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.52/5.77 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ $false @ $false ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [Uv2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [Uu2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.elims
% 5.52/5.77 thf(fact_2828_vebt__member_Opelims_I2_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.77 ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.52/5.77 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => A3 )
% 5.52/5.77 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.77 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.77 => B2 )
% 5.52/5.77 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.52/5.77 => ~ ( ( Xa2 != Mi2 )
% 5.52/5.77 => ( ( Xa2 != Ma2 )
% 5.52/5.77 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.52/5.77 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.77 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.52/5.77 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % vebt_member.pelims(2)
% 5.52/5.77 thf(fact_2829_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.52/5.77 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.77 => A3 )
% 5.52/5.77 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.77 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.77 => B2 )
% 5.52/5.77 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.52/5.77 => ( ~ Y2
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % VEBT_internal.naive_member.pelims(1)
% 5.52/5.77 thf(fact_2830_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Opelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.52/5.77 ( ( ( vEBT_T_i_n_s_e_r_t @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.52/5.77 @ ( if_nat
% 5.52/5.77 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 & ~ ( ( Xa2 = Mi2 )
% 5.52/5.77 | ( Xa2 = Ma2 ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.52/5.77 @ one_one_nat ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.pelims
% 5.52/5.77 thf(fact_2831_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.52/5.77 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [Uu2: $o,Uv2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.52/5.77 => ( ~ Y2
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.52/5.77 => ( ~ Y2
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( ( Xa2 = Mi2 )
% 5.52/5.77 | ( Xa2 = Ma2 ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( ( Xa2 = Mi2 )
% 5.52/5.77 | ( Xa2 = Ma2 )
% 5.52/5.77 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % VEBT_internal.membermima.pelims(1)
% 5.52/5.77 thf(fact_2832_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.77 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [Uu2: $o,Uv2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 5.52/5.77 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 5.52/5.77 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 5.52/5.77 => ( ( Xa2 = Mi2 )
% 5.52/5.77 | ( Xa2 = Ma2 ) ) ) )
% 5.52/5.77 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 5.52/5.77 => ( ( Xa2 = Mi2 )
% 5.52/5.77 | ( Xa2 = Ma2 )
% 5.52/5.77 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.52/5.77 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) )
% 5.52/5.77 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % VEBT_internal.membermima.pelims(3)
% 5.52/5.77 thf(fact_2833_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Oelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.52/5.77 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( ? [A3: $o,B2: $o] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ( ( ? [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( Y2 != one_one_nat ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( Y2
% 5.52/5.77 != ( if_nat
% 5.52/5.77 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 & ~ ( ( Xa2 = Mi2 )
% 5.52/5.77 | ( Xa2 = Ma2 ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.52/5.77 @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.elims
% 5.52/5.77 thf(fact_2834_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.77 ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 5.52/5.77 => ~ ( ( Xa2 = Mi2 )
% 5.52/5.77 | ( Xa2 = Ma2 ) ) ) )
% 5.52/5.77 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 5.52/5.77 => ~ ( ( Xa2 = Mi2 )
% 5.52/5.77 | ( Xa2 = Ma2 )
% 5.52/5.77 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.52/5.77 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) )
% 5.52/5.77 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.77 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % VEBT_internal.membermima.pelims(2)
% 5.52/5.77 thf(fact_2835_atLeastatMost__empty,axiom,
% 5.52/5.77 ! [B: extended_enat,A: extended_enat] :
% 5.52/5.77 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.52/5.77 => ( ( set_or5403411693681687835d_enat @ A @ B )
% 5.52/5.77 = bot_bo7653980558646680370d_enat ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty
% 5.52/5.77 thf(fact_2836_atLeastatMost__empty,axiom,
% 5.52/5.77 ! [B: rat,A: rat] :
% 5.52/5.77 ( ( ord_less_rat @ B @ A )
% 5.52/5.77 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.52/5.77 = bot_bot_set_rat ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty
% 5.52/5.77 thf(fact_2837_atLeastatMost__empty,axiom,
% 5.52/5.77 ! [B: num,A: num] :
% 5.52/5.77 ( ( ord_less_num @ B @ A )
% 5.52/5.77 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.52/5.77 = bot_bot_set_num ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty
% 5.52/5.77 thf(fact_2838_atLeastatMost__empty,axiom,
% 5.52/5.77 ! [B: nat,A: nat] :
% 5.52/5.77 ( ( ord_less_nat @ B @ A )
% 5.52/5.77 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.52/5.77 = bot_bot_set_nat ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty
% 5.52/5.77 thf(fact_2839_atLeastatMost__empty,axiom,
% 5.52/5.77 ! [B: int,A: int] :
% 5.52/5.77 ( ( ord_less_int @ B @ A )
% 5.52/5.77 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.52/5.77 = bot_bot_set_int ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty
% 5.52/5.77 thf(fact_2840_atLeastatMost__empty,axiom,
% 5.52/5.77 ! [B: real,A: real] :
% 5.52/5.77 ( ( ord_less_real @ B @ A )
% 5.52/5.77 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.52/5.77 = bot_bot_set_real ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty
% 5.52/5.77 thf(fact_2841_atLeastatMost__subset__iff,axiom,
% 5.52/5.77 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 5.52/5.77 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 5.52/5.77 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.52/5.77 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.52/5.77 & ( ord_less_eq_set_nat @ B @ D2 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_subset_iff
% 5.52/5.77 thf(fact_2842_atLeastatMost__subset__iff,axiom,
% 5.52/5.77 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.52/5.77 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 5.52/5.77 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.52/5.77 | ( ( ord_less_eq_rat @ C @ A )
% 5.52/5.77 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_subset_iff
% 5.52/5.77 thf(fact_2843_atLeastatMost__subset__iff,axiom,
% 5.52/5.77 ! [A: num,B: num,C: num,D2: num] :
% 5.52/5.77 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 5.52/5.77 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.52/5.77 | ( ( ord_less_eq_num @ C @ A )
% 5.52/5.77 & ( ord_less_eq_num @ B @ D2 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_subset_iff
% 5.52/5.77 thf(fact_2844_atLeastatMost__subset__iff,axiom,
% 5.52/5.77 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.52/5.77 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 5.52/5.77 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.52/5.77 | ( ( ord_less_eq_nat @ C @ A )
% 5.52/5.77 & ( ord_less_eq_nat @ B @ D2 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_subset_iff
% 5.52/5.77 thf(fact_2845_atLeastatMost__subset__iff,axiom,
% 5.52/5.77 ! [A: int,B: int,C: int,D2: int] :
% 5.52/5.77 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 5.52/5.77 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.52/5.77 | ( ( ord_less_eq_int @ C @ A )
% 5.52/5.77 & ( ord_less_eq_int @ B @ D2 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_subset_iff
% 5.52/5.77 thf(fact_2846_atLeastatMost__subset__iff,axiom,
% 5.52/5.77 ! [A: real,B: real,C: real,D2: real] :
% 5.52/5.77 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D2 ) )
% 5.52/5.77 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.52/5.77 | ( ( ord_less_eq_real @ C @ A )
% 5.52/5.77 & ( ord_less_eq_real @ B @ D2 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_subset_iff
% 5.52/5.77 thf(fact_2847_atLeastatMost__empty__iff,axiom,
% 5.52/5.77 ! [A: extended_enat,B: extended_enat] :
% 5.52/5.77 ( ( ( set_or5403411693681687835d_enat @ A @ B )
% 5.52/5.77 = bot_bo7653980558646680370d_enat )
% 5.52/5.77 = ( ~ ( ord_le2932123472753598470d_enat @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff
% 5.52/5.77 thf(fact_2848_atLeastatMost__empty__iff,axiom,
% 5.52/5.77 ! [A: set_nat,B: set_nat] :
% 5.52/5.77 ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 5.52/5.77 = bot_bot_set_set_nat )
% 5.52/5.77 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff
% 5.52/5.77 thf(fact_2849_atLeastatMost__empty__iff,axiom,
% 5.52/5.77 ! [A: rat,B: rat] :
% 5.52/5.77 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.52/5.77 = bot_bot_set_rat )
% 5.52/5.77 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff
% 5.52/5.77 thf(fact_2850_atLeastatMost__empty__iff,axiom,
% 5.52/5.77 ! [A: num,B: num] :
% 5.52/5.77 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.52/5.77 = bot_bot_set_num )
% 5.52/5.77 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff
% 5.52/5.77 thf(fact_2851_atLeastatMost__empty__iff,axiom,
% 5.52/5.77 ! [A: nat,B: nat] :
% 5.52/5.77 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.52/5.77 = bot_bot_set_nat )
% 5.52/5.77 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff
% 5.52/5.77 thf(fact_2852_atLeastatMost__empty__iff,axiom,
% 5.52/5.77 ! [A: int,B: int] :
% 5.52/5.77 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.52/5.77 = bot_bot_set_int )
% 5.52/5.77 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff
% 5.52/5.77 thf(fact_2853_atLeastatMost__empty__iff,axiom,
% 5.52/5.77 ! [A: real,B: real] :
% 5.52/5.77 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.52/5.77 = bot_bot_set_real )
% 5.52/5.77 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff
% 5.52/5.77 thf(fact_2854_atLeastAtMost__iff,axiom,
% 5.52/5.77 ! [I: set_nat_rat,L: set_nat_rat,U: set_nat_rat] :
% 5.52/5.77 ( ( member_set_nat_rat @ I @ ( set_or5795412311047298440at_rat @ L @ U ) )
% 5.52/5.77 = ( ( ord_le2679597024174929757at_rat @ L @ I )
% 5.52/5.77 & ( ord_le2679597024174929757at_rat @ I @ U ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastAtMost_iff
% 5.52/5.77 thf(fact_2855_atLeastAtMost__iff,axiom,
% 5.52/5.77 ! [I: set_nat,L: set_nat,U: set_nat] :
% 5.52/5.77 ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 5.52/5.77 = ( ( ord_less_eq_set_nat @ L @ I )
% 5.52/5.77 & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastAtMost_iff
% 5.52/5.77 thf(fact_2856_atLeastAtMost__iff,axiom,
% 5.52/5.77 ! [I: rat,L: rat,U: rat] :
% 5.52/5.77 ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L @ U ) )
% 5.52/5.77 = ( ( ord_less_eq_rat @ L @ I )
% 5.52/5.77 & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastAtMost_iff
% 5.52/5.77 thf(fact_2857_atLeastAtMost__iff,axiom,
% 5.52/5.77 ! [I: num,L: num,U: num] :
% 5.52/5.77 ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L @ U ) )
% 5.52/5.77 = ( ( ord_less_eq_num @ L @ I )
% 5.52/5.77 & ( ord_less_eq_num @ I @ U ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastAtMost_iff
% 5.52/5.77 thf(fact_2858_atLeastAtMost__iff,axiom,
% 5.52/5.77 ! [I: nat,L: nat,U: nat] :
% 5.52/5.77 ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.52/5.77 = ( ( ord_less_eq_nat @ L @ I )
% 5.52/5.77 & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastAtMost_iff
% 5.52/5.77 thf(fact_2859_atLeastAtMost__iff,axiom,
% 5.52/5.77 ! [I: int,L: int,U: int] :
% 5.52/5.77 ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.52/5.77 = ( ( ord_less_eq_int @ L @ I )
% 5.52/5.77 & ( ord_less_eq_int @ I @ U ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastAtMost_iff
% 5.52/5.77 thf(fact_2860_atLeastAtMost__iff,axiom,
% 5.52/5.77 ! [I: real,L: real,U: real] :
% 5.52/5.77 ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L @ U ) )
% 5.52/5.77 = ( ( ord_less_eq_real @ L @ I )
% 5.52/5.77 & ( ord_less_eq_real @ I @ U ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastAtMost_iff
% 5.52/5.77 thf(fact_2861_Icc__eq__Icc,axiom,
% 5.52/5.77 ! [L: set_nat,H2: set_nat,L3: set_nat,H3: set_nat] :
% 5.52/5.77 ( ( ( set_or4548717258645045905et_nat @ L @ H2 )
% 5.52/5.77 = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 5.52/5.77 = ( ( ( L = L3 )
% 5.52/5.77 & ( H2 = H3 ) )
% 5.52/5.77 | ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 5.52/5.77 & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % Icc_eq_Icc
% 5.52/5.77 thf(fact_2862_Icc__eq__Icc,axiom,
% 5.52/5.77 ! [L: rat,H2: rat,L3: rat,H3: rat] :
% 5.52/5.77 ( ( ( set_or633870826150836451st_rat @ L @ H2 )
% 5.52/5.77 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.52/5.77 = ( ( ( L = L3 )
% 5.52/5.77 & ( H2 = H3 ) )
% 5.52/5.77 | ( ~ ( ord_less_eq_rat @ L @ H2 )
% 5.52/5.77 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % Icc_eq_Icc
% 5.52/5.77 thf(fact_2863_Icc__eq__Icc,axiom,
% 5.52/5.77 ! [L: num,H2: num,L3: num,H3: num] :
% 5.52/5.77 ( ( ( set_or7049704709247886629st_num @ L @ H2 )
% 5.52/5.77 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.52/5.77 = ( ( ( L = L3 )
% 5.52/5.77 & ( H2 = H3 ) )
% 5.52/5.77 | ( ~ ( ord_less_eq_num @ L @ H2 )
% 5.52/5.77 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % Icc_eq_Icc
% 5.52/5.77 thf(fact_2864_Icc__eq__Icc,axiom,
% 5.52/5.77 ! [L: nat,H2: nat,L3: nat,H3: nat] :
% 5.52/5.77 ( ( ( set_or1269000886237332187st_nat @ L @ H2 )
% 5.52/5.77 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.52/5.77 = ( ( ( L = L3 )
% 5.52/5.77 & ( H2 = H3 ) )
% 5.52/5.77 | ( ~ ( ord_less_eq_nat @ L @ H2 )
% 5.52/5.77 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % Icc_eq_Icc
% 5.52/5.77 thf(fact_2865_Icc__eq__Icc,axiom,
% 5.52/5.77 ! [L: int,H2: int,L3: int,H3: int] :
% 5.52/5.77 ( ( ( set_or1266510415728281911st_int @ L @ H2 )
% 5.52/5.77 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.52/5.77 = ( ( ( L = L3 )
% 5.52/5.77 & ( H2 = H3 ) )
% 5.52/5.77 | ( ~ ( ord_less_eq_int @ L @ H2 )
% 5.52/5.77 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % Icc_eq_Icc
% 5.52/5.77 thf(fact_2866_Icc__eq__Icc,axiom,
% 5.52/5.77 ! [L: real,H2: real,L3: real,H3: real] :
% 5.52/5.77 ( ( ( set_or1222579329274155063t_real @ L @ H2 )
% 5.52/5.77 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.52/5.77 = ( ( ( L = L3 )
% 5.52/5.77 & ( H2 = H3 ) )
% 5.52/5.77 | ( ~ ( ord_less_eq_real @ L @ H2 )
% 5.52/5.77 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % Icc_eq_Icc
% 5.52/5.77 thf(fact_2867_atLeastatMost__empty__iff2,axiom,
% 5.52/5.77 ! [A: extended_enat,B: extended_enat] :
% 5.52/5.77 ( ( bot_bo7653980558646680370d_enat
% 5.52/5.77 = ( set_or5403411693681687835d_enat @ A @ B ) )
% 5.52/5.77 = ( ~ ( ord_le2932123472753598470d_enat @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff2
% 5.52/5.77 thf(fact_2868_atLeastatMost__empty__iff2,axiom,
% 5.52/5.77 ! [A: set_nat,B: set_nat] :
% 5.52/5.77 ( ( bot_bot_set_set_nat
% 5.52/5.77 = ( set_or4548717258645045905et_nat @ A @ B ) )
% 5.52/5.77 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff2
% 5.52/5.77 thf(fact_2869_atLeastatMost__empty__iff2,axiom,
% 5.52/5.77 ! [A: rat,B: rat] :
% 5.52/5.77 ( ( bot_bot_set_rat
% 5.52/5.77 = ( set_or633870826150836451st_rat @ A @ B ) )
% 5.52/5.77 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff2
% 5.52/5.77 thf(fact_2870_atLeastatMost__empty__iff2,axiom,
% 5.52/5.77 ! [A: num,B: num] :
% 5.52/5.77 ( ( bot_bot_set_num
% 5.52/5.77 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.52/5.77 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff2
% 5.52/5.77 thf(fact_2871_atLeastatMost__empty__iff2,axiom,
% 5.52/5.77 ! [A: nat,B: nat] :
% 5.52/5.77 ( ( bot_bot_set_nat
% 5.52/5.77 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.52/5.77 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff2
% 5.52/5.77 thf(fact_2872_atLeastatMost__empty__iff2,axiom,
% 5.52/5.77 ! [A: int,B: int] :
% 5.52/5.77 ( ( bot_bot_set_int
% 5.52/5.77 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.52/5.77 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff2
% 5.52/5.77 thf(fact_2873_atLeastatMost__empty__iff2,axiom,
% 5.52/5.77 ! [A: real,B: real] :
% 5.52/5.77 ( ( bot_bot_set_real
% 5.52/5.77 = ( set_or1222579329274155063t_real @ A @ B ) )
% 5.52/5.77 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_empty_iff2
% 5.52/5.77 thf(fact_2874_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I1_J,axiom,
% 5.52/5.77 ! [A: $o,B: $o,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(1)
% 5.52/5.77 thf(fact_2875_bounded__Max__nat,axiom,
% 5.52/5.77 ! [P: nat > $o,X2: nat,M7: nat] :
% 5.52/5.77 ( ( P @ X2 )
% 5.52/5.77 => ( ! [X4: nat] :
% 5.52/5.77 ( ( P @ X4 )
% 5.52/5.77 => ( ord_less_eq_nat @ X4 @ M7 ) )
% 5.52/5.77 => ~ ! [M4: nat] :
% 5.52/5.77 ( ( P @ M4 )
% 5.52/5.77 => ~ ! [X6: nat] :
% 5.52/5.77 ( ( P @ X6 )
% 5.52/5.77 => ( ord_less_eq_nat @ X6 @ M4 ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % bounded_Max_nat
% 5.52/5.77 thf(fact_2876_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.52/5.77 ! [X2: produc3368934014287244435at_num] :
% 5.52/5.77 ~ ! [F2: nat > num > num,A3: nat,B2: nat,Acc: num] :
% 5.52/5.77 ( X2
% 5.52/5.77 != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A3 @ ( product_Pair_nat_num @ B2 @ Acc ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % fold_atLeastAtMost_nat.cases
% 5.52/5.77 thf(fact_2877_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.52/5.77 ! [X2: produc4471711990508489141at_nat] :
% 5.52/5.77 ~ ! [F2: nat > nat > nat,A3: nat,B2: nat,Acc: nat] :
% 5.52/5.77 ( X2
% 5.52/5.77 != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A3 @ ( product_Pair_nat_nat @ B2 @ Acc ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % fold_atLeastAtMost_nat.cases
% 5.52/5.77 thf(fact_2878_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I2_J,axiom,
% 5.52/5.77 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X2 )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(2)
% 5.52/5.77 thf(fact_2879_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I3_J,axiom,
% 5.52/5.77 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X2 )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(3)
% 5.52/5.77 thf(fact_2880_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I4_J,axiom,
% 5.52/5.77 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X2 )
% 5.52/5.77 = one_one_nat ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(4)
% 5.52/5.77 thf(fact_2881_insersimp_H,axiom,
% 5.52/5.77 ! [T: vEBT_VEBT,N: nat,Y2: nat] :
% 5.52/5.77 ( ( vEBT_invar_vebt @ T @ N )
% 5.52/5.77 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 5.52/5.77 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ Y2 ) @ one_one_nat ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % insersimp'
% 5.52/5.77 thf(fact_2882_insertsimp_H,axiom,
% 5.52/5.77 ! [T: vEBT_VEBT,N: nat,L: nat] :
% 5.52/5.77 ( ( vEBT_invar_vebt @ T @ N )
% 5.52/5.77 => ( ( vEBT_VEBT_minNull @ T )
% 5.52/5.77 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ L ) @ one_one_nat ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % insertsimp'
% 5.52/5.77 thf(fact_2883_insert_H__bound__height,axiom,
% 5.52/5.77 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.52/5.77 ( ( vEBT_invar_vebt @ T @ N )
% 5.52/5.77 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % insert'_bound_height
% 5.52/5.77 thf(fact_2884_atLeastatMost__psubset__iff,axiom,
% 5.52/5.77 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 5.52/5.77 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 5.52/5.77 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.52/5.77 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.52/5.77 & ( ord_less_eq_set_nat @ B @ D2 )
% 5.52/5.77 & ( ( ord_less_set_nat @ C @ A )
% 5.52/5.77 | ( ord_less_set_nat @ B @ D2 ) ) ) )
% 5.52/5.77 & ( ord_less_eq_set_nat @ C @ D2 ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_psubset_iff
% 5.52/5.77 thf(fact_2885_atLeastatMost__psubset__iff,axiom,
% 5.52/5.77 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.52/5.77 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 5.52/5.77 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.52/5.77 | ( ( ord_less_eq_rat @ C @ A )
% 5.52/5.77 & ( ord_less_eq_rat @ B @ D2 )
% 5.52/5.77 & ( ( ord_less_rat @ C @ A )
% 5.52/5.77 | ( ord_less_rat @ B @ D2 ) ) ) )
% 5.52/5.77 & ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_psubset_iff
% 5.52/5.77 thf(fact_2886_atLeastatMost__psubset__iff,axiom,
% 5.52/5.77 ! [A: num,B: num,C: num,D2: num] :
% 5.52/5.77 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 5.52/5.77 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.52/5.77 | ( ( ord_less_eq_num @ C @ A )
% 5.52/5.77 & ( ord_less_eq_num @ B @ D2 )
% 5.52/5.77 & ( ( ord_less_num @ C @ A )
% 5.52/5.77 | ( ord_less_num @ B @ D2 ) ) ) )
% 5.52/5.77 & ( ord_less_eq_num @ C @ D2 ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_psubset_iff
% 5.52/5.77 thf(fact_2887_atLeastatMost__psubset__iff,axiom,
% 5.52/5.77 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.52/5.77 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 5.52/5.77 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.52/5.77 | ( ( ord_less_eq_nat @ C @ A )
% 5.52/5.77 & ( ord_less_eq_nat @ B @ D2 )
% 5.52/5.77 & ( ( ord_less_nat @ C @ A )
% 5.52/5.77 | ( ord_less_nat @ B @ D2 ) ) ) )
% 5.52/5.77 & ( ord_less_eq_nat @ C @ D2 ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_psubset_iff
% 5.52/5.77 thf(fact_2888_atLeastatMost__psubset__iff,axiom,
% 5.52/5.77 ! [A: int,B: int,C: int,D2: int] :
% 5.52/5.77 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 5.52/5.77 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.52/5.77 | ( ( ord_less_eq_int @ C @ A )
% 5.52/5.77 & ( ord_less_eq_int @ B @ D2 )
% 5.52/5.77 & ( ( ord_less_int @ C @ A )
% 5.52/5.77 | ( ord_less_int @ B @ D2 ) ) ) )
% 5.52/5.77 & ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_psubset_iff
% 5.52/5.77 thf(fact_2889_atLeastatMost__psubset__iff,axiom,
% 5.52/5.77 ! [A: real,B: real,C: real,D2: real] :
% 5.52/5.77 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D2 ) )
% 5.52/5.77 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.52/5.77 | ( ( ord_less_eq_real @ C @ A )
% 5.52/5.77 & ( ord_less_eq_real @ B @ D2 )
% 5.52/5.77 & ( ( ord_less_real @ C @ A )
% 5.52/5.77 | ( ord_less_real @ B @ D2 ) ) ) )
% 5.52/5.77 & ( ord_less_eq_real @ C @ D2 ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % atLeastatMost_psubset_iff
% 5.52/5.77 thf(fact_2890_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I5_J,axiom,
% 5.52/5.77 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.52/5.77 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.52/5.77 = ( if_nat
% 5.52/5.77 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.52/5.77 & ~ ( ( X2 = Mi )
% 5.52/5.77 | ( X2 = Ma ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.52/5.77 @ one_one_nat ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(5)
% 5.52/5.77 thf(fact_2891_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Opelims,axiom,
% 5.52/5.77 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.52/5.77 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X2 @ Xa2 )
% 5.52/5.77 = Y2 )
% 5.52/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.77 => ( ! [A3: $o,B2: $o] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( Y2 = one_one_nat )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 5.52/5.77 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.77 ( ( X2
% 5.52/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.77 => ( ( Y2
% 5.52/5.77 = ( if_nat
% 5.52/5.77 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.77 & ~ ( ( Xa2 = Mi2 )
% 5.52/5.77 | ( Xa2 = Ma2 ) ) )
% 5.52/5.77 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.52/5.77 @ one_one_nat ) )
% 5.52/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.pelims
% 5.52/5.77 thf(fact_2892_cpmi,axiom,
% 5.52/5.77 ! [D4: int,P: int > $o,P5: int > $o,B4: set_int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.77 => ( ? [Z5: int] :
% 5.52/5.77 ! [X4: int] :
% 5.52/5.77 ( ( ord_less_int @ X4 @ Z5 )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 = ( P5 @ X4 ) ) )
% 5.52/5.77 => ( ! [X4: int] :
% 5.52/5.77 ( ! [Xa: int] :
% 5.52/5.77 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.77 => ! [Xb2: int] :
% 5.52/5.77 ( ( member_int @ Xb2 @ B4 )
% 5.52/5.77 => ( X4
% 5.52/5.77 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 => ( P @ ( minus_minus_int @ X4 @ D4 ) ) ) )
% 5.52/5.77 => ( ! [X4: int,K3: int] :
% 5.52/5.77 ( ( P5 @ X4 )
% 5.52/5.77 = ( P5 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.52/5.77 => ( ( ? [X7: int] : ( P @ X7 ) )
% 5.52/5.77 = ( ? [X: int] :
% 5.52/5.77 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.77 & ( P5 @ X ) )
% 5.52/5.77 | ? [X: int] :
% 5.52/5.77 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.77 & ? [Y: int] :
% 5.52/5.77 ( ( member_int @ Y @ B4 )
% 5.52/5.77 & ( P @ ( plus_plus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % cpmi
% 5.52/5.77 thf(fact_2893_cppi,axiom,
% 5.52/5.77 ! [D4: int,P: int > $o,P5: int > $o,A2: set_int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.77 => ( ? [Z5: int] :
% 5.52/5.77 ! [X4: int] :
% 5.52/5.77 ( ( ord_less_int @ Z5 @ X4 )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 = ( P5 @ X4 ) ) )
% 5.52/5.77 => ( ! [X4: int] :
% 5.52/5.77 ( ! [Xa: int] :
% 5.52/5.77 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.77 => ! [Xb2: int] :
% 5.52/5.77 ( ( member_int @ Xb2 @ A2 )
% 5.52/5.77 => ( X4
% 5.52/5.77 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 => ( P @ ( plus_plus_int @ X4 @ D4 ) ) ) )
% 5.52/5.77 => ( ! [X4: int,K3: int] :
% 5.52/5.77 ( ( P5 @ X4 )
% 5.52/5.77 = ( P5 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.52/5.77 => ( ( ? [X7: int] : ( P @ X7 ) )
% 5.52/5.77 = ( ? [X: int] :
% 5.52/5.77 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.77 & ( P5 @ X ) )
% 5.52/5.77 | ? [X: int] :
% 5.52/5.77 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.77 & ? [Y: int] :
% 5.52/5.77 ( ( member_int @ Y @ A2 )
% 5.52/5.77 & ( P @ ( minus_minus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % cppi
% 5.52/5.77 thf(fact_2894_bset_I6_J,axiom,
% 5.52/5.77 ! [D4: int,B4: set_int,T: int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.77 => ! [X6: int] :
% 5.52/5.77 ( ! [Xa3: int] :
% 5.52/5.77 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.77 => ! [Xb3: int] :
% 5.52/5.77 ( ( member_int @ Xb3 @ B4 )
% 5.52/5.77 => ( X6
% 5.52/5.77 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.52/5.77 => ( ( ord_less_eq_int @ X6 @ T )
% 5.52/5.77 => ( ord_less_eq_int @ ( minus_minus_int @ X6 @ D4 ) @ T ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % bset(6)
% 5.52/5.77 thf(fact_2895_bset_I8_J,axiom,
% 5.52/5.77 ! [D4: int,T: int,B4: set_int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.77 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 5.52/5.77 => ! [X6: int] :
% 5.52/5.77 ( ! [Xa3: int] :
% 5.52/5.77 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.77 => ! [Xb3: int] :
% 5.52/5.77 ( ( member_int @ Xb3 @ B4 )
% 5.52/5.77 => ( X6
% 5.52/5.77 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.52/5.77 => ( ( ord_less_eq_int @ T @ X6 )
% 5.52/5.77 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X6 @ D4 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % bset(8)
% 5.52/5.77 thf(fact_2896_aset_I6_J,axiom,
% 5.52/5.77 ! [D4: int,T: int,A2: set_int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.77 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.52/5.77 => ! [X6: int] :
% 5.52/5.77 ( ! [Xa3: int] :
% 5.52/5.77 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.77 => ! [Xb3: int] :
% 5.52/5.77 ( ( member_int @ Xb3 @ A2 )
% 5.52/5.77 => ( X6
% 5.52/5.77 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.52/5.77 => ( ( ord_less_eq_int @ X6 @ T )
% 5.52/5.77 => ( ord_less_eq_int @ ( plus_plus_int @ X6 @ D4 ) @ T ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % aset(6)
% 5.52/5.77 thf(fact_2897_aset_I8_J,axiom,
% 5.52/5.77 ! [D4: int,A2: set_int,T: int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.77 => ! [X6: int] :
% 5.52/5.77 ( ! [Xa3: int] :
% 5.52/5.77 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.77 => ! [Xb3: int] :
% 5.52/5.77 ( ( member_int @ Xb3 @ A2 )
% 5.52/5.77 => ( X6
% 5.52/5.77 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.52/5.77 => ( ( ord_less_eq_int @ T @ X6 )
% 5.52/5.77 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X6 @ D4 ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % aset(8)
% 5.52/5.77 thf(fact_2898_bset_I3_J,axiom,
% 5.52/5.77 ! [D4: int,T: int,B4: set_int] :
% 5.52/5.77 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.77 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 5.52/5.77 => ! [X6: int] :
% 5.52/5.77 ( ! [Xa3: int] :
% 5.52/5.77 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.77 => ! [Xb3: int] :
% 5.52/5.77 ( ( member_int @ Xb3 @ B4 )
% 5.52/5.77 => ( X6
% 5.52/5.77 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.52/5.77 => ( ( X6 = T )
% 5.52/5.77 => ( ( minus_minus_int @ X6 @ D4 )
% 5.52/5.77 = T ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % bset(3)
% 5.52/5.77 thf(fact_2899_pinf_I1_J,axiom,
% 5.52/5.77 ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 5.52/5.77 ( ? [Z5: real] :
% 5.52/5.77 ! [X4: real] :
% 5.52/5.77 ( ( ord_less_real @ Z5 @ X4 )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 = ( P5 @ X4 ) ) )
% 5.52/5.77 => ( ? [Z5: real] :
% 5.52/5.77 ! [X4: real] :
% 5.52/5.77 ( ( ord_less_real @ Z5 @ X4 )
% 5.52/5.77 => ( ( Q @ X4 )
% 5.52/5.77 = ( Q6 @ X4 ) ) )
% 5.52/5.77 => ? [Z3: real] :
% 5.52/5.77 ! [X6: real] :
% 5.52/5.77 ( ( ord_less_real @ Z3 @ X6 )
% 5.52/5.77 => ( ( ( P @ X6 )
% 5.52/5.77 & ( Q @ X6 ) )
% 5.52/5.77 = ( ( P5 @ X6 )
% 5.52/5.77 & ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(1)
% 5.52/5.77 thf(fact_2900_pinf_I1_J,axiom,
% 5.52/5.77 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.52/5.77 ( ? [Z5: rat] :
% 5.52/5.77 ! [X4: rat] :
% 5.52/5.77 ( ( ord_less_rat @ Z5 @ X4 )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 = ( P5 @ X4 ) ) )
% 5.52/5.77 => ( ? [Z5: rat] :
% 5.52/5.77 ! [X4: rat] :
% 5.52/5.77 ( ( ord_less_rat @ Z5 @ X4 )
% 5.52/5.77 => ( ( Q @ X4 )
% 5.52/5.77 = ( Q6 @ X4 ) ) )
% 5.52/5.77 => ? [Z3: rat] :
% 5.52/5.77 ! [X6: rat] :
% 5.52/5.77 ( ( ord_less_rat @ Z3 @ X6 )
% 5.52/5.77 => ( ( ( P @ X6 )
% 5.52/5.77 & ( Q @ X6 ) )
% 5.52/5.77 = ( ( P5 @ X6 )
% 5.52/5.77 & ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(1)
% 5.52/5.77 thf(fact_2901_pinf_I1_J,axiom,
% 5.52/5.77 ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 5.52/5.77 ( ? [Z5: num] :
% 5.52/5.77 ! [X4: num] :
% 5.52/5.77 ( ( ord_less_num @ Z5 @ X4 )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 = ( P5 @ X4 ) ) )
% 5.52/5.77 => ( ? [Z5: num] :
% 5.52/5.77 ! [X4: num] :
% 5.52/5.77 ( ( ord_less_num @ Z5 @ X4 )
% 5.52/5.77 => ( ( Q @ X4 )
% 5.52/5.77 = ( Q6 @ X4 ) ) )
% 5.52/5.77 => ? [Z3: num] :
% 5.52/5.77 ! [X6: num] :
% 5.52/5.77 ( ( ord_less_num @ Z3 @ X6 )
% 5.52/5.77 => ( ( ( P @ X6 )
% 5.52/5.77 & ( Q @ X6 ) )
% 5.52/5.77 = ( ( P5 @ X6 )
% 5.52/5.77 & ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(1)
% 5.52/5.77 thf(fact_2902_pinf_I1_J,axiom,
% 5.52/5.77 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.52/5.77 ( ? [Z5: nat] :
% 5.52/5.77 ! [X4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ Z5 @ X4 )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 = ( P5 @ X4 ) ) )
% 5.52/5.77 => ( ? [Z5: nat] :
% 5.52/5.77 ! [X4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ Z5 @ X4 )
% 5.52/5.77 => ( ( Q @ X4 )
% 5.52/5.77 = ( Q6 @ X4 ) ) )
% 5.52/5.77 => ? [Z3: nat] :
% 5.52/5.77 ! [X6: nat] :
% 5.52/5.77 ( ( ord_less_nat @ Z3 @ X6 )
% 5.52/5.77 => ( ( ( P @ X6 )
% 5.52/5.77 & ( Q @ X6 ) )
% 5.52/5.77 = ( ( P5 @ X6 )
% 5.52/5.77 & ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(1)
% 5.52/5.77 thf(fact_2903_pinf_I1_J,axiom,
% 5.52/5.77 ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 5.52/5.77 ( ? [Z5: int] :
% 5.52/5.77 ! [X4: int] :
% 5.52/5.77 ( ( ord_less_int @ Z5 @ X4 )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 = ( P5 @ X4 ) ) )
% 5.52/5.77 => ( ? [Z5: int] :
% 5.52/5.77 ! [X4: int] :
% 5.52/5.77 ( ( ord_less_int @ Z5 @ X4 )
% 5.52/5.77 => ( ( Q @ X4 )
% 5.52/5.77 = ( Q6 @ X4 ) ) )
% 5.52/5.77 => ? [Z3: int] :
% 5.52/5.77 ! [X6: int] :
% 5.52/5.77 ( ( ord_less_int @ Z3 @ X6 )
% 5.52/5.77 => ( ( ( P @ X6 )
% 5.52/5.77 & ( Q @ X6 ) )
% 5.52/5.77 = ( ( P5 @ X6 )
% 5.52/5.77 & ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(1)
% 5.52/5.77 thf(fact_2904_pinf_I2_J,axiom,
% 5.52/5.77 ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 5.52/5.77 ( ? [Z5: real] :
% 5.52/5.77 ! [X4: real] :
% 5.52/5.77 ( ( ord_less_real @ Z5 @ X4 )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 = ( P5 @ X4 ) ) )
% 5.52/5.77 => ( ? [Z5: real] :
% 5.52/5.77 ! [X4: real] :
% 5.52/5.77 ( ( ord_less_real @ Z5 @ X4 )
% 5.52/5.77 => ( ( Q @ X4 )
% 5.52/5.77 = ( Q6 @ X4 ) ) )
% 5.52/5.77 => ? [Z3: real] :
% 5.52/5.77 ! [X6: real] :
% 5.52/5.77 ( ( ord_less_real @ Z3 @ X6 )
% 5.52/5.77 => ( ( ( P @ X6 )
% 5.52/5.77 | ( Q @ X6 ) )
% 5.52/5.77 = ( ( P5 @ X6 )
% 5.52/5.77 | ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(2)
% 5.52/5.77 thf(fact_2905_pinf_I2_J,axiom,
% 5.52/5.77 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.52/5.77 ( ? [Z5: rat] :
% 5.52/5.77 ! [X4: rat] :
% 5.52/5.77 ( ( ord_less_rat @ Z5 @ X4 )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 = ( P5 @ X4 ) ) )
% 5.52/5.77 => ( ? [Z5: rat] :
% 5.52/5.77 ! [X4: rat] :
% 5.52/5.77 ( ( ord_less_rat @ Z5 @ X4 )
% 5.52/5.77 => ( ( Q @ X4 )
% 5.52/5.77 = ( Q6 @ X4 ) ) )
% 5.52/5.77 => ? [Z3: rat] :
% 5.52/5.77 ! [X6: rat] :
% 5.52/5.77 ( ( ord_less_rat @ Z3 @ X6 )
% 5.52/5.77 => ( ( ( P @ X6 )
% 5.52/5.77 | ( Q @ X6 ) )
% 5.52/5.77 = ( ( P5 @ X6 )
% 5.52/5.77 | ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(2)
% 5.52/5.77 thf(fact_2906_pinf_I2_J,axiom,
% 5.52/5.77 ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 5.52/5.77 ( ? [Z5: num] :
% 5.52/5.77 ! [X4: num] :
% 5.52/5.77 ( ( ord_less_num @ Z5 @ X4 )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 = ( P5 @ X4 ) ) )
% 5.52/5.77 => ( ? [Z5: num] :
% 5.52/5.77 ! [X4: num] :
% 5.52/5.77 ( ( ord_less_num @ Z5 @ X4 )
% 5.52/5.77 => ( ( Q @ X4 )
% 5.52/5.77 = ( Q6 @ X4 ) ) )
% 5.52/5.77 => ? [Z3: num] :
% 5.52/5.77 ! [X6: num] :
% 5.52/5.77 ( ( ord_less_num @ Z3 @ X6 )
% 5.52/5.77 => ( ( ( P @ X6 )
% 5.52/5.77 | ( Q @ X6 ) )
% 5.52/5.77 = ( ( P5 @ X6 )
% 5.52/5.77 | ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(2)
% 5.52/5.77 thf(fact_2907_pinf_I2_J,axiom,
% 5.52/5.77 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.52/5.77 ( ? [Z5: nat] :
% 5.52/5.77 ! [X4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ Z5 @ X4 )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 = ( P5 @ X4 ) ) )
% 5.52/5.77 => ( ? [Z5: nat] :
% 5.52/5.77 ! [X4: nat] :
% 5.52/5.77 ( ( ord_less_nat @ Z5 @ X4 )
% 5.52/5.77 => ( ( Q @ X4 )
% 5.52/5.77 = ( Q6 @ X4 ) ) )
% 5.52/5.77 => ? [Z3: nat] :
% 5.52/5.77 ! [X6: nat] :
% 5.52/5.77 ( ( ord_less_nat @ Z3 @ X6 )
% 5.52/5.77 => ( ( ( P @ X6 )
% 5.52/5.77 | ( Q @ X6 ) )
% 5.52/5.77 = ( ( P5 @ X6 )
% 5.52/5.77 | ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(2)
% 5.52/5.77 thf(fact_2908_pinf_I2_J,axiom,
% 5.52/5.77 ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 5.52/5.77 ( ? [Z5: int] :
% 5.52/5.77 ! [X4: int] :
% 5.52/5.77 ( ( ord_less_int @ Z5 @ X4 )
% 5.52/5.77 => ( ( P @ X4 )
% 5.52/5.77 = ( P5 @ X4 ) ) )
% 5.52/5.77 => ( ? [Z5: int] :
% 5.52/5.77 ! [X4: int] :
% 5.52/5.77 ( ( ord_less_int @ Z5 @ X4 )
% 5.52/5.77 => ( ( Q @ X4 )
% 5.52/5.77 = ( Q6 @ X4 ) ) )
% 5.52/5.77 => ? [Z3: int] :
% 5.52/5.77 ! [X6: int] :
% 5.52/5.77 ( ( ord_less_int @ Z3 @ X6 )
% 5.52/5.77 => ( ( ( P @ X6 )
% 5.52/5.77 | ( Q @ X6 ) )
% 5.52/5.77 = ( ( P5 @ X6 )
% 5.52/5.77 | ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(2)
% 5.52/5.77 thf(fact_2909_pinf_I3_J,axiom,
% 5.52/5.77 ! [T: real] :
% 5.52/5.77 ? [Z3: real] :
% 5.52/5.77 ! [X6: real] :
% 5.52/5.77 ( ( ord_less_real @ Z3 @ X6 )
% 5.52/5.77 => ( X6 != T ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(3)
% 5.52/5.77 thf(fact_2910_pinf_I3_J,axiom,
% 5.52/5.77 ! [T: rat] :
% 5.52/5.77 ? [Z3: rat] :
% 5.52/5.77 ! [X6: rat] :
% 5.52/5.77 ( ( ord_less_rat @ Z3 @ X6 )
% 5.52/5.77 => ( X6 != T ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(3)
% 5.52/5.77 thf(fact_2911_pinf_I3_J,axiom,
% 5.52/5.77 ! [T: num] :
% 5.52/5.77 ? [Z3: num] :
% 5.52/5.77 ! [X6: num] :
% 5.52/5.77 ( ( ord_less_num @ Z3 @ X6 )
% 5.52/5.77 => ( X6 != T ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(3)
% 5.52/5.77 thf(fact_2912_pinf_I3_J,axiom,
% 5.52/5.77 ! [T: nat] :
% 5.52/5.77 ? [Z3: nat] :
% 5.52/5.77 ! [X6: nat] :
% 5.52/5.77 ( ( ord_less_nat @ Z3 @ X6 )
% 5.52/5.77 => ( X6 != T ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(3)
% 5.52/5.77 thf(fact_2913_pinf_I3_J,axiom,
% 5.52/5.77 ! [T: int] :
% 5.52/5.77 ? [Z3: int] :
% 5.52/5.77 ! [X6: int] :
% 5.52/5.77 ( ( ord_less_int @ Z3 @ X6 )
% 5.52/5.77 => ( X6 != T ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(3)
% 5.52/5.77 thf(fact_2914_pinf_I4_J,axiom,
% 5.52/5.77 ! [T: real] :
% 5.52/5.77 ? [Z3: real] :
% 5.52/5.77 ! [X6: real] :
% 5.52/5.77 ( ( ord_less_real @ Z3 @ X6 )
% 5.52/5.77 => ( X6 != T ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(4)
% 5.52/5.77 thf(fact_2915_pinf_I4_J,axiom,
% 5.52/5.77 ! [T: rat] :
% 5.52/5.77 ? [Z3: rat] :
% 5.52/5.77 ! [X6: rat] :
% 5.52/5.77 ( ( ord_less_rat @ Z3 @ X6 )
% 5.52/5.77 => ( X6 != T ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(4)
% 5.52/5.77 thf(fact_2916_pinf_I4_J,axiom,
% 5.52/5.77 ! [T: num] :
% 5.52/5.77 ? [Z3: num] :
% 5.52/5.77 ! [X6: num] :
% 5.52/5.77 ( ( ord_less_num @ Z3 @ X6 )
% 5.52/5.77 => ( X6 != T ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(4)
% 5.52/5.77 thf(fact_2917_pinf_I4_J,axiom,
% 5.52/5.77 ! [T: nat] :
% 5.52/5.77 ? [Z3: nat] :
% 5.52/5.77 ! [X6: nat] :
% 5.52/5.77 ( ( ord_less_nat @ Z3 @ X6 )
% 5.52/5.77 => ( X6 != T ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(4)
% 5.52/5.77 thf(fact_2918_pinf_I4_J,axiom,
% 5.52/5.77 ! [T: int] :
% 5.52/5.77 ? [Z3: int] :
% 5.52/5.77 ! [X6: int] :
% 5.52/5.77 ( ( ord_less_int @ Z3 @ X6 )
% 5.52/5.77 => ( X6 != T ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(4)
% 5.52/5.77 thf(fact_2919_pinf_I5_J,axiom,
% 5.52/5.77 ! [T: real] :
% 5.52/5.77 ? [Z3: real] :
% 5.52/5.77 ! [X6: real] :
% 5.52/5.77 ( ( ord_less_real @ Z3 @ X6 )
% 5.52/5.77 => ~ ( ord_less_real @ X6 @ T ) ) ).
% 5.52/5.77
% 5.52/5.77 % pinf(5)
% 5.52/5.77 thf(fact_2920_pinf_I5_J,axiom,
% 5.52/5.78 ! [T: rat] :
% 5.52/5.78 ? [Z3: rat] :
% 5.52/5.78 ! [X6: rat] :
% 5.52/5.78 ( ( ord_less_rat @ Z3 @ X6 )
% 5.52/5.78 => ~ ( ord_less_rat @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(5)
% 5.52/5.78 thf(fact_2921_pinf_I5_J,axiom,
% 5.52/5.78 ! [T: num] :
% 5.52/5.78 ? [Z3: num] :
% 5.52/5.78 ! [X6: num] :
% 5.52/5.78 ( ( ord_less_num @ Z3 @ X6 )
% 5.52/5.78 => ~ ( ord_less_num @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(5)
% 5.52/5.78 thf(fact_2922_pinf_I5_J,axiom,
% 5.52/5.78 ! [T: nat] :
% 5.52/5.78 ? [Z3: nat] :
% 5.52/5.78 ! [X6: nat] :
% 5.52/5.78 ( ( ord_less_nat @ Z3 @ X6 )
% 5.52/5.78 => ~ ( ord_less_nat @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(5)
% 5.52/5.78 thf(fact_2923_pinf_I5_J,axiom,
% 5.52/5.78 ! [T: int] :
% 5.52/5.78 ? [Z3: int] :
% 5.52/5.78 ! [X6: int] :
% 5.52/5.78 ( ( ord_less_int @ Z3 @ X6 )
% 5.52/5.78 => ~ ( ord_less_int @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(5)
% 5.52/5.78 thf(fact_2924_pinf_I7_J,axiom,
% 5.52/5.78 ! [T: real] :
% 5.52/5.78 ? [Z3: real] :
% 5.52/5.78 ! [X6: real] :
% 5.52/5.78 ( ( ord_less_real @ Z3 @ X6 )
% 5.52/5.78 => ( ord_less_real @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(7)
% 5.52/5.78 thf(fact_2925_pinf_I7_J,axiom,
% 5.52/5.78 ! [T: rat] :
% 5.52/5.78 ? [Z3: rat] :
% 5.52/5.78 ! [X6: rat] :
% 5.52/5.78 ( ( ord_less_rat @ Z3 @ X6 )
% 5.52/5.78 => ( ord_less_rat @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(7)
% 5.52/5.78 thf(fact_2926_pinf_I7_J,axiom,
% 5.52/5.78 ! [T: num] :
% 5.52/5.78 ? [Z3: num] :
% 5.52/5.78 ! [X6: num] :
% 5.52/5.78 ( ( ord_less_num @ Z3 @ X6 )
% 5.52/5.78 => ( ord_less_num @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(7)
% 5.52/5.78 thf(fact_2927_pinf_I7_J,axiom,
% 5.52/5.78 ! [T: nat] :
% 5.52/5.78 ? [Z3: nat] :
% 5.52/5.78 ! [X6: nat] :
% 5.52/5.78 ( ( ord_less_nat @ Z3 @ X6 )
% 5.52/5.78 => ( ord_less_nat @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(7)
% 5.52/5.78 thf(fact_2928_pinf_I7_J,axiom,
% 5.52/5.78 ! [T: int] :
% 5.52/5.78 ? [Z3: int] :
% 5.52/5.78 ! [X6: int] :
% 5.52/5.78 ( ( ord_less_int @ Z3 @ X6 )
% 5.52/5.78 => ( ord_less_int @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(7)
% 5.52/5.78 thf(fact_2929_minf_I1_J,axiom,
% 5.52/5.78 ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 5.52/5.78 ( ? [Z5: real] :
% 5.52/5.78 ! [X4: real] :
% 5.52/5.78 ( ( ord_less_real @ X4 @ Z5 )
% 5.52/5.78 => ( ( P @ X4 )
% 5.52/5.78 = ( P5 @ X4 ) ) )
% 5.52/5.78 => ( ? [Z5: real] :
% 5.52/5.78 ! [X4: real] :
% 5.52/5.78 ( ( ord_less_real @ X4 @ Z5 )
% 5.52/5.78 => ( ( Q @ X4 )
% 5.52/5.78 = ( Q6 @ X4 ) ) )
% 5.52/5.78 => ? [Z3: real] :
% 5.52/5.78 ! [X6: real] :
% 5.52/5.78 ( ( ord_less_real @ X6 @ Z3 )
% 5.52/5.78 => ( ( ( P @ X6 )
% 5.52/5.78 & ( Q @ X6 ) )
% 5.52/5.78 = ( ( P5 @ X6 )
% 5.52/5.78 & ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(1)
% 5.52/5.78 thf(fact_2930_minf_I1_J,axiom,
% 5.52/5.78 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.52/5.78 ( ? [Z5: rat] :
% 5.52/5.78 ! [X4: rat] :
% 5.52/5.78 ( ( ord_less_rat @ X4 @ Z5 )
% 5.52/5.78 => ( ( P @ X4 )
% 5.52/5.78 = ( P5 @ X4 ) ) )
% 5.52/5.78 => ( ? [Z5: rat] :
% 5.52/5.78 ! [X4: rat] :
% 5.52/5.78 ( ( ord_less_rat @ X4 @ Z5 )
% 5.52/5.78 => ( ( Q @ X4 )
% 5.52/5.78 = ( Q6 @ X4 ) ) )
% 5.52/5.78 => ? [Z3: rat] :
% 5.52/5.78 ! [X6: rat] :
% 5.52/5.78 ( ( ord_less_rat @ X6 @ Z3 )
% 5.52/5.78 => ( ( ( P @ X6 )
% 5.52/5.78 & ( Q @ X6 ) )
% 5.52/5.78 = ( ( P5 @ X6 )
% 5.52/5.78 & ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(1)
% 5.52/5.78 thf(fact_2931_minf_I1_J,axiom,
% 5.52/5.78 ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 5.52/5.78 ( ? [Z5: num] :
% 5.52/5.78 ! [X4: num] :
% 5.52/5.78 ( ( ord_less_num @ X4 @ Z5 )
% 5.52/5.78 => ( ( P @ X4 )
% 5.52/5.78 = ( P5 @ X4 ) ) )
% 5.52/5.78 => ( ? [Z5: num] :
% 5.52/5.78 ! [X4: num] :
% 5.52/5.78 ( ( ord_less_num @ X4 @ Z5 )
% 5.52/5.78 => ( ( Q @ X4 )
% 5.52/5.78 = ( Q6 @ X4 ) ) )
% 5.52/5.78 => ? [Z3: num] :
% 5.52/5.78 ! [X6: num] :
% 5.52/5.78 ( ( ord_less_num @ X6 @ Z3 )
% 5.52/5.78 => ( ( ( P @ X6 )
% 5.52/5.78 & ( Q @ X6 ) )
% 5.52/5.78 = ( ( P5 @ X6 )
% 5.52/5.78 & ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(1)
% 5.52/5.78 thf(fact_2932_minf_I1_J,axiom,
% 5.52/5.78 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.52/5.78 ( ? [Z5: nat] :
% 5.52/5.78 ! [X4: nat] :
% 5.52/5.78 ( ( ord_less_nat @ X4 @ Z5 )
% 5.52/5.78 => ( ( P @ X4 )
% 5.52/5.78 = ( P5 @ X4 ) ) )
% 5.52/5.78 => ( ? [Z5: nat] :
% 5.52/5.78 ! [X4: nat] :
% 5.52/5.78 ( ( ord_less_nat @ X4 @ Z5 )
% 5.52/5.78 => ( ( Q @ X4 )
% 5.52/5.78 = ( Q6 @ X4 ) ) )
% 5.52/5.78 => ? [Z3: nat] :
% 5.52/5.78 ! [X6: nat] :
% 5.52/5.78 ( ( ord_less_nat @ X6 @ Z3 )
% 5.52/5.78 => ( ( ( P @ X6 )
% 5.52/5.78 & ( Q @ X6 ) )
% 5.52/5.78 = ( ( P5 @ X6 )
% 5.52/5.78 & ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(1)
% 5.52/5.78 thf(fact_2933_minf_I1_J,axiom,
% 5.52/5.78 ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 5.52/5.78 ( ? [Z5: int] :
% 5.52/5.78 ! [X4: int] :
% 5.52/5.78 ( ( ord_less_int @ X4 @ Z5 )
% 5.52/5.78 => ( ( P @ X4 )
% 5.52/5.78 = ( P5 @ X4 ) ) )
% 5.52/5.78 => ( ? [Z5: int] :
% 5.52/5.78 ! [X4: int] :
% 5.52/5.78 ( ( ord_less_int @ X4 @ Z5 )
% 5.52/5.78 => ( ( Q @ X4 )
% 5.52/5.78 = ( Q6 @ X4 ) ) )
% 5.52/5.78 => ? [Z3: int] :
% 5.52/5.78 ! [X6: int] :
% 5.52/5.78 ( ( ord_less_int @ X6 @ Z3 )
% 5.52/5.78 => ( ( ( P @ X6 )
% 5.52/5.78 & ( Q @ X6 ) )
% 5.52/5.78 = ( ( P5 @ X6 )
% 5.52/5.78 & ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(1)
% 5.52/5.78 thf(fact_2934_minf_I2_J,axiom,
% 5.52/5.78 ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 5.52/5.78 ( ? [Z5: real] :
% 5.52/5.78 ! [X4: real] :
% 5.52/5.78 ( ( ord_less_real @ X4 @ Z5 )
% 5.52/5.78 => ( ( P @ X4 )
% 5.52/5.78 = ( P5 @ X4 ) ) )
% 5.52/5.78 => ( ? [Z5: real] :
% 5.52/5.78 ! [X4: real] :
% 5.52/5.78 ( ( ord_less_real @ X4 @ Z5 )
% 5.52/5.78 => ( ( Q @ X4 )
% 5.52/5.78 = ( Q6 @ X4 ) ) )
% 5.52/5.78 => ? [Z3: real] :
% 5.52/5.78 ! [X6: real] :
% 5.52/5.78 ( ( ord_less_real @ X6 @ Z3 )
% 5.52/5.78 => ( ( ( P @ X6 )
% 5.52/5.78 | ( Q @ X6 ) )
% 5.52/5.78 = ( ( P5 @ X6 )
% 5.52/5.78 | ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(2)
% 5.52/5.78 thf(fact_2935_minf_I2_J,axiom,
% 5.52/5.78 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.52/5.78 ( ? [Z5: rat] :
% 5.52/5.78 ! [X4: rat] :
% 5.52/5.78 ( ( ord_less_rat @ X4 @ Z5 )
% 5.52/5.78 => ( ( P @ X4 )
% 5.52/5.78 = ( P5 @ X4 ) ) )
% 5.52/5.78 => ( ? [Z5: rat] :
% 5.52/5.78 ! [X4: rat] :
% 5.52/5.78 ( ( ord_less_rat @ X4 @ Z5 )
% 5.52/5.78 => ( ( Q @ X4 )
% 5.52/5.78 = ( Q6 @ X4 ) ) )
% 5.52/5.78 => ? [Z3: rat] :
% 5.52/5.78 ! [X6: rat] :
% 5.52/5.78 ( ( ord_less_rat @ X6 @ Z3 )
% 5.52/5.78 => ( ( ( P @ X6 )
% 5.52/5.78 | ( Q @ X6 ) )
% 5.52/5.78 = ( ( P5 @ X6 )
% 5.52/5.78 | ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(2)
% 5.52/5.78 thf(fact_2936_minf_I2_J,axiom,
% 5.52/5.78 ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 5.52/5.78 ( ? [Z5: num] :
% 5.52/5.78 ! [X4: num] :
% 5.52/5.78 ( ( ord_less_num @ X4 @ Z5 )
% 5.52/5.78 => ( ( P @ X4 )
% 5.52/5.78 = ( P5 @ X4 ) ) )
% 5.52/5.78 => ( ? [Z5: num] :
% 5.52/5.78 ! [X4: num] :
% 5.52/5.78 ( ( ord_less_num @ X4 @ Z5 )
% 5.52/5.78 => ( ( Q @ X4 )
% 5.52/5.78 = ( Q6 @ X4 ) ) )
% 5.52/5.78 => ? [Z3: num] :
% 5.52/5.78 ! [X6: num] :
% 5.52/5.78 ( ( ord_less_num @ X6 @ Z3 )
% 5.52/5.78 => ( ( ( P @ X6 )
% 5.52/5.78 | ( Q @ X6 ) )
% 5.52/5.78 = ( ( P5 @ X6 )
% 5.52/5.78 | ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(2)
% 5.52/5.78 thf(fact_2937_minf_I2_J,axiom,
% 5.52/5.78 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.52/5.78 ( ? [Z5: nat] :
% 5.52/5.78 ! [X4: nat] :
% 5.52/5.78 ( ( ord_less_nat @ X4 @ Z5 )
% 5.52/5.78 => ( ( P @ X4 )
% 5.52/5.78 = ( P5 @ X4 ) ) )
% 5.52/5.78 => ( ? [Z5: nat] :
% 5.52/5.78 ! [X4: nat] :
% 5.52/5.78 ( ( ord_less_nat @ X4 @ Z5 )
% 5.52/5.78 => ( ( Q @ X4 )
% 5.52/5.78 = ( Q6 @ X4 ) ) )
% 5.52/5.78 => ? [Z3: nat] :
% 5.52/5.78 ! [X6: nat] :
% 5.52/5.78 ( ( ord_less_nat @ X6 @ Z3 )
% 5.52/5.78 => ( ( ( P @ X6 )
% 5.52/5.78 | ( Q @ X6 ) )
% 5.52/5.78 = ( ( P5 @ X6 )
% 5.52/5.78 | ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(2)
% 5.52/5.78 thf(fact_2938_minf_I2_J,axiom,
% 5.52/5.78 ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 5.52/5.78 ( ? [Z5: int] :
% 5.52/5.78 ! [X4: int] :
% 5.52/5.78 ( ( ord_less_int @ X4 @ Z5 )
% 5.52/5.78 => ( ( P @ X4 )
% 5.52/5.78 = ( P5 @ X4 ) ) )
% 5.52/5.78 => ( ? [Z5: int] :
% 5.52/5.78 ! [X4: int] :
% 5.52/5.78 ( ( ord_less_int @ X4 @ Z5 )
% 5.52/5.78 => ( ( Q @ X4 )
% 5.52/5.78 = ( Q6 @ X4 ) ) )
% 5.52/5.78 => ? [Z3: int] :
% 5.52/5.78 ! [X6: int] :
% 5.52/5.78 ( ( ord_less_int @ X6 @ Z3 )
% 5.52/5.78 => ( ( ( P @ X6 )
% 5.52/5.78 | ( Q @ X6 ) )
% 5.52/5.78 = ( ( P5 @ X6 )
% 5.52/5.78 | ( Q6 @ X6 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(2)
% 5.52/5.78 thf(fact_2939_minf_I3_J,axiom,
% 5.52/5.78 ! [T: real] :
% 5.52/5.78 ? [Z3: real] :
% 5.52/5.78 ! [X6: real] :
% 5.52/5.78 ( ( ord_less_real @ X6 @ Z3 )
% 5.52/5.78 => ( X6 != T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(3)
% 5.52/5.78 thf(fact_2940_minf_I3_J,axiom,
% 5.52/5.78 ! [T: rat] :
% 5.52/5.78 ? [Z3: rat] :
% 5.52/5.78 ! [X6: rat] :
% 5.52/5.78 ( ( ord_less_rat @ X6 @ Z3 )
% 5.52/5.78 => ( X6 != T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(3)
% 5.52/5.78 thf(fact_2941_minf_I3_J,axiom,
% 5.52/5.78 ! [T: num] :
% 5.52/5.78 ? [Z3: num] :
% 5.52/5.78 ! [X6: num] :
% 5.52/5.78 ( ( ord_less_num @ X6 @ Z3 )
% 5.52/5.78 => ( X6 != T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(3)
% 5.52/5.78 thf(fact_2942_minf_I3_J,axiom,
% 5.52/5.78 ! [T: nat] :
% 5.52/5.78 ? [Z3: nat] :
% 5.52/5.78 ! [X6: nat] :
% 5.52/5.78 ( ( ord_less_nat @ X6 @ Z3 )
% 5.52/5.78 => ( X6 != T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(3)
% 5.52/5.78 thf(fact_2943_minf_I3_J,axiom,
% 5.52/5.78 ! [T: int] :
% 5.52/5.78 ? [Z3: int] :
% 5.52/5.78 ! [X6: int] :
% 5.52/5.78 ( ( ord_less_int @ X6 @ Z3 )
% 5.52/5.78 => ( X6 != T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(3)
% 5.52/5.78 thf(fact_2944_minf_I4_J,axiom,
% 5.52/5.78 ! [T: real] :
% 5.52/5.78 ? [Z3: real] :
% 5.52/5.78 ! [X6: real] :
% 5.52/5.78 ( ( ord_less_real @ X6 @ Z3 )
% 5.52/5.78 => ( X6 != T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(4)
% 5.52/5.78 thf(fact_2945_minf_I4_J,axiom,
% 5.52/5.78 ! [T: rat] :
% 5.52/5.78 ? [Z3: rat] :
% 5.52/5.78 ! [X6: rat] :
% 5.52/5.78 ( ( ord_less_rat @ X6 @ Z3 )
% 5.52/5.78 => ( X6 != T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(4)
% 5.52/5.78 thf(fact_2946_minf_I4_J,axiom,
% 5.52/5.78 ! [T: num] :
% 5.52/5.78 ? [Z3: num] :
% 5.52/5.78 ! [X6: num] :
% 5.52/5.78 ( ( ord_less_num @ X6 @ Z3 )
% 5.52/5.78 => ( X6 != T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(4)
% 5.52/5.78 thf(fact_2947_minf_I4_J,axiom,
% 5.52/5.78 ! [T: nat] :
% 5.52/5.78 ? [Z3: nat] :
% 5.52/5.78 ! [X6: nat] :
% 5.52/5.78 ( ( ord_less_nat @ X6 @ Z3 )
% 5.52/5.78 => ( X6 != T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(4)
% 5.52/5.78 thf(fact_2948_minf_I4_J,axiom,
% 5.52/5.78 ! [T: int] :
% 5.52/5.78 ? [Z3: int] :
% 5.52/5.78 ! [X6: int] :
% 5.52/5.78 ( ( ord_less_int @ X6 @ Z3 )
% 5.52/5.78 => ( X6 != T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(4)
% 5.52/5.78 thf(fact_2949_minf_I5_J,axiom,
% 5.52/5.78 ! [T: real] :
% 5.52/5.78 ? [Z3: real] :
% 5.52/5.78 ! [X6: real] :
% 5.52/5.78 ( ( ord_less_real @ X6 @ Z3 )
% 5.52/5.78 => ( ord_less_real @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(5)
% 5.52/5.78 thf(fact_2950_minf_I5_J,axiom,
% 5.52/5.78 ! [T: rat] :
% 5.52/5.78 ? [Z3: rat] :
% 5.52/5.78 ! [X6: rat] :
% 5.52/5.78 ( ( ord_less_rat @ X6 @ Z3 )
% 5.52/5.78 => ( ord_less_rat @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(5)
% 5.52/5.78 thf(fact_2951_minf_I5_J,axiom,
% 5.52/5.78 ! [T: num] :
% 5.52/5.78 ? [Z3: num] :
% 5.52/5.78 ! [X6: num] :
% 5.52/5.78 ( ( ord_less_num @ X6 @ Z3 )
% 5.52/5.78 => ( ord_less_num @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(5)
% 5.52/5.78 thf(fact_2952_minf_I5_J,axiom,
% 5.52/5.78 ! [T: nat] :
% 5.52/5.78 ? [Z3: nat] :
% 5.52/5.78 ! [X6: nat] :
% 5.52/5.78 ( ( ord_less_nat @ X6 @ Z3 )
% 5.52/5.78 => ( ord_less_nat @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(5)
% 5.52/5.78 thf(fact_2953_minf_I5_J,axiom,
% 5.52/5.78 ! [T: int] :
% 5.52/5.78 ? [Z3: int] :
% 5.52/5.78 ! [X6: int] :
% 5.52/5.78 ( ( ord_less_int @ X6 @ Z3 )
% 5.52/5.78 => ( ord_less_int @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(5)
% 5.52/5.78 thf(fact_2954_minf_I7_J,axiom,
% 5.52/5.78 ! [T: real] :
% 5.52/5.78 ? [Z3: real] :
% 5.52/5.78 ! [X6: real] :
% 5.52/5.78 ( ( ord_less_real @ X6 @ Z3 )
% 5.52/5.78 => ~ ( ord_less_real @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(7)
% 5.52/5.78 thf(fact_2955_minf_I7_J,axiom,
% 5.52/5.78 ! [T: rat] :
% 5.52/5.78 ? [Z3: rat] :
% 5.52/5.78 ! [X6: rat] :
% 5.52/5.78 ( ( ord_less_rat @ X6 @ Z3 )
% 5.52/5.78 => ~ ( ord_less_rat @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(7)
% 5.52/5.78 thf(fact_2956_minf_I7_J,axiom,
% 5.52/5.78 ! [T: num] :
% 5.52/5.78 ? [Z3: num] :
% 5.52/5.78 ! [X6: num] :
% 5.52/5.78 ( ( ord_less_num @ X6 @ Z3 )
% 5.52/5.78 => ~ ( ord_less_num @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(7)
% 5.52/5.78 thf(fact_2957_minf_I7_J,axiom,
% 5.52/5.78 ! [T: nat] :
% 5.52/5.78 ? [Z3: nat] :
% 5.52/5.78 ! [X6: nat] :
% 5.52/5.78 ( ( ord_less_nat @ X6 @ Z3 )
% 5.52/5.78 => ~ ( ord_less_nat @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(7)
% 5.52/5.78 thf(fact_2958_minf_I7_J,axiom,
% 5.52/5.78 ! [T: int] :
% 5.52/5.78 ? [Z3: int] :
% 5.52/5.78 ! [X6: int] :
% 5.52/5.78 ( ( ord_less_int @ X6 @ Z3 )
% 5.52/5.78 => ~ ( ord_less_int @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(7)
% 5.52/5.78 thf(fact_2959_minf_I8_J,axiom,
% 5.52/5.78 ! [T: real] :
% 5.52/5.78 ? [Z3: real] :
% 5.52/5.78 ! [X6: real] :
% 5.52/5.78 ( ( ord_less_real @ X6 @ Z3 )
% 5.52/5.78 => ~ ( ord_less_eq_real @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(8)
% 5.52/5.78 thf(fact_2960_minf_I8_J,axiom,
% 5.52/5.78 ! [T: rat] :
% 5.52/5.78 ? [Z3: rat] :
% 5.52/5.78 ! [X6: rat] :
% 5.52/5.78 ( ( ord_less_rat @ X6 @ Z3 )
% 5.52/5.78 => ~ ( ord_less_eq_rat @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(8)
% 5.52/5.78 thf(fact_2961_minf_I8_J,axiom,
% 5.52/5.78 ! [T: num] :
% 5.52/5.78 ? [Z3: num] :
% 5.52/5.78 ! [X6: num] :
% 5.52/5.78 ( ( ord_less_num @ X6 @ Z3 )
% 5.52/5.78 => ~ ( ord_less_eq_num @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(8)
% 5.52/5.78 thf(fact_2962_minf_I8_J,axiom,
% 5.52/5.78 ! [T: nat] :
% 5.52/5.78 ? [Z3: nat] :
% 5.52/5.78 ! [X6: nat] :
% 5.52/5.78 ( ( ord_less_nat @ X6 @ Z3 )
% 5.52/5.78 => ~ ( ord_less_eq_nat @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(8)
% 5.52/5.78 thf(fact_2963_minf_I8_J,axiom,
% 5.52/5.78 ! [T: int] :
% 5.52/5.78 ? [Z3: int] :
% 5.52/5.78 ! [X6: int] :
% 5.52/5.78 ( ( ord_less_int @ X6 @ Z3 )
% 5.52/5.78 => ~ ( ord_less_eq_int @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(8)
% 5.52/5.78 thf(fact_2964_minf_I6_J,axiom,
% 5.52/5.78 ! [T: real] :
% 5.52/5.78 ? [Z3: real] :
% 5.52/5.78 ! [X6: real] :
% 5.52/5.78 ( ( ord_less_real @ X6 @ Z3 )
% 5.52/5.78 => ( ord_less_eq_real @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(6)
% 5.52/5.78 thf(fact_2965_minf_I6_J,axiom,
% 5.52/5.78 ! [T: rat] :
% 5.52/5.78 ? [Z3: rat] :
% 5.52/5.78 ! [X6: rat] :
% 5.52/5.78 ( ( ord_less_rat @ X6 @ Z3 )
% 5.52/5.78 => ( ord_less_eq_rat @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(6)
% 5.52/5.78 thf(fact_2966_minf_I6_J,axiom,
% 5.52/5.78 ! [T: num] :
% 5.52/5.78 ? [Z3: num] :
% 5.52/5.78 ! [X6: num] :
% 5.52/5.78 ( ( ord_less_num @ X6 @ Z3 )
% 5.52/5.78 => ( ord_less_eq_num @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(6)
% 5.52/5.78 thf(fact_2967_minf_I6_J,axiom,
% 5.52/5.78 ! [T: nat] :
% 5.52/5.78 ? [Z3: nat] :
% 5.52/5.78 ! [X6: nat] :
% 5.52/5.78 ( ( ord_less_nat @ X6 @ Z3 )
% 5.52/5.78 => ( ord_less_eq_nat @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(6)
% 5.52/5.78 thf(fact_2968_minf_I6_J,axiom,
% 5.52/5.78 ! [T: int] :
% 5.52/5.78 ? [Z3: int] :
% 5.52/5.78 ! [X6: int] :
% 5.52/5.78 ( ( ord_less_int @ X6 @ Z3 )
% 5.52/5.78 => ( ord_less_eq_int @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % minf(6)
% 5.52/5.78 thf(fact_2969_pinf_I8_J,axiom,
% 5.52/5.78 ! [T: real] :
% 5.52/5.78 ? [Z3: real] :
% 5.52/5.78 ! [X6: real] :
% 5.52/5.78 ( ( ord_less_real @ Z3 @ X6 )
% 5.52/5.78 => ( ord_less_eq_real @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(8)
% 5.52/5.78 thf(fact_2970_pinf_I8_J,axiom,
% 5.52/5.78 ! [T: rat] :
% 5.52/5.78 ? [Z3: rat] :
% 5.52/5.78 ! [X6: rat] :
% 5.52/5.78 ( ( ord_less_rat @ Z3 @ X6 )
% 5.52/5.78 => ( ord_less_eq_rat @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(8)
% 5.52/5.78 thf(fact_2971_pinf_I8_J,axiom,
% 5.52/5.78 ! [T: num] :
% 5.52/5.78 ? [Z3: num] :
% 5.52/5.78 ! [X6: num] :
% 5.52/5.78 ( ( ord_less_num @ Z3 @ X6 )
% 5.52/5.78 => ( ord_less_eq_num @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(8)
% 5.52/5.78 thf(fact_2972_pinf_I8_J,axiom,
% 5.52/5.78 ! [T: nat] :
% 5.52/5.78 ? [Z3: nat] :
% 5.52/5.78 ! [X6: nat] :
% 5.52/5.78 ( ( ord_less_nat @ Z3 @ X6 )
% 5.52/5.78 => ( ord_less_eq_nat @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(8)
% 5.52/5.78 thf(fact_2973_pinf_I8_J,axiom,
% 5.52/5.78 ! [T: int] :
% 5.52/5.78 ? [Z3: int] :
% 5.52/5.78 ! [X6: int] :
% 5.52/5.78 ( ( ord_less_int @ Z3 @ X6 )
% 5.52/5.78 => ( ord_less_eq_int @ T @ X6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(8)
% 5.52/5.78 thf(fact_2974_pinf_I6_J,axiom,
% 5.52/5.78 ! [T: real] :
% 5.52/5.78 ? [Z3: real] :
% 5.52/5.78 ! [X6: real] :
% 5.52/5.78 ( ( ord_less_real @ Z3 @ X6 )
% 5.52/5.78 => ~ ( ord_less_eq_real @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(6)
% 5.52/5.78 thf(fact_2975_pinf_I6_J,axiom,
% 5.52/5.78 ! [T: rat] :
% 5.52/5.78 ? [Z3: rat] :
% 5.52/5.78 ! [X6: rat] :
% 5.52/5.78 ( ( ord_less_rat @ Z3 @ X6 )
% 5.52/5.78 => ~ ( ord_less_eq_rat @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(6)
% 5.52/5.78 thf(fact_2976_pinf_I6_J,axiom,
% 5.52/5.78 ! [T: num] :
% 5.52/5.78 ? [Z3: num] :
% 5.52/5.78 ! [X6: num] :
% 5.52/5.78 ( ( ord_less_num @ Z3 @ X6 )
% 5.52/5.78 => ~ ( ord_less_eq_num @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(6)
% 5.52/5.78 thf(fact_2977_pinf_I6_J,axiom,
% 5.52/5.78 ! [T: nat] :
% 5.52/5.78 ? [Z3: nat] :
% 5.52/5.78 ! [X6: nat] :
% 5.52/5.78 ( ( ord_less_nat @ Z3 @ X6 )
% 5.52/5.78 => ~ ( ord_less_eq_nat @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(6)
% 5.52/5.78 thf(fact_2978_pinf_I6_J,axiom,
% 5.52/5.78 ! [T: int] :
% 5.52/5.78 ? [Z3: int] :
% 5.52/5.78 ! [X6: int] :
% 5.52/5.78 ( ( ord_less_int @ Z3 @ X6 )
% 5.52/5.78 => ~ ( ord_less_eq_int @ X6 @ T ) ) ).
% 5.52/5.78
% 5.52/5.78 % pinf(6)
% 5.52/5.78 thf(fact_2979_inf__period_I2_J,axiom,
% 5.52/5.78 ! [P: complex > $o,D4: complex,Q: complex > $o] :
% 5.52/5.78 ( ! [X4: complex,K3: complex] :
% 5.52/5.78 ( ( P @ X4 )
% 5.52/5.78 = ( P @ ( minus_minus_complex @ X4 @ ( times_times_complex @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ( ! [X4: complex,K3: complex] :
% 5.52/5.78 ( ( Q @ X4 )
% 5.52/5.78 = ( Q @ ( minus_minus_complex @ X4 @ ( times_times_complex @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ! [X6: complex,K4: complex] :
% 5.52/5.78 ( ( ( P @ X6 )
% 5.52/5.78 | ( Q @ X6 ) )
% 5.52/5.78 = ( ( P @ ( minus_minus_complex @ X6 @ ( times_times_complex @ K4 @ D4 ) ) )
% 5.52/5.78 | ( Q @ ( minus_minus_complex @ X6 @ ( times_times_complex @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % inf_period(2)
% 5.52/5.78 thf(fact_2980_inf__period_I2_J,axiom,
% 5.52/5.78 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.52/5.78 ( ! [X4: real,K3: real] :
% 5.52/5.78 ( ( P @ X4 )
% 5.52/5.78 = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ( ! [X4: real,K3: real] :
% 5.52/5.78 ( ( Q @ X4 )
% 5.52/5.78 = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ! [X6: real,K4: real] :
% 5.52/5.78 ( ( ( P @ X6 )
% 5.52/5.78 | ( Q @ X6 ) )
% 5.52/5.78 = ( ( P @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.52/5.78 | ( Q @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % inf_period(2)
% 5.52/5.78 thf(fact_2981_inf__period_I2_J,axiom,
% 5.52/5.78 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.52/5.78 ( ! [X4: rat,K3: rat] :
% 5.52/5.78 ( ( P @ X4 )
% 5.52/5.78 = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ( ! [X4: rat,K3: rat] :
% 5.52/5.78 ( ( Q @ X4 )
% 5.52/5.78 = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ! [X6: rat,K4: rat] :
% 5.52/5.78 ( ( ( P @ X6 )
% 5.52/5.78 | ( Q @ X6 ) )
% 5.52/5.78 = ( ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.52/5.78 | ( Q @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % inf_period(2)
% 5.52/5.78 thf(fact_2982_inf__period_I2_J,axiom,
% 5.52/5.78 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.52/5.78 ( ! [X4: int,K3: int] :
% 5.52/5.78 ( ( P @ X4 )
% 5.52/5.78 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ( ! [X4: int,K3: int] :
% 5.52/5.78 ( ( Q @ X4 )
% 5.52/5.78 = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ! [X6: int,K4: int] :
% 5.52/5.78 ( ( ( P @ X6 )
% 5.52/5.78 | ( Q @ X6 ) )
% 5.52/5.78 = ( ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.52/5.78 | ( Q @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % inf_period(2)
% 5.52/5.78 thf(fact_2983_inf__period_I1_J,axiom,
% 5.52/5.78 ! [P: complex > $o,D4: complex,Q: complex > $o] :
% 5.52/5.78 ( ! [X4: complex,K3: complex] :
% 5.52/5.78 ( ( P @ X4 )
% 5.52/5.78 = ( P @ ( minus_minus_complex @ X4 @ ( times_times_complex @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ( ! [X4: complex,K3: complex] :
% 5.52/5.78 ( ( Q @ X4 )
% 5.52/5.78 = ( Q @ ( minus_minus_complex @ X4 @ ( times_times_complex @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ! [X6: complex,K4: complex] :
% 5.52/5.78 ( ( ( P @ X6 )
% 5.52/5.78 & ( Q @ X6 ) )
% 5.52/5.78 = ( ( P @ ( minus_minus_complex @ X6 @ ( times_times_complex @ K4 @ D4 ) ) )
% 5.52/5.78 & ( Q @ ( minus_minus_complex @ X6 @ ( times_times_complex @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % inf_period(1)
% 5.52/5.78 thf(fact_2984_inf__period_I1_J,axiom,
% 5.52/5.78 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.52/5.78 ( ! [X4: real,K3: real] :
% 5.52/5.78 ( ( P @ X4 )
% 5.52/5.78 = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ( ! [X4: real,K3: real] :
% 5.52/5.78 ( ( Q @ X4 )
% 5.52/5.78 = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ! [X6: real,K4: real] :
% 5.52/5.78 ( ( ( P @ X6 )
% 5.52/5.78 & ( Q @ X6 ) )
% 5.52/5.78 = ( ( P @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.52/5.78 & ( Q @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % inf_period(1)
% 5.52/5.78 thf(fact_2985_inf__period_I1_J,axiom,
% 5.52/5.78 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.52/5.78 ( ! [X4: rat,K3: rat] :
% 5.52/5.78 ( ( P @ X4 )
% 5.52/5.78 = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ( ! [X4: rat,K3: rat] :
% 5.52/5.78 ( ( Q @ X4 )
% 5.52/5.78 = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ! [X6: rat,K4: rat] :
% 5.52/5.78 ( ( ( P @ X6 )
% 5.52/5.78 & ( Q @ X6 ) )
% 5.52/5.78 = ( ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.52/5.78 & ( Q @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % inf_period(1)
% 5.52/5.78 thf(fact_2986_inf__period_I1_J,axiom,
% 5.52/5.78 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.52/5.78 ( ! [X4: int,K3: int] :
% 5.52/5.78 ( ( P @ X4 )
% 5.52/5.78 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ( ! [X4: int,K3: int] :
% 5.52/5.78 ( ( Q @ X4 )
% 5.52/5.78 = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.52/5.78 => ! [X6: int,K4: int] :
% 5.52/5.78 ( ( ( P @ X6 )
% 5.52/5.78 & ( Q @ X6 ) )
% 5.52/5.78 = ( ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.52/5.78 & ( Q @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % inf_period(1)
% 5.52/5.78 thf(fact_2987_plusinfinity,axiom,
% 5.52/5.78 ! [D2: int,P5: int > $o,P: int > $o] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.52/5.78 => ( ! [X4: int,K3: int] :
% 5.52/5.78 ( ( P5 @ X4 )
% 5.52/5.78 = ( P5 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D2 ) ) ) )
% 5.52/5.78 => ( ? [Z5: int] :
% 5.52/5.78 ! [X4: int] :
% 5.52/5.78 ( ( ord_less_int @ Z5 @ X4 )
% 5.52/5.78 => ( ( P @ X4 )
% 5.52/5.78 = ( P5 @ X4 ) ) )
% 5.52/5.78 => ( ? [X_12: int] : ( P5 @ X_12 )
% 5.52/5.78 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % plusinfinity
% 5.52/5.78 thf(fact_2988_minusinfinity,axiom,
% 5.52/5.78 ! [D2: int,P1: int > $o,P: int > $o] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.52/5.78 => ( ! [X4: int,K3: int] :
% 5.52/5.78 ( ( P1 @ X4 )
% 5.52/5.78 = ( P1 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D2 ) ) ) )
% 5.52/5.78 => ( ? [Z5: int] :
% 5.52/5.78 ! [X4: int] :
% 5.52/5.78 ( ( ord_less_int @ X4 @ Z5 )
% 5.52/5.78 => ( ( P @ X4 )
% 5.52/5.78 = ( P1 @ X4 ) ) )
% 5.52/5.78 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.52/5.78 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minusinfinity
% 5.52/5.78 thf(fact_2989_incr__mult__lemma,axiom,
% 5.52/5.78 ! [D2: int,P: int > $o,K: int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.52/5.78 => ( ! [X4: int] :
% 5.52/5.78 ( ( P @ X4 )
% 5.52/5.78 => ( P @ ( plus_plus_int @ X4 @ D2 ) ) )
% 5.52/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.78 => ! [X6: int] :
% 5.52/5.78 ( ( P @ X6 )
% 5.52/5.78 => ( P @ ( plus_plus_int @ X6 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % incr_mult_lemma
% 5.52/5.78 thf(fact_2990_decr__mult__lemma,axiom,
% 5.52/5.78 ! [D2: int,P: int > $o,K: int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.52/5.78 => ( ! [X4: int] :
% 5.52/5.78 ( ( P @ X4 )
% 5.52/5.78 => ( P @ ( minus_minus_int @ X4 @ D2 ) ) )
% 5.52/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.78 => ! [X6: int] :
% 5.52/5.78 ( ( P @ X6 )
% 5.52/5.78 => ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % decr_mult_lemma
% 5.52/5.78 thf(fact_2991_periodic__finite__ex,axiom,
% 5.52/5.78 ! [D2: int,P: int > $o] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.52/5.78 => ( ! [X4: int,K3: int] :
% 5.52/5.78 ( ( P @ X4 )
% 5.52/5.78 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D2 ) ) ) )
% 5.52/5.78 => ( ( ? [X7: int] : ( P @ X7 ) )
% 5.52/5.78 = ( ? [X: int] :
% 5.52/5.78 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 5.52/5.78 & ( P @ X ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % periodic_finite_ex
% 5.52/5.78 thf(fact_2992_aset_I7_J,axiom,
% 5.52/5.78 ! [D4: int,A2: set_int,T: int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.78 => ! [X6: int] :
% 5.52/5.78 ( ! [Xa3: int] :
% 5.52/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.78 => ! [Xb3: int] :
% 5.52/5.78 ( ( member_int @ Xb3 @ A2 )
% 5.52/5.78 => ( X6
% 5.52/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.52/5.78 => ( ( ord_less_int @ T @ X6 )
% 5.52/5.78 => ( ord_less_int @ T @ ( plus_plus_int @ X6 @ D4 ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % aset(7)
% 5.52/5.78 thf(fact_2993_aset_I5_J,axiom,
% 5.52/5.78 ! [D4: int,T: int,A2: set_int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.78 => ( ( member_int @ T @ A2 )
% 5.52/5.78 => ! [X6: int] :
% 5.52/5.78 ( ! [Xa3: int] :
% 5.52/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.78 => ! [Xb3: int] :
% 5.52/5.78 ( ( member_int @ Xb3 @ A2 )
% 5.52/5.78 => ( X6
% 5.52/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.52/5.78 => ( ( ord_less_int @ X6 @ T )
% 5.52/5.78 => ( ord_less_int @ ( plus_plus_int @ X6 @ D4 ) @ T ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % aset(5)
% 5.52/5.78 thf(fact_2994_aset_I4_J,axiom,
% 5.52/5.78 ! [D4: int,T: int,A2: set_int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.78 => ( ( member_int @ T @ A2 )
% 5.52/5.78 => ! [X6: int] :
% 5.52/5.78 ( ! [Xa3: int] :
% 5.52/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.78 => ! [Xb3: int] :
% 5.52/5.78 ( ( member_int @ Xb3 @ A2 )
% 5.52/5.78 => ( X6
% 5.52/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.52/5.78 => ( ( X6 != T )
% 5.52/5.78 => ( ( plus_plus_int @ X6 @ D4 )
% 5.52/5.78 != T ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % aset(4)
% 5.52/5.78 thf(fact_2995_aset_I3_J,axiom,
% 5.52/5.78 ! [D4: int,T: int,A2: set_int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.78 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.52/5.78 => ! [X6: int] :
% 5.52/5.78 ( ! [Xa3: int] :
% 5.52/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.78 => ! [Xb3: int] :
% 5.52/5.78 ( ( member_int @ Xb3 @ A2 )
% 5.52/5.78 => ( X6
% 5.52/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.52/5.78 => ( ( X6 = T )
% 5.52/5.78 => ( ( plus_plus_int @ X6 @ D4 )
% 5.52/5.78 = T ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % aset(3)
% 5.52/5.78 thf(fact_2996_bset_I7_J,axiom,
% 5.52/5.78 ! [D4: int,T: int,B4: set_int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.78 => ( ( member_int @ T @ B4 )
% 5.52/5.78 => ! [X6: int] :
% 5.52/5.78 ( ! [Xa3: int] :
% 5.52/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.78 => ! [Xb3: int] :
% 5.52/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.52/5.78 => ( X6
% 5.52/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.52/5.78 => ( ( ord_less_int @ T @ X6 )
% 5.52/5.78 => ( ord_less_int @ T @ ( minus_minus_int @ X6 @ D4 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % bset(7)
% 5.52/5.78 thf(fact_2997_bset_I5_J,axiom,
% 5.52/5.78 ! [D4: int,B4: set_int,T: int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.78 => ! [X6: int] :
% 5.52/5.78 ( ! [Xa3: int] :
% 5.52/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.78 => ! [Xb3: int] :
% 5.52/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.52/5.78 => ( X6
% 5.52/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.52/5.78 => ( ( ord_less_int @ X6 @ T )
% 5.52/5.78 => ( ord_less_int @ ( minus_minus_int @ X6 @ D4 ) @ T ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % bset(5)
% 5.52/5.78 thf(fact_2998_bset_I4_J,axiom,
% 5.52/5.78 ! [D4: int,T: int,B4: set_int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.52/5.78 => ( ( member_int @ T @ B4 )
% 5.52/5.78 => ! [X6: int] :
% 5.52/5.78 ( ! [Xa3: int] :
% 5.52/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.52/5.78 => ! [Xb3: int] :
% 5.52/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.52/5.78 => ( X6
% 5.52/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.52/5.78 => ( ( X6 != T )
% 5.52/5.78 => ( ( minus_minus_int @ X6 @ D4 )
% 5.52/5.78 != T ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % bset(4)
% 5.52/5.78 thf(fact_2999_psubsetI,axiom,
% 5.52/5.78 ! [A2: set_nat,B4: set_nat] :
% 5.52/5.78 ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.52/5.78 => ( ( A2 != B4 )
% 5.52/5.78 => ( ord_less_set_nat @ A2 @ B4 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubsetI
% 5.52/5.78 thf(fact_3000_unset__bit__0,axiom,
% 5.52/5.78 ! [A: int] :
% 5.52/5.78 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.52/5.78 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % unset_bit_0
% 5.52/5.78 thf(fact_3001_unset__bit__0,axiom,
% 5.52/5.78 ! [A: nat] :
% 5.52/5.78 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.52/5.78 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % unset_bit_0
% 5.52/5.78 thf(fact_3002_Bolzano,axiom,
% 5.52/5.78 ! [A: real,B: real,P: real > real > $o] :
% 5.52/5.78 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.78 => ( ! [A3: real,B2: real,C2: real] :
% 5.52/5.78 ( ( P @ A3 @ B2 )
% 5.52/5.78 => ( ( P @ B2 @ C2 )
% 5.52/5.78 => ( ( ord_less_eq_real @ A3 @ B2 )
% 5.52/5.78 => ( ( ord_less_eq_real @ B2 @ C2 )
% 5.52/5.78 => ( P @ A3 @ C2 ) ) ) ) )
% 5.52/5.78 => ( ! [X4: real] :
% 5.52/5.78 ( ( ord_less_eq_real @ A @ X4 )
% 5.52/5.78 => ( ( ord_less_eq_real @ X4 @ B )
% 5.52/5.78 => ? [D5: real] :
% 5.52/5.78 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.52/5.78 & ! [A3: real,B2: real] :
% 5.52/5.78 ( ( ( ord_less_eq_real @ A3 @ X4 )
% 5.52/5.78 & ( ord_less_eq_real @ X4 @ B2 )
% 5.52/5.78 & ( ord_less_real @ ( minus_minus_real @ B2 @ A3 ) @ D5 ) )
% 5.52/5.78 => ( P @ A3 @ B2 ) ) ) ) )
% 5.52/5.78 => ( P @ A @ B ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % Bolzano
% 5.52/5.78 thf(fact_3003_divmod__algorithm__code_I8_J,axiom,
% 5.52/5.78 ! [M: num,N: num] :
% 5.52/5.78 ( ( ( ord_less_num @ M @ N )
% 5.52/5.78 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.52/5.78 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.52/5.78 & ( ~ ( ord_less_num @ M @ N )
% 5.52/5.78 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.52/5.78 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_algorithm_code(8)
% 5.52/5.78 thf(fact_3004_divmod__algorithm__code_I8_J,axiom,
% 5.52/5.78 ! [M: num,N: num] :
% 5.52/5.78 ( ( ( ord_less_num @ M @ N )
% 5.52/5.78 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.52/5.78 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.52/5.78 & ( ~ ( ord_less_num @ M @ N )
% 5.52/5.78 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.52/5.78 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_algorithm_code(8)
% 5.52/5.78 thf(fact_3005_divmod__algorithm__code_I8_J,axiom,
% 5.52/5.78 ! [M: num,N: num] :
% 5.52/5.78 ( ( ( ord_less_num @ M @ N )
% 5.52/5.78 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.52/5.78 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.52/5.78 & ( ~ ( ord_less_num @ M @ N )
% 5.52/5.78 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.52/5.78 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_algorithm_code(8)
% 5.52/5.78 thf(fact_3006_divmod__algorithm__code_I7_J,axiom,
% 5.52/5.78 ! [M: num,N: num] :
% 5.52/5.78 ( ( ( ord_less_eq_num @ M @ N )
% 5.52/5.78 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.52/5.78 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.52/5.78 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.52/5.78 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.52/5.78 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_algorithm_code(7)
% 5.52/5.78 thf(fact_3007_divmod__algorithm__code_I7_J,axiom,
% 5.52/5.78 ! [M: num,N: num] :
% 5.52/5.78 ( ( ( ord_less_eq_num @ M @ N )
% 5.52/5.78 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.52/5.78 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.52/5.78 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.52/5.78 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.52/5.78 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_algorithm_code(7)
% 5.52/5.78 thf(fact_3008_divmod__algorithm__code_I7_J,axiom,
% 5.52/5.78 ! [M: num,N: num] :
% 5.52/5.78 ( ( ( ord_less_eq_num @ M @ N )
% 5.52/5.78 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.52/5.78 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.52/5.78 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.52/5.78 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.52/5.78 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_algorithm_code(7)
% 5.52/5.78 thf(fact_3009_mult__le__cancel__iff1,axiom,
% 5.52/5.78 ! [Z: real,X2: real,Y2: real] :
% 5.52/5.78 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.52/5.78 => ( ( ord_less_eq_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y2 @ Z ) )
% 5.52/5.78 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_le_cancel_iff1
% 5.52/5.78 thf(fact_3010_mult__le__cancel__iff1,axiom,
% 5.52/5.78 ! [Z: rat,X2: rat,Y2: rat] :
% 5.52/5.78 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.52/5.78 => ( ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y2 @ Z ) )
% 5.52/5.78 = ( ord_less_eq_rat @ X2 @ Y2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_le_cancel_iff1
% 5.52/5.78 thf(fact_3011_mult__le__cancel__iff1,axiom,
% 5.52/5.78 ! [Z: int,X2: int,Y2: int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.52/5.78 => ( ( ord_less_eq_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y2 @ Z ) )
% 5.52/5.78 = ( ord_less_eq_int @ X2 @ Y2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_le_cancel_iff1
% 5.52/5.78 thf(fact_3012_unset__bit__nonnegative__int__iff,axiom,
% 5.52/5.78 ! [N: nat,K: int] :
% 5.52/5.78 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 5.52/5.78 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.52/5.78
% 5.52/5.78 % unset_bit_nonnegative_int_iff
% 5.52/5.78 thf(fact_3013_unset__bit__negative__int__iff,axiom,
% 5.52/5.78 ! [N: nat,K: int] :
% 5.52/5.78 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 5.52/5.78 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.52/5.78
% 5.52/5.78 % unset_bit_negative_int_iff
% 5.52/5.78 thf(fact_3014_divmod__algorithm__code_I2_J,axiom,
% 5.52/5.78 ! [M: num] :
% 5.52/5.78 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.52/5.78 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_algorithm_code(2)
% 5.52/5.78 thf(fact_3015_divmod__algorithm__code_I2_J,axiom,
% 5.52/5.78 ! [M: num] :
% 5.52/5.78 ( ( unique5052692396658037445od_int @ M @ one )
% 5.52/5.78 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_algorithm_code(2)
% 5.52/5.78 thf(fact_3016_divmod__algorithm__code_I3_J,axiom,
% 5.52/5.78 ! [N: num] :
% 5.52/5.78 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.52/5.78 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_algorithm_code(3)
% 5.52/5.78 thf(fact_3017_divmod__algorithm__code_I3_J,axiom,
% 5.52/5.78 ! [N: num] :
% 5.52/5.78 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.52/5.78 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_algorithm_code(3)
% 5.52/5.78 thf(fact_3018_divmod__algorithm__code_I4_J,axiom,
% 5.52/5.78 ! [N: num] :
% 5.52/5.78 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.52/5.78 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_algorithm_code(4)
% 5.52/5.78 thf(fact_3019_divmod__algorithm__code_I4_J,axiom,
% 5.52/5.78 ! [N: num] :
% 5.52/5.78 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.52/5.78 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_algorithm_code(4)
% 5.52/5.78 thf(fact_3020_unset__bit__less__eq,axiom,
% 5.52/5.78 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 5.52/5.78
% 5.52/5.78 % unset_bit_less_eq
% 5.52/5.78 thf(fact_3021_psubsetD,axiom,
% 5.52/5.78 ! [A2: set_option_nat,B4: set_option_nat,C: option_nat] :
% 5.52/5.78 ( ( ord_le1792839605950587050on_nat @ A2 @ B4 )
% 5.52/5.78 => ( ( member_option_nat @ C @ A2 )
% 5.52/5.78 => ( member_option_nat @ C @ B4 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubsetD
% 5.52/5.78 thf(fact_3022_psubsetD,axiom,
% 5.52/5.78 ! [A2: set_real,B4: set_real,C: real] :
% 5.52/5.78 ( ( ord_less_set_real @ A2 @ B4 )
% 5.52/5.78 => ( ( member_real @ C @ A2 )
% 5.52/5.78 => ( member_real @ C @ B4 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubsetD
% 5.52/5.78 thf(fact_3023_psubsetD,axiom,
% 5.52/5.78 ! [A2: set_set_nat_rat,B4: set_set_nat_rat,C: set_nat_rat] :
% 5.52/5.78 ( ( ord_le1311537459589289991at_rat @ A2 @ B4 )
% 5.52/5.78 => ( ( member_set_nat_rat @ C @ A2 )
% 5.52/5.78 => ( member_set_nat_rat @ C @ B4 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubsetD
% 5.52/5.78 thf(fact_3024_psubsetD,axiom,
% 5.52/5.78 ! [A2: set_nat,B4: set_nat,C: nat] :
% 5.52/5.78 ( ( ord_less_set_nat @ A2 @ B4 )
% 5.52/5.78 => ( ( member_nat @ C @ A2 )
% 5.52/5.78 => ( member_nat @ C @ B4 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubsetD
% 5.52/5.78 thf(fact_3025_psubsetD,axiom,
% 5.52/5.78 ! [A2: set_int,B4: set_int,C: int] :
% 5.52/5.78 ( ( ord_less_set_int @ A2 @ B4 )
% 5.52/5.78 => ( ( member_int @ C @ A2 )
% 5.52/5.78 => ( member_int @ C @ B4 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubsetD
% 5.52/5.78 thf(fact_3026_psubset__imp__ex__mem,axiom,
% 5.52/5.78 ! [A2: set_option_nat,B4: set_option_nat] :
% 5.52/5.78 ( ( ord_le1792839605950587050on_nat @ A2 @ B4 )
% 5.52/5.78 => ? [B2: option_nat] : ( member_option_nat @ B2 @ ( minus_5999362281193037231on_nat @ B4 @ A2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubset_imp_ex_mem
% 5.52/5.78 thf(fact_3027_psubset__imp__ex__mem,axiom,
% 5.52/5.78 ! [A2: set_real,B4: set_real] :
% 5.52/5.78 ( ( ord_less_set_real @ A2 @ B4 )
% 5.52/5.78 => ? [B2: real] : ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubset_imp_ex_mem
% 5.52/5.78 thf(fact_3028_psubset__imp__ex__mem,axiom,
% 5.52/5.78 ! [A2: set_set_nat_rat,B4: set_set_nat_rat] :
% 5.52/5.78 ( ( ord_le1311537459589289991at_rat @ A2 @ B4 )
% 5.52/5.78 => ? [B2: set_nat_rat] : ( member_set_nat_rat @ B2 @ ( minus_1626877696091177228at_rat @ B4 @ A2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubset_imp_ex_mem
% 5.52/5.78 thf(fact_3029_psubset__imp__ex__mem,axiom,
% 5.52/5.78 ! [A2: set_nat,B4: set_nat] :
% 5.52/5.78 ( ( ord_less_set_nat @ A2 @ B4 )
% 5.52/5.78 => ? [B2: nat] : ( member_nat @ B2 @ ( minus_minus_set_nat @ B4 @ A2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubset_imp_ex_mem
% 5.52/5.78 thf(fact_3030_psubset__imp__ex__mem,axiom,
% 5.52/5.78 ! [A2: set_int,B4: set_int] :
% 5.52/5.78 ( ( ord_less_set_int @ A2 @ B4 )
% 5.52/5.78 => ? [B2: int] : ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubset_imp_ex_mem
% 5.52/5.78 thf(fact_3031_less__set__def,axiom,
% 5.52/5.78 ( ord_le1792839605950587050on_nat
% 5.52/5.78 = ( ^ [A6: set_option_nat,B6: set_option_nat] :
% 5.52/5.78 ( ord_le1154456971122042459_nat_o
% 5.52/5.78 @ ^ [X: option_nat] : ( member_option_nat @ X @ A6 )
% 5.52/5.78 @ ^ [X: option_nat] : ( member_option_nat @ X @ B6 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % less_set_def
% 5.52/5.78 thf(fact_3032_less__set__def,axiom,
% 5.52/5.78 ( ord_less_set_real
% 5.52/5.78 = ( ^ [A6: set_real,B6: set_real] :
% 5.52/5.78 ( ord_less_real_o
% 5.52/5.78 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.52/5.78 @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % less_set_def
% 5.52/5.78 thf(fact_3033_less__set__def,axiom,
% 5.52/5.78 ( ord_le1311537459589289991at_rat
% 5.52/5.78 = ( ^ [A6: set_set_nat_rat,B6: set_set_nat_rat] :
% 5.52/5.78 ( ord_le6823063569548456766_rat_o
% 5.52/5.78 @ ^ [X: set_nat_rat] : ( member_set_nat_rat @ X @ A6 )
% 5.52/5.78 @ ^ [X: set_nat_rat] : ( member_set_nat_rat @ X @ B6 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % less_set_def
% 5.52/5.78 thf(fact_3034_less__set__def,axiom,
% 5.52/5.78 ( ord_less_set_nat
% 5.52/5.78 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.52/5.78 ( ord_less_nat_o
% 5.52/5.78 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.52/5.78 @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % less_set_def
% 5.52/5.78 thf(fact_3035_less__set__def,axiom,
% 5.52/5.78 ( ord_less_set_int
% 5.52/5.78 = ( ^ [A6: set_int,B6: set_int] :
% 5.52/5.78 ( ord_less_int_o
% 5.52/5.78 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.52/5.78 @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % less_set_def
% 5.52/5.78 thf(fact_3036_not__psubset__empty,axiom,
% 5.52/5.78 ! [A2: set_nat] :
% 5.52/5.78 ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 5.52/5.78
% 5.52/5.78 % not_psubset_empty
% 5.52/5.78 thf(fact_3037_not__psubset__empty,axiom,
% 5.52/5.78 ! [A2: set_int] :
% 5.52/5.78 ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 5.52/5.78
% 5.52/5.78 % not_psubset_empty
% 5.52/5.78 thf(fact_3038_not__psubset__empty,axiom,
% 5.52/5.78 ! [A2: set_Extended_enat] :
% 5.52/5.78 ~ ( ord_le2529575680413868914d_enat @ A2 @ bot_bo7653980558646680370d_enat ) ).
% 5.52/5.78
% 5.52/5.78 % not_psubset_empty
% 5.52/5.78 thf(fact_3039_psubsetE,axiom,
% 5.52/5.78 ! [A2: set_nat,B4: set_nat] :
% 5.52/5.78 ( ( ord_less_set_nat @ A2 @ B4 )
% 5.52/5.78 => ~ ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.52/5.78 => ( ord_less_eq_set_nat @ B4 @ A2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubsetE
% 5.52/5.78 thf(fact_3040_psubset__eq,axiom,
% 5.52/5.78 ( ord_less_set_nat
% 5.52/5.78 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.52/5.78 ( ( ord_less_eq_set_nat @ A6 @ B6 )
% 5.52/5.78 & ( A6 != B6 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubset_eq
% 5.52/5.78 thf(fact_3041_psubset__imp__subset,axiom,
% 5.52/5.78 ! [A2: set_nat,B4: set_nat] :
% 5.52/5.78 ( ( ord_less_set_nat @ A2 @ B4 )
% 5.52/5.78 => ( ord_less_eq_set_nat @ A2 @ B4 ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubset_imp_subset
% 5.52/5.78 thf(fact_3042_psubset__subset__trans,axiom,
% 5.52/5.78 ! [A2: set_nat,B4: set_nat,C4: set_nat] :
% 5.52/5.78 ( ( ord_less_set_nat @ A2 @ B4 )
% 5.52/5.78 => ( ( ord_less_eq_set_nat @ B4 @ C4 )
% 5.52/5.78 => ( ord_less_set_nat @ A2 @ C4 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % psubset_subset_trans
% 5.52/5.78 thf(fact_3043_subset__not__subset__eq,axiom,
% 5.52/5.78 ( ord_less_set_nat
% 5.52/5.78 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.52/5.78 ( ( ord_less_eq_set_nat @ A6 @ B6 )
% 5.52/5.78 & ~ ( ord_less_eq_set_nat @ B6 @ A6 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % subset_not_subset_eq
% 5.52/5.78 thf(fact_3044_subset__psubset__trans,axiom,
% 5.52/5.78 ! [A2: set_nat,B4: set_nat,C4: set_nat] :
% 5.52/5.78 ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.52/5.78 => ( ( ord_less_set_nat @ B4 @ C4 )
% 5.52/5.78 => ( ord_less_set_nat @ A2 @ C4 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % subset_psubset_trans
% 5.52/5.78 thf(fact_3045_subset__iff__psubset__eq,axiom,
% 5.52/5.78 ( ord_less_eq_set_nat
% 5.52/5.78 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.52/5.78 ( ( ord_less_set_nat @ A6 @ B6 )
% 5.52/5.78 | ( A6 = B6 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % subset_iff_psubset_eq
% 5.52/5.78 thf(fact_3046_divmod__divmod__step,axiom,
% 5.52/5.78 ( unique5055182867167087721od_nat
% 5.52/5.78 = ( ^ [M3: num,N3: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M3 @ N3 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M3 ) ) @ ( unique5026877609467782581ep_nat @ N3 @ ( unique5055182867167087721od_nat @ M3 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_divmod_step
% 5.52/5.78 thf(fact_3047_divmod__divmod__step,axiom,
% 5.52/5.78 ( unique5052692396658037445od_int
% 5.52/5.78 = ( ^ [M3: num,N3: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M3 @ N3 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M3 ) ) @ ( unique5024387138958732305ep_int @ N3 @ ( unique5052692396658037445od_int @ M3 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_divmod_step
% 5.52/5.78 thf(fact_3048_divmod__divmod__step,axiom,
% 5.52/5.78 ( unique3479559517661332726nteger
% 5.52/5.78 = ( ^ [M3: num,N3: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M3 @ N3 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M3 ) ) @ ( unique4921790084139445826nteger @ N3 @ ( unique3479559517661332726nteger @ M3 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_divmod_step
% 5.52/5.78 thf(fact_3049_mult__less__iff1,axiom,
% 5.52/5.78 ! [Z: real,X2: real,Y2: real] :
% 5.52/5.78 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.52/5.78 => ( ( ord_less_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y2 @ Z ) )
% 5.52/5.78 = ( ord_less_real @ X2 @ Y2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_less_iff1
% 5.52/5.78 thf(fact_3050_mult__less__iff1,axiom,
% 5.52/5.78 ! [Z: rat,X2: rat,Y2: rat] :
% 5.52/5.78 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.52/5.78 => ( ( ord_less_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y2 @ Z ) )
% 5.52/5.78 = ( ord_less_rat @ X2 @ Y2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_less_iff1
% 5.52/5.78 thf(fact_3051_mult__less__iff1,axiom,
% 5.52/5.78 ! [Z: int,X2: int,Y2: int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.52/5.78 => ( ( ord_less_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y2 @ Z ) )
% 5.52/5.78 = ( ord_less_int @ X2 @ Y2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_less_iff1
% 5.52/5.78 thf(fact_3052_mult__le__cancel__iff2,axiom,
% 5.52/5.78 ! [Z: real,X2: real,Y2: real] :
% 5.52/5.78 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.52/5.78 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X2 ) @ ( times_times_real @ Z @ Y2 ) )
% 5.52/5.78 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_le_cancel_iff2
% 5.52/5.78 thf(fact_3053_mult__le__cancel__iff2,axiom,
% 5.52/5.78 ! [Z: rat,X2: rat,Y2: rat] :
% 5.52/5.78 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.52/5.78 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X2 ) @ ( times_times_rat @ Z @ Y2 ) )
% 5.52/5.78 = ( ord_less_eq_rat @ X2 @ Y2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_le_cancel_iff2
% 5.52/5.78 thf(fact_3054_mult__le__cancel__iff2,axiom,
% 5.52/5.78 ! [Z: int,X2: int,Y2: int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.52/5.78 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X2 ) @ ( times_times_int @ Z @ Y2 ) )
% 5.52/5.78 = ( ord_less_eq_int @ X2 @ Y2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_le_cancel_iff2
% 5.52/5.78 thf(fact_3055_divides__aux__eq,axiom,
% 5.52/5.78 ! [Q2: nat,R: nat] :
% 5.52/5.78 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.52/5.78 = ( R = zero_zero_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % divides_aux_eq
% 5.52/5.78 thf(fact_3056_divides__aux__eq,axiom,
% 5.52/5.78 ! [Q2: int,R: int] :
% 5.52/5.78 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.52/5.78 = ( R = zero_zero_int ) ) ).
% 5.52/5.78
% 5.52/5.78 % divides_aux_eq
% 5.52/5.78 thf(fact_3057_neg__eucl__rel__int__mult__2,axiom,
% 5.52/5.78 ! [B: int,A: int,Q2: int,R: int] :
% 5.52/5.78 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.52/5.78 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.52/5.78 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % neg_eucl_rel_int_mult_2
% 5.52/5.78 thf(fact_3058_low__def,axiom,
% 5.52/5.78 ( vEBT_VEBT_low
% 5.52/5.78 = ( ^ [X: nat,N3: nat] : ( modulo_modulo_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % low_def
% 5.52/5.78 thf(fact_3059_obtain__set__pred,axiom,
% 5.52/5.78 ! [Z: nat,X2: nat,A2: set_nat] :
% 5.52/5.78 ( ( ord_less_nat @ Z @ X2 )
% 5.52/5.78 => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 5.52/5.78 => ( ( finite_finite_nat @ A2 )
% 5.52/5.78 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A2 @ X2 @ X_1 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % obtain_set_pred
% 5.52/5.78 thf(fact_3060_obtain__set__succ,axiom,
% 5.52/5.78 ! [X2: nat,Z: nat,A2: set_nat,B4: set_nat] :
% 5.52/5.78 ( ( ord_less_nat @ X2 @ Z )
% 5.52/5.78 => ( ( vEBT_VEBT_max_in_set @ A2 @ Z )
% 5.52/5.78 => ( ( finite_finite_nat @ B4 )
% 5.52/5.78 => ( ( A2 = B4 )
% 5.52/5.78 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A2 @ X2 @ X_1 ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % obtain_set_succ
% 5.52/5.78 thf(fact_3061_set__vebt__finite,axiom,
% 5.52/5.78 ! [T: vEBT_VEBT,N: nat] :
% 5.52/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.52/5.78 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % set_vebt_finite
% 5.52/5.78 thf(fact_3062_succ__none__empty,axiom,
% 5.52/5.78 ! [Xs2: set_nat,A: nat] :
% 5.52/5.78 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_1 )
% 5.52/5.78 => ( ( finite_finite_nat @ Xs2 )
% 5.52/5.78 => ~ ? [X6: nat] :
% 5.52/5.78 ( ( member_nat @ X6 @ Xs2 )
% 5.52/5.78 & ( ord_less_nat @ A @ X6 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % succ_none_empty
% 5.52/5.78 thf(fact_3063_pred__none__empty,axiom,
% 5.52/5.78 ! [Xs2: set_nat,A: nat] :
% 5.52/5.78 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_1 )
% 5.52/5.78 => ( ( finite_finite_nat @ Xs2 )
% 5.52/5.78 => ~ ? [X6: nat] :
% 5.52/5.78 ( ( member_nat @ X6 @ Xs2 )
% 5.52/5.78 & ( ord_less_nat @ X6 @ A ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % pred_none_empty
% 5.52/5.78 thf(fact_3064_prod_Oinject,axiom,
% 5.52/5.78 ! [X1: product_prod_nat_nat,X23: product_prod_nat_nat,Y1: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 5.52/5.78 ( ( ( produc6161850002892822231at_nat @ X1 @ X23 )
% 5.52/5.78 = ( produc6161850002892822231at_nat @ Y1 @ Y22 ) )
% 5.52/5.78 = ( ( X1 = Y1 )
% 5.52/5.78 & ( X23 = Y22 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % prod.inject
% 5.52/5.78 thf(fact_3065_prod_Oinject,axiom,
% 5.52/5.78 ! [X1: num,X23: num,Y1: num,Y22: num] :
% 5.52/5.78 ( ( ( product_Pair_num_num @ X1 @ X23 )
% 5.52/5.78 = ( product_Pair_num_num @ Y1 @ Y22 ) )
% 5.52/5.78 = ( ( X1 = Y1 )
% 5.52/5.78 & ( X23 = Y22 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % prod.inject
% 5.52/5.78 thf(fact_3066_prod_Oinject,axiom,
% 5.52/5.78 ! [X1: nat,X23: num,Y1: nat,Y22: num] :
% 5.52/5.78 ( ( ( product_Pair_nat_num @ X1 @ X23 )
% 5.52/5.78 = ( product_Pair_nat_num @ Y1 @ Y22 ) )
% 5.52/5.78 = ( ( X1 = Y1 )
% 5.52/5.78 & ( X23 = Y22 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % prod.inject
% 5.52/5.78 thf(fact_3067_prod_Oinject,axiom,
% 5.52/5.78 ! [X1: nat,X23: nat,Y1: nat,Y22: nat] :
% 5.52/5.78 ( ( ( product_Pair_nat_nat @ X1 @ X23 )
% 5.52/5.78 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 5.52/5.78 = ( ( X1 = Y1 )
% 5.52/5.78 & ( X23 = Y22 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % prod.inject
% 5.52/5.78 thf(fact_3068_prod_Oinject,axiom,
% 5.52/5.78 ! [X1: int,X23: int,Y1: int,Y22: int] :
% 5.52/5.78 ( ( ( product_Pair_int_int @ X1 @ X23 )
% 5.52/5.78 = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 5.52/5.78 = ( ( X1 = Y1 )
% 5.52/5.78 & ( X23 = Y22 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % prod.inject
% 5.52/5.78 thf(fact_3069_old_Oprod_Oinject,axiom,
% 5.52/5.78 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 5.52/5.78 ( ( ( produc6161850002892822231at_nat @ A @ B )
% 5.52/5.78 = ( produc6161850002892822231at_nat @ A5 @ B5 ) )
% 5.52/5.78 = ( ( A = A5 )
% 5.52/5.78 & ( B = B5 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % old.prod.inject
% 5.52/5.78 thf(fact_3070_old_Oprod_Oinject,axiom,
% 5.52/5.78 ! [A: num,B: num,A5: num,B5: num] :
% 5.52/5.78 ( ( ( product_Pair_num_num @ A @ B )
% 5.52/5.78 = ( product_Pair_num_num @ A5 @ B5 ) )
% 5.52/5.78 = ( ( A = A5 )
% 5.52/5.78 & ( B = B5 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % old.prod.inject
% 5.52/5.78 thf(fact_3071_old_Oprod_Oinject,axiom,
% 5.52/5.78 ! [A: nat,B: num,A5: nat,B5: num] :
% 5.52/5.78 ( ( ( product_Pair_nat_num @ A @ B )
% 5.52/5.78 = ( product_Pair_nat_num @ A5 @ B5 ) )
% 5.52/5.78 = ( ( A = A5 )
% 5.52/5.78 & ( B = B5 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % old.prod.inject
% 5.52/5.78 thf(fact_3072_old_Oprod_Oinject,axiom,
% 5.52/5.78 ! [A: nat,B: nat,A5: nat,B5: nat] :
% 5.52/5.78 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.52/5.78 = ( product_Pair_nat_nat @ A5 @ B5 ) )
% 5.52/5.78 = ( ( A = A5 )
% 5.52/5.78 & ( B = B5 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % old.prod.inject
% 5.52/5.78 thf(fact_3073_old_Oprod_Oinject,axiom,
% 5.52/5.78 ! [A: int,B: int,A5: int,B5: int] :
% 5.52/5.78 ( ( ( product_Pair_int_int @ A @ B )
% 5.52/5.78 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.52/5.78 = ( ( A = A5 )
% 5.52/5.78 & ( B = B5 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % old.prod.inject
% 5.52/5.78 thf(fact_3074_mod__mod__trivial,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.52/5.78 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mod_trivial
% 5.52/5.78 thf(fact_3075_mod__mod__trivial,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.52/5.78 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mod_trivial
% 5.52/5.78 thf(fact_3076_mod__0,axiom,
% 5.52/5.78 ! [A: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.52/5.78 = zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % mod_0
% 5.52/5.78 thf(fact_3077_mod__0,axiom,
% 5.52/5.78 ! [A: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.52/5.78 = zero_zero_int ) ).
% 5.52/5.78
% 5.52/5.78 % mod_0
% 5.52/5.78 thf(fact_3078_mod__by__0,axiom,
% 5.52/5.78 ! [A: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 5.52/5.78 = A ) ).
% 5.52/5.78
% 5.52/5.78 % mod_by_0
% 5.52/5.78 thf(fact_3079_mod__by__0,axiom,
% 5.52/5.78 ! [A: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 5.52/5.78 = A ) ).
% 5.52/5.78
% 5.52/5.78 % mod_by_0
% 5.52/5.78 thf(fact_3080_mod__self,axiom,
% 5.52/5.78 ! [A: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ A @ A )
% 5.52/5.78 = zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % mod_self
% 5.52/5.78 thf(fact_3081_mod__self,axiom,
% 5.52/5.78 ! [A: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ A @ A )
% 5.52/5.78 = zero_zero_int ) ).
% 5.52/5.78
% 5.52/5.78 % mod_self
% 5.52/5.78 thf(fact_3082_bits__mod__0,axiom,
% 5.52/5.78 ! [A: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.52/5.78 = zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % bits_mod_0
% 5.52/5.78 thf(fact_3083_bits__mod__0,axiom,
% 5.52/5.78 ! [A: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.52/5.78 = zero_zero_int ) ).
% 5.52/5.78
% 5.52/5.78 % bits_mod_0
% 5.52/5.78 thf(fact_3084_mod__add__self1,axiom,
% 5.52/5.78 ! [B: nat,A: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.52/5.78 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_add_self1
% 5.52/5.78 thf(fact_3085_mod__add__self1,axiom,
% 5.52/5.78 ! [B: int,A: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.52/5.78 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_add_self1
% 5.52/5.78 thf(fact_3086_mod__add__self2,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.52/5.78 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_add_self2
% 5.52/5.78 thf(fact_3087_mod__add__self2,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.52/5.78 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_add_self2
% 5.52/5.78 thf(fact_3088_minus__mod__self2,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.52/5.78 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % minus_mod_self2
% 5.52/5.78 thf(fact_3089_mod__less,axiom,
% 5.52/5.78 ! [M: nat,N: nat] :
% 5.52/5.78 ( ( ord_less_nat @ M @ N )
% 5.52/5.78 => ( ( modulo_modulo_nat @ M @ N )
% 5.52/5.78 = M ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_less
% 5.52/5.78 thf(fact_3090_mod__mult__self2__is__0,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.52/5.78 = zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_self2_is_0
% 5.52/5.78 thf(fact_3091_mod__mult__self2__is__0,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.52/5.78 = zero_zero_int ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_self2_is_0
% 5.52/5.78 thf(fact_3092_mod__mult__self1__is__0,axiom,
% 5.52/5.78 ! [B: nat,A: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.52/5.78 = zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_self1_is_0
% 5.52/5.78 thf(fact_3093_mod__mult__self1__is__0,axiom,
% 5.52/5.78 ! [B: int,A: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.52/5.78 = zero_zero_int ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_self1_is_0
% 5.52/5.78 thf(fact_3094_mod__by__1,axiom,
% 5.52/5.78 ! [A: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.52/5.78 = zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % mod_by_1
% 5.52/5.78 thf(fact_3095_mod__by__1,axiom,
% 5.52/5.78 ! [A: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.52/5.78 = zero_zero_int ) ).
% 5.52/5.78
% 5.52/5.78 % mod_by_1
% 5.52/5.78 thf(fact_3096_bits__mod__by__1,axiom,
% 5.52/5.78 ! [A: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.52/5.78 = zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % bits_mod_by_1
% 5.52/5.78 thf(fact_3097_bits__mod__by__1,axiom,
% 5.52/5.78 ! [A: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.52/5.78 = zero_zero_int ) ).
% 5.52/5.78
% 5.52/5.78 % bits_mod_by_1
% 5.52/5.78 thf(fact_3098_mod__div__trivial,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.52/5.78 = zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % mod_div_trivial
% 5.52/5.78 thf(fact_3099_mod__div__trivial,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.52/5.78 = zero_zero_int ) ).
% 5.52/5.78
% 5.52/5.78 % mod_div_trivial
% 5.52/5.78 thf(fact_3100_bits__mod__div__trivial,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.52/5.78 = zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % bits_mod_div_trivial
% 5.52/5.78 thf(fact_3101_bits__mod__div__trivial,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.52/5.78 = zero_zero_int ) ).
% 5.52/5.78
% 5.52/5.78 % bits_mod_div_trivial
% 5.52/5.78 thf(fact_3102_mod__mult__self1,axiom,
% 5.52/5.78 ! [A: nat,C: nat,B: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.52/5.78 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_self1
% 5.52/5.78 thf(fact_3103_mod__mult__self1,axiom,
% 5.52/5.78 ! [A: int,C: int,B: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.52/5.78 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_self1
% 5.52/5.78 thf(fact_3104_mod__mult__self2,axiom,
% 5.52/5.78 ! [A: nat,B: nat,C: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.52/5.78 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_self2
% 5.52/5.78 thf(fact_3105_mod__mult__self2,axiom,
% 5.52/5.78 ! [A: int,B: int,C: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.52/5.78 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_self2
% 5.52/5.78 thf(fact_3106_mod__mult__self3,axiom,
% 5.52/5.78 ! [C: nat,B: nat,A: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.52/5.78 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_self3
% 5.52/5.78 thf(fact_3107_mod__mult__self3,axiom,
% 5.52/5.78 ! [C: int,B: int,A: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.52/5.78 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_self3
% 5.52/5.78 thf(fact_3108_mod__mult__self4,axiom,
% 5.52/5.78 ! [B: nat,C: nat,A: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.52/5.78 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_self4
% 5.52/5.78 thf(fact_3109_mod__mult__self4,axiom,
% 5.52/5.78 ! [B: int,C: int,A: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.52/5.78 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_self4
% 5.52/5.78 thf(fact_3110_infinite__Icc__iff,axiom,
% 5.52/5.78 ! [A: rat,B: rat] :
% 5.52/5.78 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 5.52/5.78 = ( ord_less_rat @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % infinite_Icc_iff
% 5.52/5.78 thf(fact_3111_infinite__Icc__iff,axiom,
% 5.52/5.78 ! [A: real,B: real] :
% 5.52/5.78 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 5.52/5.78 = ( ord_less_real @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % infinite_Icc_iff
% 5.52/5.78 thf(fact_3112_mod__by__Suc__0,axiom,
% 5.52/5.78 ! [M: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.52/5.78 = zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % mod_by_Suc_0
% 5.52/5.78 thf(fact_3113_Suc__mod__mult__self1,axiom,
% 5.52/5.78 ! [M: nat,K: nat,N: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 5.52/5.78 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.52/5.78
% 5.52/5.78 % Suc_mod_mult_self1
% 5.52/5.78 thf(fact_3114_Suc__mod__mult__self2,axiom,
% 5.52/5.78 ! [M: nat,N: nat,K: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 5.52/5.78 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.52/5.78
% 5.52/5.78 % Suc_mod_mult_self2
% 5.52/5.78 thf(fact_3115_Suc__mod__mult__self3,axiom,
% 5.52/5.78 ! [K: nat,N: nat,M: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 5.52/5.78 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.52/5.78
% 5.52/5.78 % Suc_mod_mult_self3
% 5.52/5.78 thf(fact_3116_Suc__mod__mult__self4,axiom,
% 5.52/5.78 ! [N: nat,K: nat,M: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 5.52/5.78 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.52/5.78
% 5.52/5.78 % Suc_mod_mult_self4
% 5.52/5.78 thf(fact_3117_one__mod__two__eq__one,axiom,
% 5.52/5.78 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.78 = one_one_nat ) ).
% 5.52/5.78
% 5.52/5.78 % one_mod_two_eq_one
% 5.52/5.78 thf(fact_3118_one__mod__two__eq__one,axiom,
% 5.52/5.78 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.78 = one_one_int ) ).
% 5.52/5.78
% 5.52/5.78 % one_mod_two_eq_one
% 5.52/5.78 thf(fact_3119_bits__one__mod__two__eq__one,axiom,
% 5.52/5.78 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.78 = one_one_nat ) ).
% 5.52/5.78
% 5.52/5.78 % bits_one_mod_two_eq_one
% 5.52/5.78 thf(fact_3120_bits__one__mod__two__eq__one,axiom,
% 5.52/5.78 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.78 = one_one_int ) ).
% 5.52/5.78
% 5.52/5.78 % bits_one_mod_two_eq_one
% 5.52/5.78 thf(fact_3121_mod2__Suc__Suc,axiom,
% 5.52/5.78 ! [M: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.78 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod2_Suc_Suc
% 5.52/5.78 thf(fact_3122_Suc__times__numeral__mod__eq,axiom,
% 5.52/5.78 ! [K: num,N: nat] :
% 5.52/5.78 ( ( ( numeral_numeral_nat @ K )
% 5.52/5.78 != one_one_nat )
% 5.52/5.78 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 5.52/5.78 = one_one_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % Suc_times_numeral_mod_eq
% 5.52/5.78 thf(fact_3123_not__mod__2__eq__0__eq__1,axiom,
% 5.52/5.78 ! [A: nat] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.78 != zero_zero_nat )
% 5.52/5.78 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.78 = one_one_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % not_mod_2_eq_0_eq_1
% 5.52/5.78 thf(fact_3124_not__mod__2__eq__0__eq__1,axiom,
% 5.52/5.78 ! [A: int] :
% 5.52/5.78 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.78 != zero_zero_int )
% 5.52/5.78 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.78 = one_one_int ) ) ).
% 5.52/5.78
% 5.52/5.78 % not_mod_2_eq_0_eq_1
% 5.52/5.78 thf(fact_3125_not__mod__2__eq__1__eq__0,axiom,
% 5.52/5.78 ! [A: nat] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.78 != one_one_nat )
% 5.52/5.78 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.78 = zero_zero_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % not_mod_2_eq_1_eq_0
% 5.52/5.78 thf(fact_3126_not__mod__2__eq__1__eq__0,axiom,
% 5.52/5.78 ! [A: int] :
% 5.52/5.78 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.78 != one_one_int )
% 5.52/5.78 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.78 = zero_zero_int ) ) ).
% 5.52/5.78
% 5.52/5.78 % not_mod_2_eq_1_eq_0
% 5.52/5.78 thf(fact_3127_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.52/5.78 ! [N: nat] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.78 != ( suc @ zero_zero_nat ) )
% 5.52/5.78 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.78 = zero_zero_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % not_mod2_eq_Suc_0_eq_0
% 5.52/5.78 thf(fact_3128_add__self__mod__2,axiom,
% 5.52/5.78 ! [M: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.78 = zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % add_self_mod_2
% 5.52/5.78 thf(fact_3129_mod__Suc__eq__mod__add3,axiom,
% 5.52/5.78 ! [M: nat,N: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.52/5.78 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_Suc_eq_mod_add3
% 5.52/5.78 thf(fact_3130_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.52/5.78 ! [M: nat,V: num] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.52/5.78 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % Suc_mod_eq_add3_mod_numeral
% 5.52/5.78 thf(fact_3131_mod2__gr__0,axiom,
% 5.52/5.78 ! [M: nat] :
% 5.52/5.78 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.78 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.78 = one_one_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod2_gr_0
% 5.52/5.78 thf(fact_3132_unique__remainder,axiom,
% 5.52/5.78 ! [A: int,B: int,Q2: int,R: int,Q5: int,R4: int] :
% 5.52/5.78 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.52/5.78 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.52/5.78 => ( R = R4 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % unique_remainder
% 5.52/5.78 thf(fact_3133_unique__quotient,axiom,
% 5.52/5.78 ! [A: int,B: int,Q2: int,R: int,Q5: int,R4: int] :
% 5.52/5.78 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.52/5.78 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.52/5.78 => ( Q2 = Q5 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % unique_quotient
% 5.52/5.78 thf(fact_3134_mod__mult__eq,axiom,
% 5.52/5.78 ! [A: nat,C: nat,B: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.52/5.78 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_eq
% 5.52/5.78 thf(fact_3135_mod__mult__eq,axiom,
% 5.52/5.78 ! [A: int,C: int,B: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.52/5.78 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_eq
% 5.52/5.78 thf(fact_3136_mod__mult__cong,axiom,
% 5.52/5.78 ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ A @ C )
% 5.52/5.78 = ( modulo_modulo_nat @ A5 @ C ) )
% 5.52/5.78 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.52/5.78 = ( modulo_modulo_nat @ B5 @ C ) )
% 5.52/5.78 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.52/5.78 = ( modulo_modulo_nat @ ( times_times_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_cong
% 5.52/5.78 thf(fact_3137_mod__mult__cong,axiom,
% 5.52/5.78 ! [A: int,C: int,A5: int,B: int,B5: int] :
% 5.52/5.78 ( ( ( modulo_modulo_int @ A @ C )
% 5.52/5.78 = ( modulo_modulo_int @ A5 @ C ) )
% 5.52/5.78 => ( ( ( modulo_modulo_int @ B @ C )
% 5.52/5.78 = ( modulo_modulo_int @ B5 @ C ) )
% 5.52/5.78 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.52/5.78 = ( modulo_modulo_int @ ( times_times_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_cong
% 5.52/5.78 thf(fact_3138_mod__mult__mult2,axiom,
% 5.52/5.78 ! [A: nat,C: nat,B: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.52/5.78 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_mult2
% 5.52/5.78 thf(fact_3139_mod__mult__mult2,axiom,
% 5.52/5.78 ! [A: int,C: int,B: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.52/5.78 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_mult2
% 5.52/5.78 thf(fact_3140_mult__mod__right,axiom,
% 5.52/5.78 ! [C: nat,A: nat,B: nat] :
% 5.52/5.78 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.52/5.78 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_mod_right
% 5.52/5.78 thf(fact_3141_mult__mod__right,axiom,
% 5.52/5.78 ! [C: int,A: int,B: int] :
% 5.52/5.78 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.52/5.78 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_mod_right
% 5.52/5.78 thf(fact_3142_mod__mult__left__eq,axiom,
% 5.52/5.78 ! [A: nat,C: nat,B: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.52/5.78 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_left_eq
% 5.52/5.78 thf(fact_3143_mod__mult__left__eq,axiom,
% 5.52/5.78 ! [A: int,C: int,B: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.52/5.78 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_left_eq
% 5.52/5.78 thf(fact_3144_mod__mult__right__eq,axiom,
% 5.52/5.78 ! [A: nat,B: nat,C: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.52/5.78 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_right_eq
% 5.52/5.78 thf(fact_3145_mod__mult__right__eq,axiom,
% 5.52/5.78 ! [A: int,B: int,C: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.52/5.78 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_right_eq
% 5.52/5.78 thf(fact_3146_mod__add__eq,axiom,
% 5.52/5.78 ! [A: nat,C: nat,B: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.52/5.78 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_add_eq
% 5.52/5.78 thf(fact_3147_mod__add__eq,axiom,
% 5.52/5.78 ! [A: int,C: int,B: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.52/5.78 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_add_eq
% 5.52/5.78 thf(fact_3148_mod__add__cong,axiom,
% 5.52/5.78 ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ A @ C )
% 5.52/5.78 = ( modulo_modulo_nat @ A5 @ C ) )
% 5.52/5.78 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.52/5.78 = ( modulo_modulo_nat @ B5 @ C ) )
% 5.52/5.78 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.52/5.78 = ( modulo_modulo_nat @ ( plus_plus_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_add_cong
% 5.52/5.78 thf(fact_3149_mod__add__cong,axiom,
% 5.52/5.78 ! [A: int,C: int,A5: int,B: int,B5: int] :
% 5.52/5.78 ( ( ( modulo_modulo_int @ A @ C )
% 5.52/5.78 = ( modulo_modulo_int @ A5 @ C ) )
% 5.52/5.78 => ( ( ( modulo_modulo_int @ B @ C )
% 5.52/5.78 = ( modulo_modulo_int @ B5 @ C ) )
% 5.52/5.78 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.52/5.78 = ( modulo_modulo_int @ ( plus_plus_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_add_cong
% 5.52/5.78 thf(fact_3150_mod__add__left__eq,axiom,
% 5.52/5.78 ! [A: nat,C: nat,B: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.52/5.78 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_add_left_eq
% 5.52/5.78 thf(fact_3151_mod__add__left__eq,axiom,
% 5.52/5.78 ! [A: int,C: int,B: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.52/5.78 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_add_left_eq
% 5.52/5.78 thf(fact_3152_mod__add__right__eq,axiom,
% 5.52/5.78 ! [A: nat,B: nat,C: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.52/5.78 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_add_right_eq
% 5.52/5.78 thf(fact_3153_mod__add__right__eq,axiom,
% 5.52/5.78 ! [A: int,B: int,C: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.52/5.78 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_add_right_eq
% 5.52/5.78 thf(fact_3154_mod__diff__eq,axiom,
% 5.52/5.78 ! [A: int,C: int,B: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.52/5.78 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_diff_eq
% 5.52/5.78 thf(fact_3155_mod__diff__cong,axiom,
% 5.52/5.78 ! [A: int,C: int,A5: int,B: int,B5: int] :
% 5.52/5.78 ( ( ( modulo_modulo_int @ A @ C )
% 5.52/5.78 = ( modulo_modulo_int @ A5 @ C ) )
% 5.52/5.78 => ( ( ( modulo_modulo_int @ B @ C )
% 5.52/5.78 = ( modulo_modulo_int @ B5 @ C ) )
% 5.52/5.78 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.52/5.78 = ( modulo_modulo_int @ ( minus_minus_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_diff_cong
% 5.52/5.78 thf(fact_3156_mod__diff__left__eq,axiom,
% 5.52/5.78 ! [A: int,C: int,B: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.52/5.78 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_diff_left_eq
% 5.52/5.78 thf(fact_3157_mod__diff__right__eq,axiom,
% 5.52/5.78 ! [A: int,B: int,C: int] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.52/5.78 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_diff_right_eq
% 5.52/5.78 thf(fact_3158_power__mod,axiom,
% 5.52/5.78 ! [A: nat,B: nat,N: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 5.52/5.78 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % power_mod
% 5.52/5.78 thf(fact_3159_power__mod,axiom,
% 5.52/5.78 ! [A: int,B: int,N: nat] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 5.52/5.78 = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % power_mod
% 5.52/5.78 thf(fact_3160_mod__Suc__eq,axiom,
% 5.52/5.78 ! [M: nat,N: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 5.52/5.78 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_Suc_eq
% 5.52/5.78 thf(fact_3161_mod__Suc__Suc__eq,axiom,
% 5.52/5.78 ! [M: nat,N: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 5.52/5.78 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_Suc_Suc_eq
% 5.52/5.78 thf(fact_3162_mod__less__eq__dividend,axiom,
% 5.52/5.78 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 5.52/5.78
% 5.52/5.78 % mod_less_eq_dividend
% 5.52/5.78 thf(fact_3163_finite__nat__set__iff__bounded,axiom,
% 5.52/5.78 ( finite_finite_nat
% 5.52/5.78 = ( ^ [N6: set_nat] :
% 5.52/5.78 ? [M3: nat] :
% 5.52/5.78 ! [X: nat] :
% 5.52/5.78 ( ( member_nat @ X @ N6 )
% 5.52/5.78 => ( ord_less_nat @ X @ M3 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_nat_set_iff_bounded
% 5.52/5.78 thf(fact_3164_bounded__nat__set__is__finite,axiom,
% 5.52/5.78 ! [N4: set_nat,N: nat] :
% 5.52/5.78 ( ! [X4: nat] :
% 5.52/5.78 ( ( member_nat @ X4 @ N4 )
% 5.52/5.78 => ( ord_less_nat @ X4 @ N ) )
% 5.52/5.78 => ( finite_finite_nat @ N4 ) ) ).
% 5.52/5.78
% 5.52/5.78 % bounded_nat_set_is_finite
% 5.52/5.78 thf(fact_3165_finite__nat__set__iff__bounded__le,axiom,
% 5.52/5.78 ( finite_finite_nat
% 5.52/5.78 = ( ^ [N6: set_nat] :
% 5.52/5.78 ? [M3: nat] :
% 5.52/5.78 ! [X: nat] :
% 5.52/5.78 ( ( member_nat @ X @ N6 )
% 5.52/5.78 => ( ord_less_eq_nat @ X @ M3 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_nat_set_iff_bounded_le
% 5.52/5.78 thf(fact_3166_finite__M__bounded__by__nat,axiom,
% 5.52/5.78 ! [P: nat > $o,I: nat] :
% 5.52/5.78 ( finite_finite_nat
% 5.52/5.78 @ ( collect_nat
% 5.52/5.78 @ ^ [K2: nat] :
% 5.52/5.78 ( ( P @ K2 )
% 5.52/5.78 & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_M_bounded_by_nat
% 5.52/5.78 thf(fact_3167_finite__less__ub,axiom,
% 5.52/5.78 ! [F: nat > nat,U: nat] :
% 5.52/5.78 ( ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( F @ N2 ) )
% 5.52/5.78 => ( finite_finite_nat
% 5.52/5.78 @ ( collect_nat
% 5.52/5.78 @ ^ [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ U ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_less_ub
% 5.52/5.78 thf(fact_3168_finite__lists__length__eq,axiom,
% 5.52/5.78 ! [A2: set_int,N: nat] :
% 5.52/5.78 ( ( finite_finite_int @ A2 )
% 5.52/5.78 => ( finite3922522038869484883st_int
% 5.52/5.78 @ ( collect_list_int
% 5.52/5.78 @ ^ [Xs: list_int] :
% 5.52/5.78 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.52/5.78 & ( ( size_size_list_int @ Xs )
% 5.52/5.78 = N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_lists_length_eq
% 5.52/5.78 thf(fact_3169_finite__lists__length__eq,axiom,
% 5.52/5.78 ! [A2: set_complex,N: nat] :
% 5.52/5.78 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.78 => ( finite8712137658972009173omplex
% 5.52/5.78 @ ( collect_list_complex
% 5.52/5.78 @ ^ [Xs: list_complex] :
% 5.52/5.78 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.52/5.78 & ( ( size_s3451745648224563538omplex @ Xs )
% 5.52/5.78 = N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_lists_length_eq
% 5.52/5.78 thf(fact_3170_finite__lists__length__eq,axiom,
% 5.52/5.78 ! [A2: set_Extended_enat,N: nat] :
% 5.52/5.78 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.78 => ( finite1862508098717546133d_enat
% 5.52/5.78 @ ( collec8433460942617342167d_enat
% 5.52/5.78 @ ^ [Xs: list_Extended_enat] :
% 5.52/5.78 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs ) @ A2 )
% 5.52/5.78 & ( ( size_s3941691890525107288d_enat @ Xs )
% 5.52/5.78 = N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_lists_length_eq
% 5.52/5.78 thf(fact_3171_finite__lists__length__eq,axiom,
% 5.52/5.78 ! [A2: set_VEBT_VEBT,N: nat] :
% 5.52/5.78 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.78 => ( finite3004134309566078307T_VEBT
% 5.52/5.78 @ ( collec5608196760682091941T_VEBT
% 5.52/5.78 @ ^ [Xs: list_VEBT_VEBT] :
% 5.52/5.78 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.52/5.78 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.52/5.78 = N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_lists_length_eq
% 5.52/5.78 thf(fact_3172_finite__lists__length__eq,axiom,
% 5.52/5.78 ! [A2: set_o,N: nat] :
% 5.52/5.78 ( ( finite_finite_o @ A2 )
% 5.52/5.78 => ( finite_finite_list_o
% 5.52/5.78 @ ( collect_list_o
% 5.52/5.78 @ ^ [Xs: list_o] :
% 5.52/5.78 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.52/5.78 & ( ( size_size_list_o @ Xs )
% 5.52/5.78 = N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_lists_length_eq
% 5.52/5.78 thf(fact_3173_finite__lists__length__eq,axiom,
% 5.52/5.78 ! [A2: set_nat,N: nat] :
% 5.52/5.78 ( ( finite_finite_nat @ A2 )
% 5.52/5.78 => ( finite8100373058378681591st_nat
% 5.52/5.78 @ ( collect_list_nat
% 5.52/5.78 @ ^ [Xs: list_nat] :
% 5.52/5.78 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.52/5.78 & ( ( size_size_list_nat @ Xs )
% 5.52/5.78 = N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_lists_length_eq
% 5.52/5.78 thf(fact_3174_eucl__rel__int__by0,axiom,
% 5.52/5.78 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.52/5.78
% 5.52/5.78 % eucl_rel_int_by0
% 5.52/5.78 thf(fact_3175_div__int__unique,axiom,
% 5.52/5.78 ! [K: int,L: int,Q2: int,R: int] :
% 5.52/5.78 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.52/5.78 => ( ( divide_divide_int @ K @ L )
% 5.52/5.78 = Q2 ) ) ).
% 5.52/5.78
% 5.52/5.78 % div_int_unique
% 5.52/5.78 thf(fact_3176_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.78 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.52/5.78
% 5.52/5.78 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.52/5.78 thf(fact_3177_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.78 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.52/5.78
% 5.52/5.78 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.52/5.78 thf(fact_3178_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.52/5.78 ! [B: nat,A: nat] :
% 5.52/5.78 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.78 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.52/5.78 thf(fact_3179_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.52/5.78 ! [B: int,A: int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.78 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.52/5.78 thf(fact_3180_cong__exp__iff__simps_I9_J,axiom,
% 5.52/5.78 ! [M: num,Q2: num,N: num] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.52/5.78 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.52/5.78 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(9)
% 5.52/5.78 thf(fact_3181_cong__exp__iff__simps_I9_J,axiom,
% 5.52/5.78 ! [M: num,Q2: num,N: num] :
% 5.52/5.78 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.52/5.78 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.52/5.78 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(9)
% 5.52/5.78 thf(fact_3182_mod__eq__self__iff__div__eq__0,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ A @ B )
% 5.52/5.78 = A )
% 5.52/5.78 = ( ( divide_divide_nat @ A @ B )
% 5.52/5.78 = zero_zero_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_eq_self_iff_div_eq_0
% 5.52/5.78 thf(fact_3183_mod__eq__self__iff__div__eq__0,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( ( modulo_modulo_int @ A @ B )
% 5.52/5.78 = A )
% 5.52/5.78 = ( ( divide_divide_int @ A @ B )
% 5.52/5.78 = zero_zero_int ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_eq_self_iff_div_eq_0
% 5.52/5.78 thf(fact_3184_cong__exp__iff__simps_I4_J,axiom,
% 5.52/5.78 ! [M: num,N: num] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.52/5.78 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(4)
% 5.52/5.78 thf(fact_3185_cong__exp__iff__simps_I4_J,axiom,
% 5.52/5.78 ! [M: num,N: num] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.52/5.78 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(4)
% 5.52/5.78 thf(fact_3186_mod__eqE,axiom,
% 5.52/5.78 ! [A: int,C: int,B: int] :
% 5.52/5.78 ( ( ( modulo_modulo_int @ A @ C )
% 5.52/5.78 = ( modulo_modulo_int @ B @ C ) )
% 5.52/5.78 => ~ ! [D3: int] :
% 5.52/5.78 ( B
% 5.52/5.78 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_eqE
% 5.52/5.78 thf(fact_3187_div__add1__eq,axiom,
% 5.52/5.78 ! [A: nat,B: nat,C: nat] :
% 5.52/5.78 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.52/5.78 = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % div_add1_eq
% 5.52/5.78 thf(fact_3188_div__add1__eq,axiom,
% 5.52/5.78 ! [A: int,B: int,C: int] :
% 5.52/5.78 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.52/5.78 = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % div_add1_eq
% 5.52/5.78 thf(fact_3189_mod__Suc,axiom,
% 5.52/5.78 ! [M: nat,N: nat] :
% 5.52/5.78 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.52/5.78 = N )
% 5.52/5.78 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.52/5.78 = zero_zero_nat ) )
% 5.52/5.78 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.52/5.78 != N )
% 5.52/5.78 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.52/5.78 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_Suc
% 5.52/5.78 thf(fact_3190_mod__induct,axiom,
% 5.52/5.78 ! [P: nat > $o,N: nat,P6: nat,M: nat] :
% 5.52/5.78 ( ( P @ N )
% 5.52/5.78 => ( ( ord_less_nat @ N @ P6 )
% 5.52/5.78 => ( ( ord_less_nat @ M @ P6 )
% 5.52/5.78 => ( ! [N2: nat] :
% 5.52/5.78 ( ( ord_less_nat @ N2 @ P6 )
% 5.52/5.78 => ( ( P @ N2 )
% 5.52/5.78 => ( P @ ( modulo_modulo_nat @ ( suc @ N2 ) @ P6 ) ) ) )
% 5.52/5.78 => ( P @ M ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_induct
% 5.52/5.78 thf(fact_3191_mod__less__divisor,axiom,
% 5.52/5.78 ! [N: nat,M: nat] :
% 5.52/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.78 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_less_divisor
% 5.52/5.78 thf(fact_3192_mod__Suc__le__divisor,axiom,
% 5.52/5.78 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 5.52/5.78
% 5.52/5.78 % mod_Suc_le_divisor
% 5.52/5.78 thf(fact_3193_mod__eq__0D,axiom,
% 5.52/5.78 ! [M: nat,D2: nat] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ M @ D2 )
% 5.52/5.78 = zero_zero_nat )
% 5.52/5.78 => ? [Q3: nat] :
% 5.52/5.78 ( M
% 5.52/5.78 = ( times_times_nat @ D2 @ Q3 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_eq_0D
% 5.52/5.78 thf(fact_3194_mod__geq,axiom,
% 5.52/5.78 ! [M: nat,N: nat] :
% 5.52/5.78 ( ~ ( ord_less_nat @ M @ N )
% 5.52/5.78 => ( ( modulo_modulo_nat @ M @ N )
% 5.52/5.78 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_geq
% 5.52/5.78 thf(fact_3195_mod__if,axiom,
% 5.52/5.78 ( modulo_modulo_nat
% 5.52/5.78 = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N3 ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N3 ) @ N3 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_if
% 5.52/5.78 thf(fact_3196_le__mod__geq,axiom,
% 5.52/5.78 ! [N: nat,M: nat] :
% 5.52/5.78 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.78 => ( ( modulo_modulo_nat @ M @ N )
% 5.52/5.78 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % le_mod_geq
% 5.52/5.78 thf(fact_3197_nat__mod__eq__iff,axiom,
% 5.52/5.78 ! [X2: nat,N: nat,Y2: nat] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ X2 @ N )
% 5.52/5.78 = ( modulo_modulo_nat @ Y2 @ N ) )
% 5.52/5.78 = ( ? [Q1: nat,Q22: nat] :
% 5.52/5.78 ( ( plus_plus_nat @ X2 @ ( times_times_nat @ N @ Q1 ) )
% 5.52/5.78 = ( plus_plus_nat @ Y2 @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % nat_mod_eq_iff
% 5.52/5.78 thf(fact_3198_infinite__Icc,axiom,
% 5.52/5.78 ! [A: rat,B: rat] :
% 5.52/5.78 ( ( ord_less_rat @ A @ B )
% 5.52/5.78 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % infinite_Icc
% 5.52/5.78 thf(fact_3199_infinite__Icc,axiom,
% 5.52/5.78 ! [A: real,B: real] :
% 5.52/5.78 ( ( ord_less_real @ A @ B )
% 5.52/5.78 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % infinite_Icc
% 5.52/5.78 thf(fact_3200_finite__lists__length__le,axiom,
% 5.52/5.78 ! [A2: set_int,N: nat] :
% 5.52/5.78 ( ( finite_finite_int @ A2 )
% 5.52/5.78 => ( finite3922522038869484883st_int
% 5.52/5.78 @ ( collect_list_int
% 5.52/5.78 @ ^ [Xs: list_int] :
% 5.52/5.78 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.52/5.78 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_lists_length_le
% 5.52/5.78 thf(fact_3201_finite__lists__length__le,axiom,
% 5.52/5.78 ! [A2: set_complex,N: nat] :
% 5.52/5.78 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.78 => ( finite8712137658972009173omplex
% 5.52/5.78 @ ( collect_list_complex
% 5.52/5.78 @ ^ [Xs: list_complex] :
% 5.52/5.78 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.52/5.78 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_lists_length_le
% 5.52/5.78 thf(fact_3202_finite__lists__length__le,axiom,
% 5.52/5.78 ! [A2: set_Extended_enat,N: nat] :
% 5.52/5.78 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.78 => ( finite1862508098717546133d_enat
% 5.52/5.78 @ ( collec8433460942617342167d_enat
% 5.52/5.78 @ ^ [Xs: list_Extended_enat] :
% 5.52/5.78 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs ) @ A2 )
% 5.52/5.78 & ( ord_less_eq_nat @ ( size_s3941691890525107288d_enat @ Xs ) @ N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_lists_length_le
% 5.52/5.78 thf(fact_3203_finite__lists__length__le,axiom,
% 5.52/5.78 ! [A2: set_VEBT_VEBT,N: nat] :
% 5.52/5.78 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.78 => ( finite3004134309566078307T_VEBT
% 5.52/5.78 @ ( collec5608196760682091941T_VEBT
% 5.52/5.78 @ ^ [Xs: list_VEBT_VEBT] :
% 5.52/5.78 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.52/5.78 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_lists_length_le
% 5.52/5.78 thf(fact_3204_finite__lists__length__le,axiom,
% 5.52/5.78 ! [A2: set_o,N: nat] :
% 5.52/5.78 ( ( finite_finite_o @ A2 )
% 5.52/5.78 => ( finite_finite_list_o
% 5.52/5.78 @ ( collect_list_o
% 5.52/5.78 @ ^ [Xs: list_o] :
% 5.52/5.78 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.52/5.78 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_lists_length_le
% 5.52/5.78 thf(fact_3205_finite__lists__length__le,axiom,
% 5.52/5.78 ! [A2: set_nat,N: nat] :
% 5.52/5.78 ( ( finite_finite_nat @ A2 )
% 5.52/5.78 => ( finite8100373058378681591st_nat
% 5.52/5.78 @ ( collect_list_nat
% 5.52/5.78 @ ^ [Xs: list_nat] :
% 5.52/5.78 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.52/5.78 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % finite_lists_length_le
% 5.52/5.78 thf(fact_3206_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.78 => ( ( ord_less_nat @ A @ B )
% 5.52/5.78 => ( ( modulo_modulo_nat @ A @ B )
% 5.52/5.78 = A ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % unique_euclidean_semiring_numeral_class.mod_less
% 5.52/5.78 thf(fact_3207_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.78 => ( ( ord_less_int @ A @ B )
% 5.52/5.78 => ( ( modulo_modulo_int @ A @ B )
% 5.52/5.78 = A ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % unique_euclidean_semiring_numeral_class.mod_less
% 5.52/5.78 thf(fact_3208_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.52/5.78 ! [B: nat,A: nat] :
% 5.52/5.78 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.78 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.52/5.78 thf(fact_3209_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.52/5.78 ! [B: int,A: int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.78 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.52/5.78 thf(fact_3210_cong__exp__iff__simps_I2_J,axiom,
% 5.52/5.78 ! [N: num,Q2: num] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 = zero_zero_nat )
% 5.52/5.78 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.52/5.78 = zero_zero_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(2)
% 5.52/5.78 thf(fact_3211_cong__exp__iff__simps_I2_J,axiom,
% 5.52/5.78 ! [N: num,Q2: num] :
% 5.52/5.78 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 = zero_zero_int )
% 5.52/5.78 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.52/5.78 = zero_zero_int ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(2)
% 5.52/5.78 thf(fact_3212_cong__exp__iff__simps_I1_J,axiom,
% 5.52/5.78 ! [N: num] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.52/5.78 = zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(1)
% 5.52/5.78 thf(fact_3213_cong__exp__iff__simps_I1_J,axiom,
% 5.52/5.78 ! [N: num] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.52/5.78 = zero_zero_int ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(1)
% 5.52/5.78 thf(fact_3214_cong__exp__iff__simps_I8_J,axiom,
% 5.52/5.78 ! [M: num,Q2: num] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(8)
% 5.52/5.78 thf(fact_3215_cong__exp__iff__simps_I8_J,axiom,
% 5.52/5.78 ! [M: num,Q2: num] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(8)
% 5.52/5.78 thf(fact_3216_cong__exp__iff__simps_I6_J,axiom,
% 5.52/5.78 ! [Q2: num,N: num] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(6)
% 5.52/5.78 thf(fact_3217_cong__exp__iff__simps_I6_J,axiom,
% 5.52/5.78 ! [Q2: num,N: num] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(6)
% 5.52/5.78 thf(fact_3218_div__mult1__eq,axiom,
% 5.52/5.78 ! [A: nat,B: nat,C: nat] :
% 5.52/5.78 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.52/5.78 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % div_mult1_eq
% 5.52/5.78 thf(fact_3219_div__mult1__eq,axiom,
% 5.52/5.78 ! [A: int,B: int,C: int] :
% 5.52/5.78 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.52/5.78 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % div_mult1_eq
% 5.52/5.78 thf(fact_3220_cancel__div__mod__rules_I2_J,axiom,
% 5.52/5.78 ! [B: nat,A: nat,C: nat] :
% 5.52/5.78 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.52/5.78 = ( plus_plus_nat @ A @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % cancel_div_mod_rules(2)
% 5.52/5.78 thf(fact_3221_cancel__div__mod__rules_I2_J,axiom,
% 5.52/5.78 ! [B: int,A: int,C: int] :
% 5.52/5.78 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.52/5.78 = ( plus_plus_int @ A @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % cancel_div_mod_rules(2)
% 5.52/5.78 thf(fact_3222_cancel__div__mod__rules_I1_J,axiom,
% 5.52/5.78 ! [A: nat,B: nat,C: nat] :
% 5.52/5.78 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.52/5.78 = ( plus_plus_nat @ A @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % cancel_div_mod_rules(1)
% 5.52/5.78 thf(fact_3223_cancel__div__mod__rules_I1_J,axiom,
% 5.52/5.78 ! [A: int,B: int,C: int] :
% 5.52/5.78 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.52/5.78 = ( plus_plus_int @ A @ C ) ) ).
% 5.52/5.78
% 5.52/5.78 % cancel_div_mod_rules(1)
% 5.52/5.78 thf(fact_3224_mod__div__decomp,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( A
% 5.52/5.78 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_div_decomp
% 5.52/5.78 thf(fact_3225_mod__div__decomp,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( A
% 5.52/5.78 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_div_decomp
% 5.52/5.78 thf(fact_3226_div__mult__mod__eq,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.52/5.78 = A ) ).
% 5.52/5.78
% 5.52/5.78 % div_mult_mod_eq
% 5.52/5.78 thf(fact_3227_div__mult__mod__eq,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.52/5.78 = A ) ).
% 5.52/5.78
% 5.52/5.78 % div_mult_mod_eq
% 5.52/5.78 thf(fact_3228_mod__div__mult__eq,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.52/5.78 = A ) ).
% 5.52/5.78
% 5.52/5.78 % mod_div_mult_eq
% 5.52/5.78 thf(fact_3229_mod__div__mult__eq,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.52/5.78 = A ) ).
% 5.52/5.78
% 5.52/5.78 % mod_div_mult_eq
% 5.52/5.78 thf(fact_3230_mod__mult__div__eq,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.52/5.78 = A ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_div_eq
% 5.52/5.78 thf(fact_3231_mod__mult__div__eq,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.52/5.78 = A ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult_div_eq
% 5.52/5.78 thf(fact_3232_mult__div__mod__eq,axiom,
% 5.52/5.78 ! [B: nat,A: nat] :
% 5.52/5.78 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.52/5.78 = A ) ).
% 5.52/5.78
% 5.52/5.78 % mult_div_mod_eq
% 5.52/5.78 thf(fact_3233_mult__div__mod__eq,axiom,
% 5.52/5.78 ! [B: int,A: int] :
% 5.52/5.78 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.52/5.78 = A ) ).
% 5.52/5.78
% 5.52/5.78 % mult_div_mod_eq
% 5.52/5.78 thf(fact_3234_minus__mult__div__eq__mod,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.52/5.78 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % minus_mult_div_eq_mod
% 5.52/5.78 thf(fact_3235_minus__mult__div__eq__mod,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.52/5.78 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % minus_mult_div_eq_mod
% 5.52/5.78 thf(fact_3236_minus__mod__eq__mult__div,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.52/5.78 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minus_mod_eq_mult_div
% 5.52/5.78 thf(fact_3237_minus__mod__eq__mult__div,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.52/5.78 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % minus_mod_eq_mult_div
% 5.52/5.78 thf(fact_3238_minus__mod__eq__div__mult,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.52/5.78 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % minus_mod_eq_div_mult
% 5.52/5.78 thf(fact_3239_minus__mod__eq__div__mult,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.52/5.78 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % minus_mod_eq_div_mult
% 5.52/5.78 thf(fact_3240_minus__div__mult__eq__mod,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.52/5.78 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % minus_div_mult_eq_mod
% 5.52/5.78 thf(fact_3241_minus__div__mult__eq__mod,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.52/5.78 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.52/5.78
% 5.52/5.78 % minus_div_mult_eq_mod
% 5.52/5.78 thf(fact_3242_cong__exp__iff__simps_I13_J,axiom,
% 5.52/5.78 ! [M: num,Q2: num,N: num] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.52/5.78 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.52/5.78 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(13)
% 5.52/5.78 thf(fact_3243_cong__exp__iff__simps_I13_J,axiom,
% 5.52/5.78 ! [M: num,Q2: num,N: num] :
% 5.52/5.78 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.52/5.78 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.52/5.78 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(13)
% 5.52/5.78 thf(fact_3244_cong__exp__iff__simps_I12_J,axiom,
% 5.52/5.78 ! [M: num,Q2: num,N: num] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(12)
% 5.52/5.78 thf(fact_3245_cong__exp__iff__simps_I12_J,axiom,
% 5.52/5.78 ! [M: num,Q2: num,N: num] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(12)
% 5.52/5.78 thf(fact_3246_cong__exp__iff__simps_I10_J,axiom,
% 5.52/5.78 ! [M: num,Q2: num,N: num] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(10)
% 5.52/5.78 thf(fact_3247_cong__exp__iff__simps_I10_J,axiom,
% 5.52/5.78 ! [M: num,Q2: num,N: num] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(10)
% 5.52/5.78 thf(fact_3248_mod__le__divisor,axiom,
% 5.52/5.78 ! [N: nat,M: nat] :
% 5.52/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.78 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_le_divisor
% 5.52/5.78 thf(fact_3249_mod__eq__nat1E,axiom,
% 5.52/5.78 ! [M: nat,Q2: nat,N: nat] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.52/5.78 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.52/5.78 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.78 => ~ ! [S2: nat] :
% 5.52/5.78 ( M
% 5.52/5.78 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S2 ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_eq_nat1E
% 5.52/5.78 thf(fact_3250_mod__eq__nat2E,axiom,
% 5.52/5.78 ! [M: nat,Q2: nat,N: nat] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.52/5.78 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.52/5.78 => ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.78 => ~ ! [S2: nat] :
% 5.52/5.78 ( N
% 5.52/5.78 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S2 ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_eq_nat2E
% 5.52/5.78 thf(fact_3251_nat__mod__eq__lemma,axiom,
% 5.52/5.78 ! [X2: nat,N: nat,Y2: nat] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ X2 @ N )
% 5.52/5.78 = ( modulo_modulo_nat @ Y2 @ N ) )
% 5.52/5.78 => ( ( ord_less_eq_nat @ Y2 @ X2 )
% 5.52/5.78 => ? [Q3: nat] :
% 5.52/5.78 ( X2
% 5.52/5.78 = ( plus_plus_nat @ Y2 @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % nat_mod_eq_lemma
% 5.52/5.78 thf(fact_3252_eucl__rel__int__dividesI,axiom,
% 5.52/5.78 ! [L: int,K: int,Q2: int] :
% 5.52/5.78 ( ( L != zero_zero_int )
% 5.52/5.78 => ( ( K
% 5.52/5.78 = ( times_times_int @ Q2 @ L ) )
% 5.52/5.78 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % eucl_rel_int_dividesI
% 5.52/5.78 thf(fact_3253_mod__mult2__eq,axiom,
% 5.52/5.78 ! [M: nat,N: nat,Q2: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.52/5.78 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_mult2_eq
% 5.52/5.78 thf(fact_3254_divmod_H__nat__def,axiom,
% 5.52/5.78 ( unique5055182867167087721od_nat
% 5.52/5.78 = ( ^ [M3: num,N3: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N3 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N3 ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod'_nat_def
% 5.52/5.78 thf(fact_3255_modulo__nat__def,axiom,
% 5.52/5.78 ( modulo_modulo_nat
% 5.52/5.78 = ( ^ [M3: nat,N3: nat] : ( minus_minus_nat @ M3 @ ( times_times_nat @ ( divide_divide_nat @ M3 @ N3 ) @ N3 ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % modulo_nat_def
% 5.52/5.78 thf(fact_3256_old_Oprod_Oexhaust,axiom,
% 5.52/5.78 ! [Y2: produc859450856879609959at_nat] :
% 5.52/5.78 ~ ! [A3: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.52/5.78 ( Y2
% 5.52/5.78 != ( produc6161850002892822231at_nat @ A3 @ B2 ) ) ).
% 5.52/5.78
% 5.52/5.78 % old.prod.exhaust
% 5.52/5.78 thf(fact_3257_old_Oprod_Oexhaust,axiom,
% 5.52/5.78 ! [Y2: product_prod_num_num] :
% 5.52/5.78 ~ ! [A3: num,B2: num] :
% 5.52/5.78 ( Y2
% 5.52/5.78 != ( product_Pair_num_num @ A3 @ B2 ) ) ).
% 5.52/5.78
% 5.52/5.78 % old.prod.exhaust
% 5.52/5.78 thf(fact_3258_old_Oprod_Oexhaust,axiom,
% 5.52/5.78 ! [Y2: product_prod_nat_num] :
% 5.52/5.78 ~ ! [A3: nat,B2: num] :
% 5.52/5.78 ( Y2
% 5.52/5.78 != ( product_Pair_nat_num @ A3 @ B2 ) ) ).
% 5.52/5.78
% 5.52/5.78 % old.prod.exhaust
% 5.52/5.78 thf(fact_3259_old_Oprod_Oexhaust,axiom,
% 5.52/5.78 ! [Y2: product_prod_nat_nat] :
% 5.52/5.78 ~ ! [A3: nat,B2: nat] :
% 5.52/5.78 ( Y2
% 5.52/5.78 != ( product_Pair_nat_nat @ A3 @ B2 ) ) ).
% 5.52/5.78
% 5.52/5.78 % old.prod.exhaust
% 5.52/5.78 thf(fact_3260_old_Oprod_Oexhaust,axiom,
% 5.52/5.78 ! [Y2: product_prod_int_int] :
% 5.52/5.78 ~ ! [A3: int,B2: int] :
% 5.52/5.78 ( Y2
% 5.52/5.78 != ( product_Pair_int_int @ A3 @ B2 ) ) ).
% 5.52/5.78
% 5.52/5.78 % old.prod.exhaust
% 5.52/5.78 thf(fact_3261_surj__pair,axiom,
% 5.52/5.78 ! [P6: produc859450856879609959at_nat] :
% 5.52/5.78 ? [X4: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.52/5.78 ( P6
% 5.52/5.78 = ( produc6161850002892822231at_nat @ X4 @ Y3 ) ) ).
% 5.52/5.78
% 5.52/5.78 % surj_pair
% 5.52/5.78 thf(fact_3262_surj__pair,axiom,
% 5.52/5.78 ! [P6: product_prod_num_num] :
% 5.52/5.78 ? [X4: num,Y3: num] :
% 5.52/5.78 ( P6
% 5.52/5.78 = ( product_Pair_num_num @ X4 @ Y3 ) ) ).
% 5.52/5.78
% 5.52/5.78 % surj_pair
% 5.52/5.78 thf(fact_3263_surj__pair,axiom,
% 5.52/5.78 ! [P6: product_prod_nat_num] :
% 5.52/5.78 ? [X4: nat,Y3: num] :
% 5.52/5.78 ( P6
% 5.52/5.78 = ( product_Pair_nat_num @ X4 @ Y3 ) ) ).
% 5.52/5.78
% 5.52/5.78 % surj_pair
% 5.52/5.78 thf(fact_3264_surj__pair,axiom,
% 5.52/5.78 ! [P6: product_prod_nat_nat] :
% 5.52/5.78 ? [X4: nat,Y3: nat] :
% 5.52/5.78 ( P6
% 5.52/5.78 = ( product_Pair_nat_nat @ X4 @ Y3 ) ) ).
% 5.52/5.78
% 5.52/5.78 % surj_pair
% 5.52/5.78 thf(fact_3265_surj__pair,axiom,
% 5.52/5.78 ! [P6: product_prod_int_int] :
% 5.52/5.78 ? [X4: int,Y3: int] :
% 5.52/5.78 ( P6
% 5.52/5.78 = ( product_Pair_int_int @ X4 @ Y3 ) ) ).
% 5.52/5.78
% 5.52/5.78 % surj_pair
% 5.52/5.78 thf(fact_3266_prod__cases,axiom,
% 5.52/5.78 ! [P: produc859450856879609959at_nat > $o,P6: produc859450856879609959at_nat] :
% 5.52/5.78 ( ! [A3: product_prod_nat_nat,B2: product_prod_nat_nat] : ( P @ ( produc6161850002892822231at_nat @ A3 @ B2 ) )
% 5.52/5.78 => ( P @ P6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % prod_cases
% 5.52/5.78 thf(fact_3267_prod__cases,axiom,
% 5.52/5.78 ! [P: product_prod_num_num > $o,P6: product_prod_num_num] :
% 5.52/5.78 ( ! [A3: num,B2: num] : ( P @ ( product_Pair_num_num @ A3 @ B2 ) )
% 5.52/5.78 => ( P @ P6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % prod_cases
% 5.52/5.78 thf(fact_3268_prod__cases,axiom,
% 5.52/5.78 ! [P: product_prod_nat_num > $o,P6: product_prod_nat_num] :
% 5.52/5.78 ( ! [A3: nat,B2: num] : ( P @ ( product_Pair_nat_num @ A3 @ B2 ) )
% 5.52/5.78 => ( P @ P6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % prod_cases
% 5.52/5.78 thf(fact_3269_prod__cases,axiom,
% 5.52/5.78 ! [P: product_prod_nat_nat > $o,P6: product_prod_nat_nat] :
% 5.52/5.78 ( ! [A3: nat,B2: nat] : ( P @ ( product_Pair_nat_nat @ A3 @ B2 ) )
% 5.52/5.78 => ( P @ P6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % prod_cases
% 5.52/5.78 thf(fact_3270_prod__cases,axiom,
% 5.52/5.78 ! [P: product_prod_int_int > $o,P6: product_prod_int_int] :
% 5.52/5.78 ( ! [A3: int,B2: int] : ( P @ ( product_Pair_int_int @ A3 @ B2 ) )
% 5.52/5.78 => ( P @ P6 ) ) ).
% 5.52/5.78
% 5.52/5.78 % prod_cases
% 5.52/5.78 thf(fact_3271_Pair__inject,axiom,
% 5.52/5.78 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 5.52/5.78 ( ( ( produc6161850002892822231at_nat @ A @ B )
% 5.52/5.78 = ( produc6161850002892822231at_nat @ A5 @ B5 ) )
% 5.52/5.78 => ~ ( ( A = A5 )
% 5.52/5.78 => ( B != B5 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % Pair_inject
% 5.52/5.78 thf(fact_3272_Pair__inject,axiom,
% 5.52/5.78 ! [A: num,B: num,A5: num,B5: num] :
% 5.52/5.78 ( ( ( product_Pair_num_num @ A @ B )
% 5.52/5.78 = ( product_Pair_num_num @ A5 @ B5 ) )
% 5.52/5.78 => ~ ( ( A = A5 )
% 5.52/5.78 => ( B != B5 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % Pair_inject
% 5.52/5.78 thf(fact_3273_Pair__inject,axiom,
% 5.52/5.78 ! [A: nat,B: num,A5: nat,B5: num] :
% 5.52/5.78 ( ( ( product_Pair_nat_num @ A @ B )
% 5.52/5.78 = ( product_Pair_nat_num @ A5 @ B5 ) )
% 5.52/5.78 => ~ ( ( A = A5 )
% 5.52/5.78 => ( B != B5 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % Pair_inject
% 5.52/5.78 thf(fact_3274_Pair__inject,axiom,
% 5.52/5.78 ! [A: nat,B: nat,A5: nat,B5: nat] :
% 5.52/5.78 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.52/5.78 = ( product_Pair_nat_nat @ A5 @ B5 ) )
% 5.52/5.78 => ~ ( ( A = A5 )
% 5.52/5.78 => ( B != B5 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % Pair_inject
% 5.52/5.78 thf(fact_3275_Pair__inject,axiom,
% 5.52/5.78 ! [A: int,B: int,A5: int,B5: int] :
% 5.52/5.78 ( ( ( product_Pair_int_int @ A @ B )
% 5.52/5.78 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.52/5.78 => ~ ( ( A = A5 )
% 5.52/5.78 => ( B != B5 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % Pair_inject
% 5.52/5.78 thf(fact_3276_cong__exp__iff__simps_I3_J,axiom,
% 5.52/5.78 ! [N: num,Q2: num] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 != zero_zero_nat ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(3)
% 5.52/5.78 thf(fact_3277_cong__exp__iff__simps_I3_J,axiom,
% 5.52/5.78 ! [N: num,Q2: num] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 != zero_zero_int ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(3)
% 5.52/5.78 thf(fact_3278_split__mod,axiom,
% 5.52/5.78 ! [P: nat > $o,M: nat,N: nat] :
% 5.52/5.78 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 5.52/5.78 = ( ( ( N = zero_zero_nat )
% 5.52/5.78 => ( P @ M ) )
% 5.52/5.78 & ( ( N != zero_zero_nat )
% 5.52/5.78 => ! [I4: nat,J3: nat] :
% 5.52/5.78 ( ( ord_less_nat @ J3 @ N )
% 5.52/5.78 => ( ( M
% 5.52/5.78 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.52/5.78 => ( P @ J3 ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % split_mod
% 5.52/5.78 thf(fact_3279_divmod__def,axiom,
% 5.52/5.78 ( unique5055182867167087721od_nat
% 5.52/5.78 = ( ^ [M3: num,N3: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N3 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N3 ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_def
% 5.52/5.78 thf(fact_3280_divmod__def,axiom,
% 5.52/5.78 ( unique5052692396658037445od_int
% 5.52/5.78 = ( ^ [M3: num,N3: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_def
% 5.52/5.78 thf(fact_3281_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.52/5.78 ! [C: nat,A: nat,B: nat] :
% 5.52/5.78 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.52/5.78 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.52/5.78 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.52/5.78 thf(fact_3282_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.52/5.78 ! [C: int,A: int,B: int] :
% 5.52/5.78 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.78 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.52/5.78 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.52/5.78 thf(fact_3283_cong__exp__iff__simps_I11_J,axiom,
% 5.52/5.78 ! [M: num,Q2: num] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.52/5.78 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.52/5.78 = zero_zero_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(11)
% 5.52/5.78 thf(fact_3284_cong__exp__iff__simps_I11_J,axiom,
% 5.52/5.78 ! [M: num,Q2: num] :
% 5.52/5.78 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.52/5.78 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.52/5.78 = zero_zero_int ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(11)
% 5.52/5.78 thf(fact_3285_cong__exp__iff__simps_I7_J,axiom,
% 5.52/5.78 ! [Q2: num,N: num] :
% 5.52/5.78 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.52/5.78 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.52/5.78 = zero_zero_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(7)
% 5.52/5.78 thf(fact_3286_cong__exp__iff__simps_I7_J,axiom,
% 5.52/5.78 ! [Q2: num,N: num] :
% 5.52/5.78 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.52/5.78 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.52/5.78 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.52/5.78 = zero_zero_int ) ) ).
% 5.52/5.78
% 5.52/5.78 % cong_exp_iff_simps(7)
% 5.52/5.78 thf(fact_3287_Suc__mod__eq__add3__mod,axiom,
% 5.52/5.78 ! [M: nat,N: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.52/5.78 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.52/5.78
% 5.52/5.78 % Suc_mod_eq_add3_mod
% 5.52/5.78 thf(fact_3288_Suc__times__mod__eq,axiom,
% 5.52/5.78 ! [M: nat,N: nat] :
% 5.52/5.78 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.52/5.78 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 5.52/5.78 = one_one_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % Suc_times_mod_eq
% 5.52/5.78 thf(fact_3289_divmod__digit__0_I2_J,axiom,
% 5.52/5.78 ! [B: nat,A: nat] :
% 5.52/5.78 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.78 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.52/5.78 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.52/5.78 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_digit_0(2)
% 5.52/5.78 thf(fact_3290_divmod__digit__0_I2_J,axiom,
% 5.52/5.78 ! [B: int,A: int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.78 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.52/5.78 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.52/5.78 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_digit_0(2)
% 5.52/5.78 thf(fact_3291_bits__stable__imp__add__self,axiom,
% 5.52/5.78 ! [A: nat] :
% 5.52/5.78 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.78 = A )
% 5.52/5.78 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.78 = zero_zero_nat ) ) ).
% 5.52/5.78
% 5.52/5.78 % bits_stable_imp_add_self
% 5.52/5.78 thf(fact_3292_bits__stable__imp__add__self,axiom,
% 5.52/5.78 ! [A: int] :
% 5.52/5.78 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.78 = A )
% 5.52/5.78 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.52/5.78 = zero_zero_int ) ) ).
% 5.52/5.78
% 5.52/5.78 % bits_stable_imp_add_self
% 5.52/5.78 thf(fact_3293_div__exp__mod__exp__eq,axiom,
% 5.52/5.78 ! [A: nat,N: nat,M: nat] :
% 5.52/5.78 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.52/5.78 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % div_exp_mod_exp_eq
% 5.52/5.78 thf(fact_3294_div__exp__mod__exp__eq,axiom,
% 5.52/5.78 ! [A: int,N: nat,M: nat] :
% 5.52/5.78 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.52/5.78 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % div_exp_mod_exp_eq
% 5.52/5.78 thf(fact_3295_divmod__digit__0_I1_J,axiom,
% 5.52/5.78 ! [B: nat,A: nat] :
% 5.52/5.78 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.78 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.52/5.78 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.52/5.78 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_digit_0(1)
% 5.52/5.78 thf(fact_3296_divmod__digit__0_I1_J,axiom,
% 5.52/5.78 ! [B: int,A: int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.78 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.52/5.78 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.52/5.78 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_digit_0(1)
% 5.52/5.78 thf(fact_3297_mult__exp__mod__exp__eq,axiom,
% 5.52/5.78 ! [M: nat,N: nat,A: nat] :
% 5.52/5.78 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.78 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.78 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_exp_mod_exp_eq
% 5.52/5.78 thf(fact_3298_mult__exp__mod__exp__eq,axiom,
% 5.52/5.78 ! [M: nat,N: nat,A: int] :
% 5.52/5.78 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.78 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.78 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mult_exp_mod_exp_eq
% 5.52/5.78 thf(fact_3299_prod__cases3,axiom,
% 5.52/5.78 ! [Y2: produc859450856879609959at_nat] :
% 5.52/5.78 ~ ! [A3: product_prod_nat_nat,B2: nat,C2: nat] :
% 5.52/5.78 ( Y2
% 5.52/5.78 != ( produc6161850002892822231at_nat @ A3 @ ( product_Pair_nat_nat @ B2 @ C2 ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % prod_cases3
% 5.52/5.78 thf(fact_3300_prod__induct3,axiom,
% 5.52/5.78 ! [P: produc859450856879609959at_nat > $o,X2: produc859450856879609959at_nat] :
% 5.52/5.78 ( ! [A3: product_prod_nat_nat,B2: nat,C2: nat] : ( P @ ( produc6161850002892822231at_nat @ A3 @ ( product_Pair_nat_nat @ B2 @ C2 ) ) )
% 5.52/5.78 => ( P @ X2 ) ) ).
% 5.52/5.78
% 5.52/5.78 % prod_induct3
% 5.52/5.78 thf(fact_3301_eucl__rel__int__iff,axiom,
% 5.52/5.78 ! [K: int,L: int,Q2: int,R: int] :
% 5.52/5.78 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.52/5.78 = ( ( K
% 5.52/5.78 = ( plus_plus_int @ ( times_times_int @ L @ Q2 ) @ R ) )
% 5.52/5.78 & ( ( ord_less_int @ zero_zero_int @ L )
% 5.52/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.52/5.78 & ( ord_less_int @ R @ L ) ) )
% 5.52/5.78 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 5.52/5.78 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 5.52/5.78 => ( ( ord_less_int @ L @ R )
% 5.52/5.78 & ( ord_less_eq_int @ R @ zero_zero_int ) ) )
% 5.52/5.78 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 5.52/5.78 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % eucl_rel_int_iff
% 5.52/5.78 thf(fact_3302_mod__double__modulus,axiom,
% 5.52/5.78 ! [M: nat,X2: nat] :
% 5.52/5.78 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.52/5.78 => ( ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.52/5.78 = ( modulo_modulo_nat @ X2 @ M ) )
% 5.52/5.78 | ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.52/5.78 = ( plus_plus_nat @ ( modulo_modulo_nat @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_double_modulus
% 5.52/5.78 thf(fact_3303_mod__double__modulus,axiom,
% 5.52/5.78 ! [M: int,X2: int] :
% 5.52/5.78 ( ( ord_less_int @ zero_zero_int @ M )
% 5.52/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.78 => ( ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.52/5.78 = ( modulo_modulo_int @ X2 @ M ) )
% 5.52/5.78 | ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.52/5.78 = ( plus_plus_int @ ( modulo_modulo_int @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % mod_double_modulus
% 5.52/5.78 thf(fact_3304_divmod__digit__1_I2_J,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.78 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.78 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.52/5.78 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.52/5.78 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_digit_1(2)
% 5.52/5.78 thf(fact_3305_divmod__digit__1_I2_J,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.78 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.78 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.52/5.78 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.52/5.78 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_digit_1(2)
% 5.52/5.78 thf(fact_3306_unset__bit__Suc,axiom,
% 5.52/5.78 ! [N: nat,A: int] :
% 5.52/5.78 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 5.52/5.78 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % unset_bit_Suc
% 5.52/5.78 thf(fact_3307_unset__bit__Suc,axiom,
% 5.52/5.78 ! [N: nat,A: nat] :
% 5.52/5.78 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 5.52/5.78 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % unset_bit_Suc
% 5.52/5.78 thf(fact_3308_set__bit__Suc,axiom,
% 5.52/5.78 ! [N: nat,A: int] :
% 5.52/5.78 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 5.52/5.78 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % set_bit_Suc
% 5.52/5.78 thf(fact_3309_set__bit__Suc,axiom,
% 5.52/5.78 ! [N: nat,A: nat] :
% 5.52/5.78 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 5.52/5.78 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % set_bit_Suc
% 5.52/5.78 thf(fact_3310_divmod__digit__1_I1_J,axiom,
% 5.52/5.78 ! [A: nat,B: nat] :
% 5.52/5.78 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.52/5.78 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.52/5.78 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.52/5.78 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 5.52/5.78 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_digit_1(1)
% 5.52/5.78 thf(fact_3311_divmod__digit__1_I1_J,axiom,
% 5.52/5.78 ! [A: int,B: int] :
% 5.52/5.78 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.78 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.78 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.52/5.78 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 5.52/5.78 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % divmod_digit_1(1)
% 5.52/5.78 thf(fact_3312_pos__eucl__rel__int__mult__2,axiom,
% 5.52/5.78 ! [B: int,A: int,Q2: int,R: int] :
% 5.52/5.78 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.78 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.52/5.78 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 5.52/5.78
% 5.52/5.78 % pos_eucl_rel_int_mult_2
% 5.52/5.78 thf(fact_3313_verit__le__mono__div,axiom,
% 5.52/5.78 ! [A2: nat,B4: nat,N: nat] :
% 5.52/5.78 ( ( ord_less_nat @ A2 @ B4 )
% 5.52/5.78 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.78 => ( ord_less_eq_nat
% 5.52/5.78 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 5.52/5.78 @ ( if_nat
% 5.52/5.78 @ ( ( modulo_modulo_nat @ B4 @ N )
% 5.52/5.78 = zero_zero_nat )
% 5.52/5.78 @ one_one_nat
% 5.52/5.78 @ zero_zero_nat ) )
% 5.52/5.79 @ ( divide_divide_nat @ B4 @ N ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_le_mono_div
% 5.52/5.79 thf(fact_3314_mod__exhaust__less__4,axiom,
% 5.52/5.79 ! [M: nat] :
% 5.52/5.79 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.52/5.79 = zero_zero_nat )
% 5.52/5.79 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.52/5.79 = one_one_nat )
% 5.52/5.79 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.52/5.79 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.79 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.52/5.79 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % mod_exhaust_less_4
% 5.52/5.79 thf(fact_3315_finite__Collect__le__nat,axiom,
% 5.52/5.79 ! [K: nat] :
% 5.52/5.79 ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [N3: nat] : ( ord_less_eq_nat @ N3 @ K ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_Collect_le_nat
% 5.52/5.79 thf(fact_3316_finite__Collect__less__nat,axiom,
% 5.52/5.79 ! [K: nat] :
% 5.52/5.79 ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [N3: nat] : ( ord_less_nat @ N3 @ K ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_Collect_less_nat
% 5.52/5.79 thf(fact_3317_finite__roots__unity,axiom,
% 5.52/5.79 ! [N: nat] :
% 5.52/5.79 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.52/5.79 => ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [Z2: real] :
% 5.52/5.79 ( ( power_power_real @ Z2 @ N )
% 5.52/5.79 = one_one_real ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_roots_unity
% 5.52/5.79 thf(fact_3318_finite__roots__unity,axiom,
% 5.52/5.79 ! [N: nat] :
% 5.52/5.79 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.52/5.79 => ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [Z2: complex] :
% 5.52/5.79 ( ( power_power_complex @ Z2 @ N )
% 5.52/5.79 = one_one_complex ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_roots_unity
% 5.52/5.79 thf(fact_3319_div__mod__decomp,axiom,
% 5.52/5.79 ! [A2: nat,N: nat] :
% 5.52/5.79 ( A2
% 5.52/5.79 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % div_mod_decomp
% 5.52/5.79 thf(fact_3320_flip__bit__Suc,axiom,
% 5.52/5.79 ! [N: nat,A: int] :
% 5.52/5.79 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 5.52/5.79 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % flip_bit_Suc
% 5.52/5.79 thf(fact_3321_flip__bit__Suc,axiom,
% 5.52/5.79 ! [N: nat,A: nat] :
% 5.52/5.79 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 5.52/5.79 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % flip_bit_Suc
% 5.52/5.79 thf(fact_3322_div__less__mono,axiom,
% 5.52/5.79 ! [A2: nat,B4: nat,N: nat] :
% 5.52/5.79 ( ( ord_less_nat @ A2 @ B4 )
% 5.52/5.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.79 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 5.52/5.79 = zero_zero_nat )
% 5.52/5.79 => ( ( ( modulo_modulo_nat @ B4 @ N )
% 5.52/5.79 = zero_zero_nat )
% 5.52/5.79 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B4 @ N ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % div_less_mono
% 5.52/5.79 thf(fact_3323_verit__eq__simplify_I8_J,axiom,
% 5.52/5.79 ! [X23: num,Y22: num] :
% 5.52/5.79 ( ( ( bit0 @ X23 )
% 5.52/5.79 = ( bit0 @ Y22 ) )
% 5.52/5.79 = ( X23 = Y22 ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_eq_simplify(8)
% 5.52/5.79 thf(fact_3324_verit__eq__simplify_I9_J,axiom,
% 5.52/5.79 ! [X32: num,Y32: num] :
% 5.52/5.79 ( ( ( bit1 @ X32 )
% 5.52/5.79 = ( bit1 @ Y32 ) )
% 5.52/5.79 = ( X32 = Y32 ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_eq_simplify(9)
% 5.52/5.79 thf(fact_3325_finite__interval__int4,axiom,
% 5.52/5.79 ! [A: int,B: int] :
% 5.52/5.79 ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( ord_less_int @ A @ I4 )
% 5.52/5.79 & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_interval_int4
% 5.52/5.79 thf(fact_3326_flip__bit__nonnegative__int__iff,axiom,
% 5.52/5.79 ! [N: nat,K: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 5.52/5.79 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.52/5.79
% 5.52/5.79 % flip_bit_nonnegative_int_iff
% 5.52/5.79 thf(fact_3327_flip__bit__negative__int__iff,axiom,
% 5.52/5.79 ! [N: nat,K: int] :
% 5.52/5.79 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 5.52/5.79 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.52/5.79
% 5.52/5.79 % flip_bit_negative_int_iff
% 5.52/5.79 thf(fact_3328_finite__interval__int3,axiom,
% 5.52/5.79 ! [A: int,B: int] :
% 5.52/5.79 ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( ord_less_int @ A @ I4 )
% 5.52/5.79 & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_interval_int3
% 5.52/5.79 thf(fact_3329_finite__interval__int2,axiom,
% 5.52/5.79 ! [A: int,B: int] :
% 5.52/5.79 ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ A @ I4 )
% 5.52/5.79 & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_interval_int2
% 5.52/5.79 thf(fact_3330_mod__pos__pos__trivial,axiom,
% 5.52/5.79 ! [K: int,L: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.79 => ( ( ord_less_int @ K @ L )
% 5.52/5.79 => ( ( modulo_modulo_int @ K @ L )
% 5.52/5.79 = K ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % mod_pos_pos_trivial
% 5.52/5.79 thf(fact_3331_mod__neg__neg__trivial,axiom,
% 5.52/5.79 ! [K: int,L: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.52/5.79 => ( ( ord_less_int @ L @ K )
% 5.52/5.79 => ( ( modulo_modulo_int @ K @ L )
% 5.52/5.79 = K ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % mod_neg_neg_trivial
% 5.52/5.79 thf(fact_3332_zmod__numeral__Bit0,axiom,
% 5.52/5.79 ! [V: num,W: num] :
% 5.52/5.79 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.52/5.79 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % zmod_numeral_Bit0
% 5.52/5.79 thf(fact_3333_zmod__numeral__Bit1,axiom,
% 5.52/5.79 ! [V: num,W: num] :
% 5.52/5.79 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.52/5.79 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 5.52/5.79
% 5.52/5.79 % zmod_numeral_Bit1
% 5.52/5.79 thf(fact_3334_zmod__le__nonneg__dividend,axiom,
% 5.52/5.79 ! [M: int,K: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.52/5.79 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.52/5.79
% 5.52/5.79 % zmod_le_nonneg_dividend
% 5.52/5.79 thf(fact_3335_Euclidean__Division_Opos__mod__bound,axiom,
% 5.52/5.79 ! [L: int,K: int] :
% 5.52/5.79 ( ( ord_less_int @ zero_zero_int @ L )
% 5.52/5.79 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 5.52/5.79
% 5.52/5.79 % Euclidean_Division.pos_mod_bound
% 5.52/5.79 thf(fact_3336_neg__mod__bound,axiom,
% 5.52/5.79 ! [L: int,K: int] :
% 5.52/5.79 ( ( ord_less_int @ L @ zero_zero_int )
% 5.52/5.79 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % neg_mod_bound
% 5.52/5.79 thf(fact_3337_zmod__eq__0__iff,axiom,
% 5.52/5.79 ! [M: int,D2: int] :
% 5.52/5.79 ( ( ( modulo_modulo_int @ M @ D2 )
% 5.52/5.79 = zero_zero_int )
% 5.52/5.79 = ( ? [Q4: int] :
% 5.52/5.79 ( M
% 5.52/5.79 = ( times_times_int @ D2 @ Q4 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % zmod_eq_0_iff
% 5.52/5.79 thf(fact_3338_zmod__eq__0D,axiom,
% 5.52/5.79 ! [M: int,D2: int] :
% 5.52/5.79 ( ( ( modulo_modulo_int @ M @ D2 )
% 5.52/5.79 = zero_zero_int )
% 5.52/5.79 => ? [Q3: int] :
% 5.52/5.79 ( M
% 5.52/5.79 = ( times_times_int @ D2 @ Q3 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % zmod_eq_0D
% 5.52/5.79 thf(fact_3339_zdiv__mono__strict,axiom,
% 5.52/5.79 ! [A2: int,B4: int,N: int] :
% 5.52/5.79 ( ( ord_less_int @ A2 @ B4 )
% 5.52/5.79 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.52/5.79 => ( ( ( modulo_modulo_int @ A2 @ N )
% 5.52/5.79 = zero_zero_int )
% 5.52/5.79 => ( ( ( modulo_modulo_int @ B4 @ N )
% 5.52/5.79 = zero_zero_int )
% 5.52/5.79 => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B4 @ N ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % zdiv_mono_strict
% 5.52/5.79 thf(fact_3340_finite__maxlen,axiom,
% 5.52/5.79 ! [M7: set_list_VEBT_VEBT] :
% 5.52/5.79 ( ( finite3004134309566078307T_VEBT @ M7 )
% 5.52/5.79 => ? [N2: nat] :
% 5.52/5.79 ! [X6: list_VEBT_VEBT] :
% 5.52/5.79 ( ( member2936631157270082147T_VEBT @ X6 @ M7 )
% 5.52/5.79 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X6 ) @ N2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_maxlen
% 5.52/5.79 thf(fact_3341_finite__maxlen,axiom,
% 5.52/5.79 ! [M7: set_list_o] :
% 5.52/5.79 ( ( finite_finite_list_o @ M7 )
% 5.52/5.79 => ? [N2: nat] :
% 5.52/5.79 ! [X6: list_o] :
% 5.52/5.79 ( ( member_list_o @ X6 @ M7 )
% 5.52/5.79 => ( ord_less_nat @ ( size_size_list_o @ X6 ) @ N2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_maxlen
% 5.52/5.79 thf(fact_3342_finite__maxlen,axiom,
% 5.52/5.79 ! [M7: set_list_nat] :
% 5.52/5.79 ( ( finite8100373058378681591st_nat @ M7 )
% 5.52/5.79 => ? [N2: nat] :
% 5.52/5.79 ! [X6: list_nat] :
% 5.52/5.79 ( ( member_list_nat @ X6 @ M7 )
% 5.52/5.79 => ( ord_less_nat @ ( size_size_list_nat @ X6 ) @ N2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_maxlen
% 5.52/5.79 thf(fact_3343_div__mod__decomp__int,axiom,
% 5.52/5.79 ! [A2: int,N: int] :
% 5.52/5.79 ( A2
% 5.52/5.79 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % div_mod_decomp_int
% 5.52/5.79 thf(fact_3344_mod__int__unique,axiom,
% 5.52/5.79 ! [K: int,L: int,Q2: int,R: int] :
% 5.52/5.79 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.52/5.79 => ( ( modulo_modulo_int @ K @ L )
% 5.52/5.79 = R ) ) ).
% 5.52/5.79
% 5.52/5.79 % mod_int_unique
% 5.52/5.79 thf(fact_3345_neg__mod__conj,axiom,
% 5.52/5.79 ! [B: int,A: int] :
% 5.52/5.79 ( ( ord_less_int @ B @ zero_zero_int )
% 5.52/5.79 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.52/5.79 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % neg_mod_conj
% 5.52/5.79 thf(fact_3346_pos__mod__conj,axiom,
% 5.52/5.79 ! [B: int,A: int] :
% 5.52/5.79 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.79 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.52/5.79 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % pos_mod_conj
% 5.52/5.79 thf(fact_3347_zmod__trivial__iff,axiom,
% 5.52/5.79 ! [I: int,K: int] :
% 5.52/5.79 ( ( ( modulo_modulo_int @ I @ K )
% 5.52/5.79 = I )
% 5.52/5.79 = ( ( K = zero_zero_int )
% 5.52/5.79 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.52/5.79 & ( ord_less_int @ I @ K ) )
% 5.52/5.79 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.52/5.79 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % zmod_trivial_iff
% 5.52/5.79 thf(fact_3348_Euclidean__Division_Opos__mod__sign,axiom,
% 5.52/5.79 ! [L: int,K: int] :
% 5.52/5.79 ( ( ord_less_int @ zero_zero_int @ L )
% 5.52/5.79 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % Euclidean_Division.pos_mod_sign
% 5.52/5.79 thf(fact_3349_neg__mod__sign,axiom,
% 5.52/5.79 ! [L: int,K: int] :
% 5.52/5.79 ( ( ord_less_int @ L @ zero_zero_int )
% 5.52/5.79 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 5.52/5.79
% 5.52/5.79 % neg_mod_sign
% 5.52/5.79 thf(fact_3350_verit__la__disequality,axiom,
% 5.52/5.79 ! [A: rat,B: rat] :
% 5.52/5.79 ( ( A = B )
% 5.52/5.79 | ~ ( ord_less_eq_rat @ A @ B )
% 5.52/5.79 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_la_disequality
% 5.52/5.79 thf(fact_3351_verit__la__disequality,axiom,
% 5.52/5.79 ! [A: num,B: num] :
% 5.52/5.79 ( ( A = B )
% 5.52/5.79 | ~ ( ord_less_eq_num @ A @ B )
% 5.52/5.79 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_la_disequality
% 5.52/5.79 thf(fact_3352_verit__la__disequality,axiom,
% 5.52/5.79 ! [A: nat,B: nat] :
% 5.52/5.79 ( ( A = B )
% 5.52/5.79 | ~ ( ord_less_eq_nat @ A @ B )
% 5.52/5.79 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_la_disequality
% 5.52/5.79 thf(fact_3353_verit__la__disequality,axiom,
% 5.52/5.79 ! [A: int,B: int] :
% 5.52/5.79 ( ( A = B )
% 5.52/5.79 | ~ ( ord_less_eq_int @ A @ B )
% 5.52/5.79 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_la_disequality
% 5.52/5.79 thf(fact_3354_verit__comp__simplify1_I2_J,axiom,
% 5.52/5.79 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(2)
% 5.52/5.79 thf(fact_3355_verit__comp__simplify1_I2_J,axiom,
% 5.52/5.79 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(2)
% 5.52/5.79 thf(fact_3356_verit__comp__simplify1_I2_J,axiom,
% 5.52/5.79 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(2)
% 5.52/5.79 thf(fact_3357_verit__comp__simplify1_I2_J,axiom,
% 5.52/5.79 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(2)
% 5.52/5.79 thf(fact_3358_verit__comp__simplify1_I2_J,axiom,
% 5.52/5.79 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(2)
% 5.52/5.79 thf(fact_3359_divmod__int__def,axiom,
% 5.52/5.79 ( unique5052692396658037445od_int
% 5.52/5.79 = ( ^ [M3: num,N3: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % divmod_int_def
% 5.52/5.79 thf(fact_3360_verit__comp__simplify1_I1_J,axiom,
% 5.52/5.79 ! [A: real] :
% 5.52/5.79 ~ ( ord_less_real @ A @ A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(1)
% 5.52/5.79 thf(fact_3361_verit__comp__simplify1_I1_J,axiom,
% 5.52/5.79 ! [A: rat] :
% 5.52/5.79 ~ ( ord_less_rat @ A @ A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(1)
% 5.52/5.79 thf(fact_3362_verit__comp__simplify1_I1_J,axiom,
% 5.52/5.79 ! [A: num] :
% 5.52/5.79 ~ ( ord_less_num @ A @ A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(1)
% 5.52/5.79 thf(fact_3363_verit__comp__simplify1_I1_J,axiom,
% 5.52/5.79 ! [A: nat] :
% 5.52/5.79 ~ ( ord_less_nat @ A @ A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(1)
% 5.52/5.79 thf(fact_3364_verit__comp__simplify1_I1_J,axiom,
% 5.52/5.79 ! [A: int] :
% 5.52/5.79 ~ ( ord_less_int @ A @ A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(1)
% 5.52/5.79 thf(fact_3365_eucl__rel__int,axiom,
% 5.52/5.79 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % eucl_rel_int
% 5.52/5.79 thf(fact_3366_mod__pos__neg__trivial,axiom,
% 5.52/5.79 ! [K: int,L: int] :
% 5.52/5.79 ( ( ord_less_int @ zero_zero_int @ K )
% 5.52/5.79 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.52/5.79 => ( ( modulo_modulo_int @ K @ L )
% 5.52/5.79 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % mod_pos_neg_trivial
% 5.52/5.79 thf(fact_3367_mod__pos__geq,axiom,
% 5.52/5.79 ! [L: int,K: int] :
% 5.52/5.79 ( ( ord_less_int @ zero_zero_int @ L )
% 5.52/5.79 => ( ( ord_less_eq_int @ L @ K )
% 5.52/5.79 => ( ( modulo_modulo_int @ K @ L )
% 5.52/5.79 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % mod_pos_geq
% 5.52/5.79 thf(fact_3368_verit__le__mono__div__int,axiom,
% 5.52/5.79 ! [A2: int,B4: int,N: int] :
% 5.52/5.79 ( ( ord_less_int @ A2 @ B4 )
% 5.52/5.79 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.52/5.79 => ( ord_less_eq_int
% 5.52/5.79 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 5.52/5.79 @ ( if_int
% 5.52/5.79 @ ( ( modulo_modulo_int @ B4 @ N )
% 5.52/5.79 = zero_zero_int )
% 5.52/5.79 @ one_one_int
% 5.52/5.79 @ zero_zero_int ) )
% 5.52/5.79 @ ( divide_divide_int @ B4 @ N ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_le_mono_div_int
% 5.52/5.79 thf(fact_3369_split__zmod,axiom,
% 5.52/5.79 ! [P: int > $o,N: int,K: int] :
% 5.52/5.79 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.52/5.79 = ( ( ( K = zero_zero_int )
% 5.52/5.79 => ( P @ N ) )
% 5.52/5.79 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.52/5.79 => ! [I4: int,J3: int] :
% 5.52/5.79 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.52/5.79 & ( ord_less_int @ J3 @ K )
% 5.52/5.79 & ( N
% 5.52/5.79 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.52/5.79 => ( P @ J3 ) ) )
% 5.52/5.79 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.52/5.79 => ! [I4: int,J3: int] :
% 5.52/5.79 ( ( ( ord_less_int @ K @ J3 )
% 5.52/5.79 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.52/5.79 & ( N
% 5.52/5.79 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.52/5.79 => ( P @ J3 ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % split_zmod
% 5.52/5.79 thf(fact_3370_int__mod__neg__eq,axiom,
% 5.52/5.79 ! [A: int,B: int,Q2: int,R: int] :
% 5.52/5.79 ( ( A
% 5.52/5.79 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.52/5.79 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 5.52/5.79 => ( ( ord_less_int @ B @ R )
% 5.52/5.79 => ( ( modulo_modulo_int @ A @ B )
% 5.52/5.79 = R ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % int_mod_neg_eq
% 5.52/5.79 thf(fact_3371_int__mod__pos__eq,axiom,
% 5.52/5.79 ! [A: int,B: int,Q2: int,R: int] :
% 5.52/5.79 ( ( A
% 5.52/5.79 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.52/5.79 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.52/5.79 => ( ( ord_less_int @ R @ B )
% 5.52/5.79 => ( ( modulo_modulo_int @ A @ B )
% 5.52/5.79 = R ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % int_mod_pos_eq
% 5.52/5.79 thf(fact_3372_zmod__zmult2__eq,axiom,
% 5.52/5.79 ! [C: int,A: int,B: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.52/5.79 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.52/5.79 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % zmod_zmult2_eq
% 5.52/5.79 thf(fact_3373_split__pos__lemma,axiom,
% 5.52/5.79 ! [K: int,P: int > int > $o,N: int] :
% 5.52/5.79 ( ( ord_less_int @ zero_zero_int @ K )
% 5.52/5.79 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.52/5.79 = ( ! [I4: int,J3: int] :
% 5.52/5.79 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.52/5.79 & ( ord_less_int @ J3 @ K )
% 5.52/5.79 & ( N
% 5.52/5.79 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.52/5.79 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % split_pos_lemma
% 5.52/5.79 thf(fact_3374_split__neg__lemma,axiom,
% 5.52/5.79 ! [K: int,P: int > int > $o,N: int] :
% 5.52/5.79 ( ( ord_less_int @ K @ zero_zero_int )
% 5.52/5.79 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.52/5.79 = ( ! [I4: int,J3: int] :
% 5.52/5.79 ( ( ( ord_less_int @ K @ J3 )
% 5.52/5.79 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.52/5.79 & ( N
% 5.52/5.79 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.52/5.79 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % split_neg_lemma
% 5.52/5.79 thf(fact_3375_verit__comp__simplify1_I3_J,axiom,
% 5.52/5.79 ! [B5: real,A5: real] :
% 5.52/5.79 ( ( ~ ( ord_less_eq_real @ B5 @ A5 ) )
% 5.52/5.79 = ( ord_less_real @ A5 @ B5 ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(3)
% 5.52/5.79 thf(fact_3376_verit__comp__simplify1_I3_J,axiom,
% 5.52/5.79 ! [B5: rat,A5: rat] :
% 5.52/5.79 ( ( ~ ( ord_less_eq_rat @ B5 @ A5 ) )
% 5.52/5.79 = ( ord_less_rat @ A5 @ B5 ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(3)
% 5.52/5.79 thf(fact_3377_verit__comp__simplify1_I3_J,axiom,
% 5.52/5.79 ! [B5: num,A5: num] :
% 5.52/5.79 ( ( ~ ( ord_less_eq_num @ B5 @ A5 ) )
% 5.52/5.79 = ( ord_less_num @ A5 @ B5 ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(3)
% 5.52/5.79 thf(fact_3378_verit__comp__simplify1_I3_J,axiom,
% 5.52/5.79 ! [B5: nat,A5: nat] :
% 5.52/5.79 ( ( ~ ( ord_less_eq_nat @ B5 @ A5 ) )
% 5.52/5.79 = ( ord_less_nat @ A5 @ B5 ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(3)
% 5.52/5.79 thf(fact_3379_verit__comp__simplify1_I3_J,axiom,
% 5.52/5.79 ! [B5: int,A5: int] :
% 5.52/5.79 ( ( ~ ( ord_less_eq_int @ B5 @ A5 ) )
% 5.52/5.79 = ( ord_less_int @ A5 @ B5 ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_comp_simplify1(3)
% 5.52/5.79 thf(fact_3380_verit__sum__simplify,axiom,
% 5.52/5.79 ! [A: complex] :
% 5.52/5.79 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.52/5.79 = A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_sum_simplify
% 5.52/5.79 thf(fact_3381_verit__sum__simplify,axiom,
% 5.52/5.79 ! [A: real] :
% 5.52/5.79 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.52/5.79 = A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_sum_simplify
% 5.52/5.79 thf(fact_3382_verit__sum__simplify,axiom,
% 5.52/5.79 ! [A: rat] :
% 5.52/5.79 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.52/5.79 = A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_sum_simplify
% 5.52/5.79 thf(fact_3383_verit__sum__simplify,axiom,
% 5.52/5.79 ! [A: nat] :
% 5.52/5.79 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.52/5.79 = A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_sum_simplify
% 5.52/5.79 thf(fact_3384_verit__sum__simplify,axiom,
% 5.52/5.79 ! [A: int] :
% 5.52/5.79 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.52/5.79 = A ) ).
% 5.52/5.79
% 5.52/5.79 % verit_sum_simplify
% 5.52/5.79 thf(fact_3385_verit__eq__simplify_I10_J,axiom,
% 5.52/5.79 ! [X23: num] :
% 5.52/5.79 ( one
% 5.52/5.79 != ( bit0 @ X23 ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_eq_simplify(10)
% 5.52/5.79 thf(fact_3386_finite__has__maximal2,axiom,
% 5.52/5.79 ! [A2: set_real,A: real] :
% 5.52/5.79 ( ( finite_finite_real @ A2 )
% 5.52/5.79 => ( ( member_real @ A @ A2 )
% 5.52/5.79 => ? [X4: real] :
% 5.52/5.79 ( ( member_real @ X4 @ A2 )
% 5.52/5.79 & ( ord_less_eq_real @ A @ X4 )
% 5.52/5.79 & ! [Xa: real] :
% 5.52/5.79 ( ( member_real @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_real @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal2
% 5.52/5.79 thf(fact_3387_finite__has__maximal2,axiom,
% 5.52/5.79 ! [A2: set_set_nat_rat,A: set_nat_rat] :
% 5.52/5.79 ( ( finite6430367030675640852at_rat @ A2 )
% 5.52/5.79 => ( ( member_set_nat_rat @ A @ A2 )
% 5.52/5.79 => ? [X4: set_nat_rat] :
% 5.52/5.79 ( ( member_set_nat_rat @ X4 @ A2 )
% 5.52/5.79 & ( ord_le2679597024174929757at_rat @ A @ X4 )
% 5.52/5.79 & ! [Xa: set_nat_rat] :
% 5.52/5.79 ( ( member_set_nat_rat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_le2679597024174929757at_rat @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal2
% 5.52/5.79 thf(fact_3388_finite__has__maximal2,axiom,
% 5.52/5.79 ! [A2: set_Extended_enat,A: extended_enat] :
% 5.52/5.79 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.79 => ( ( member_Extended_enat @ A @ A2 )
% 5.52/5.79 => ? [X4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ X4 @ A2 )
% 5.52/5.79 & ( ord_le2932123472753598470d_enat @ A @ X4 )
% 5.52/5.79 & ! [Xa: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_le2932123472753598470d_enat @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal2
% 5.52/5.79 thf(fact_3389_finite__has__maximal2,axiom,
% 5.52/5.79 ! [A2: set_set_nat,A: set_nat] :
% 5.52/5.79 ( ( finite1152437895449049373et_nat @ A2 )
% 5.52/5.79 => ( ( member_set_nat @ A @ A2 )
% 5.52/5.79 => ? [X4: set_nat] :
% 5.52/5.79 ( ( member_set_nat @ X4 @ A2 )
% 5.52/5.79 & ( ord_less_eq_set_nat @ A @ X4 )
% 5.52/5.79 & ! [Xa: set_nat] :
% 5.52/5.79 ( ( member_set_nat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_set_nat @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal2
% 5.52/5.79 thf(fact_3390_finite__has__maximal2,axiom,
% 5.52/5.79 ! [A2: set_rat,A: rat] :
% 5.52/5.79 ( ( finite_finite_rat @ A2 )
% 5.52/5.79 => ( ( member_rat @ A @ A2 )
% 5.52/5.79 => ? [X4: rat] :
% 5.52/5.79 ( ( member_rat @ X4 @ A2 )
% 5.52/5.79 & ( ord_less_eq_rat @ A @ X4 )
% 5.52/5.79 & ! [Xa: rat] :
% 5.52/5.79 ( ( member_rat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_rat @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal2
% 5.52/5.79 thf(fact_3391_finite__has__maximal2,axiom,
% 5.52/5.79 ! [A2: set_num,A: num] :
% 5.52/5.79 ( ( finite_finite_num @ A2 )
% 5.52/5.79 => ( ( member_num @ A @ A2 )
% 5.52/5.79 => ? [X4: num] :
% 5.52/5.79 ( ( member_num @ X4 @ A2 )
% 5.52/5.79 & ( ord_less_eq_num @ A @ X4 )
% 5.52/5.79 & ! [Xa: num] :
% 5.52/5.79 ( ( member_num @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_num @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal2
% 5.52/5.79 thf(fact_3392_finite__has__maximal2,axiom,
% 5.52/5.79 ! [A2: set_nat,A: nat] :
% 5.52/5.79 ( ( finite_finite_nat @ A2 )
% 5.52/5.79 => ( ( member_nat @ A @ A2 )
% 5.52/5.79 => ? [X4: nat] :
% 5.52/5.79 ( ( member_nat @ X4 @ A2 )
% 5.52/5.79 & ( ord_less_eq_nat @ A @ X4 )
% 5.52/5.79 & ! [Xa: nat] :
% 5.52/5.79 ( ( member_nat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal2
% 5.52/5.79 thf(fact_3393_finite__has__maximal2,axiom,
% 5.52/5.79 ! [A2: set_int,A: int] :
% 5.52/5.79 ( ( finite_finite_int @ A2 )
% 5.52/5.79 => ( ( member_int @ A @ A2 )
% 5.52/5.79 => ? [X4: int] :
% 5.52/5.79 ( ( member_int @ X4 @ A2 )
% 5.52/5.79 & ( ord_less_eq_int @ A @ X4 )
% 5.52/5.79 & ! [Xa: int] :
% 5.52/5.79 ( ( member_int @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_int @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal2
% 5.52/5.79 thf(fact_3394_finite__has__minimal2,axiom,
% 5.52/5.79 ! [A2: set_real,A: real] :
% 5.52/5.79 ( ( finite_finite_real @ A2 )
% 5.52/5.79 => ( ( member_real @ A @ A2 )
% 5.52/5.79 => ? [X4: real] :
% 5.52/5.79 ( ( member_real @ X4 @ A2 )
% 5.52/5.79 & ( ord_less_eq_real @ X4 @ A )
% 5.52/5.79 & ! [Xa: real] :
% 5.52/5.79 ( ( member_real @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_real @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal2
% 5.52/5.79 thf(fact_3395_finite__has__minimal2,axiom,
% 5.52/5.79 ! [A2: set_set_nat_rat,A: set_nat_rat] :
% 5.52/5.79 ( ( finite6430367030675640852at_rat @ A2 )
% 5.52/5.79 => ( ( member_set_nat_rat @ A @ A2 )
% 5.52/5.79 => ? [X4: set_nat_rat] :
% 5.52/5.79 ( ( member_set_nat_rat @ X4 @ A2 )
% 5.52/5.79 & ( ord_le2679597024174929757at_rat @ X4 @ A )
% 5.52/5.79 & ! [Xa: set_nat_rat] :
% 5.52/5.79 ( ( member_set_nat_rat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_le2679597024174929757at_rat @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal2
% 5.52/5.79 thf(fact_3396_finite__has__minimal2,axiom,
% 5.52/5.79 ! [A2: set_Extended_enat,A: extended_enat] :
% 5.52/5.79 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.79 => ( ( member_Extended_enat @ A @ A2 )
% 5.52/5.79 => ? [X4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ X4 @ A2 )
% 5.52/5.79 & ( ord_le2932123472753598470d_enat @ X4 @ A )
% 5.52/5.79 & ! [Xa: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_le2932123472753598470d_enat @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal2
% 5.52/5.79 thf(fact_3397_finite__has__minimal2,axiom,
% 5.52/5.79 ! [A2: set_set_nat,A: set_nat] :
% 5.52/5.79 ( ( finite1152437895449049373et_nat @ A2 )
% 5.52/5.79 => ( ( member_set_nat @ A @ A2 )
% 5.52/5.79 => ? [X4: set_nat] :
% 5.52/5.79 ( ( member_set_nat @ X4 @ A2 )
% 5.52/5.79 & ( ord_less_eq_set_nat @ X4 @ A )
% 5.52/5.79 & ! [Xa: set_nat] :
% 5.52/5.79 ( ( member_set_nat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_set_nat @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal2
% 5.52/5.79 thf(fact_3398_finite__has__minimal2,axiom,
% 5.52/5.79 ! [A2: set_rat,A: rat] :
% 5.52/5.79 ( ( finite_finite_rat @ A2 )
% 5.52/5.79 => ( ( member_rat @ A @ A2 )
% 5.52/5.79 => ? [X4: rat] :
% 5.52/5.79 ( ( member_rat @ X4 @ A2 )
% 5.52/5.79 & ( ord_less_eq_rat @ X4 @ A )
% 5.52/5.79 & ! [Xa: rat] :
% 5.52/5.79 ( ( member_rat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_rat @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal2
% 5.52/5.79 thf(fact_3399_finite__has__minimal2,axiom,
% 5.52/5.79 ! [A2: set_num,A: num] :
% 5.52/5.79 ( ( finite_finite_num @ A2 )
% 5.52/5.79 => ( ( member_num @ A @ A2 )
% 5.52/5.79 => ? [X4: num] :
% 5.52/5.79 ( ( member_num @ X4 @ A2 )
% 5.52/5.79 & ( ord_less_eq_num @ X4 @ A )
% 5.52/5.79 & ! [Xa: num] :
% 5.52/5.79 ( ( member_num @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_num @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal2
% 5.52/5.79 thf(fact_3400_finite__has__minimal2,axiom,
% 5.52/5.79 ! [A2: set_nat,A: nat] :
% 5.52/5.79 ( ( finite_finite_nat @ A2 )
% 5.52/5.79 => ( ( member_nat @ A @ A2 )
% 5.52/5.79 => ? [X4: nat] :
% 5.52/5.79 ( ( member_nat @ X4 @ A2 )
% 5.52/5.79 & ( ord_less_eq_nat @ X4 @ A )
% 5.52/5.79 & ! [Xa: nat] :
% 5.52/5.79 ( ( member_nat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal2
% 5.52/5.79 thf(fact_3401_finite__has__minimal2,axiom,
% 5.52/5.79 ! [A2: set_int,A: int] :
% 5.52/5.79 ( ( finite_finite_int @ A2 )
% 5.52/5.79 => ( ( member_int @ A @ A2 )
% 5.52/5.79 => ? [X4: int] :
% 5.52/5.79 ( ( member_int @ X4 @ A2 )
% 5.52/5.79 & ( ord_less_eq_int @ X4 @ A )
% 5.52/5.79 & ! [Xa: int] :
% 5.52/5.79 ( ( member_int @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_int @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal2
% 5.52/5.79 thf(fact_3402_verit__eq__simplify_I14_J,axiom,
% 5.52/5.79 ! [X23: num,X32: num] :
% 5.52/5.79 ( ( bit0 @ X23 )
% 5.52/5.79 != ( bit1 @ X32 ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_eq_simplify(14)
% 5.52/5.79 thf(fact_3403_verit__eq__simplify_I12_J,axiom,
% 5.52/5.79 ! [X32: num] :
% 5.52/5.79 ( one
% 5.52/5.79 != ( bit1 @ X32 ) ) ).
% 5.52/5.79
% 5.52/5.79 % verit_eq_simplify(12)
% 5.52/5.79 thf(fact_3404_finite__psubset__induct,axiom,
% 5.52/5.79 ! [A2: set_nat,P: set_nat > $o] :
% 5.52/5.79 ( ( finite_finite_nat @ A2 )
% 5.52/5.79 => ( ! [A7: set_nat] :
% 5.52/5.79 ( ( finite_finite_nat @ A7 )
% 5.52/5.79 => ( ! [B7: set_nat] :
% 5.52/5.79 ( ( ord_less_set_nat @ B7 @ A7 )
% 5.52/5.79 => ( P @ B7 ) )
% 5.52/5.79 => ( P @ A7 ) ) )
% 5.52/5.79 => ( P @ A2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_psubset_induct
% 5.52/5.79 thf(fact_3405_finite__psubset__induct,axiom,
% 5.52/5.79 ! [A2: set_int,P: set_int > $o] :
% 5.52/5.79 ( ( finite_finite_int @ A2 )
% 5.52/5.79 => ( ! [A7: set_int] :
% 5.52/5.79 ( ( finite_finite_int @ A7 )
% 5.52/5.79 => ( ! [B7: set_int] :
% 5.52/5.79 ( ( ord_less_set_int @ B7 @ A7 )
% 5.52/5.79 => ( P @ B7 ) )
% 5.52/5.79 => ( P @ A7 ) ) )
% 5.52/5.79 => ( P @ A2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_psubset_induct
% 5.52/5.79 thf(fact_3406_finite__psubset__induct,axiom,
% 5.52/5.79 ! [A2: set_complex,P: set_complex > $o] :
% 5.52/5.79 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.79 => ( ! [A7: set_complex] :
% 5.52/5.79 ( ( finite3207457112153483333omplex @ A7 )
% 5.52/5.79 => ( ! [B7: set_complex] :
% 5.52/5.79 ( ( ord_less_set_complex @ B7 @ A7 )
% 5.52/5.79 => ( P @ B7 ) )
% 5.52/5.79 => ( P @ A7 ) ) )
% 5.52/5.79 => ( P @ A2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_psubset_induct
% 5.52/5.79 thf(fact_3407_finite__psubset__induct,axiom,
% 5.52/5.79 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.52/5.79 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.79 => ( ! [A7: set_Extended_enat] :
% 5.52/5.79 ( ( finite4001608067531595151d_enat @ A7 )
% 5.52/5.79 => ( ! [B7: set_Extended_enat] :
% 5.52/5.79 ( ( ord_le2529575680413868914d_enat @ B7 @ A7 )
% 5.52/5.79 => ( P @ B7 ) )
% 5.52/5.79 => ( P @ A7 ) ) )
% 5.52/5.79 => ( P @ A2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_psubset_induct
% 5.52/5.79 thf(fact_3408_pos__zmod__mult__2,axiom,
% 5.52/5.79 ! [A: int,B: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.79 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.79 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % pos_zmod_mult_2
% 5.52/5.79 thf(fact_3409_neg__zmod__mult__2,axiom,
% 5.52/5.79 ! [A: int,B: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.79 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.79 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % neg_zmod_mult_2
% 5.52/5.79 thf(fact_3410_finite__has__minimal,axiom,
% 5.52/5.79 ! [A2: set_Extended_enat] :
% 5.52/5.79 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.79 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 5.52/5.79 => ? [X4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ X4 @ A2 )
% 5.52/5.79 & ! [Xa: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_le2932123472753598470d_enat @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal
% 5.52/5.79 thf(fact_3411_finite__has__minimal,axiom,
% 5.52/5.79 ! [A2: set_set_nat] :
% 5.52/5.79 ( ( finite1152437895449049373et_nat @ A2 )
% 5.52/5.79 => ( ( A2 != bot_bot_set_set_nat )
% 5.52/5.79 => ? [X4: set_nat] :
% 5.52/5.79 ( ( member_set_nat @ X4 @ A2 )
% 5.52/5.79 & ! [Xa: set_nat] :
% 5.52/5.79 ( ( member_set_nat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_set_nat @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal
% 5.52/5.79 thf(fact_3412_finite__has__minimal,axiom,
% 5.52/5.79 ! [A2: set_rat] :
% 5.52/5.79 ( ( finite_finite_rat @ A2 )
% 5.52/5.79 => ( ( A2 != bot_bot_set_rat )
% 5.52/5.79 => ? [X4: rat] :
% 5.52/5.79 ( ( member_rat @ X4 @ A2 )
% 5.52/5.79 & ! [Xa: rat] :
% 5.52/5.79 ( ( member_rat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_rat @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal
% 5.52/5.79 thf(fact_3413_finite__has__minimal,axiom,
% 5.52/5.79 ! [A2: set_num] :
% 5.52/5.79 ( ( finite_finite_num @ A2 )
% 5.52/5.79 => ( ( A2 != bot_bot_set_num )
% 5.52/5.79 => ? [X4: num] :
% 5.52/5.79 ( ( member_num @ X4 @ A2 )
% 5.52/5.79 & ! [Xa: num] :
% 5.52/5.79 ( ( member_num @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_num @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal
% 5.52/5.79 thf(fact_3414_finite__has__minimal,axiom,
% 5.52/5.79 ! [A2: set_nat] :
% 5.52/5.79 ( ( finite_finite_nat @ A2 )
% 5.52/5.79 => ( ( A2 != bot_bot_set_nat )
% 5.52/5.79 => ? [X4: nat] :
% 5.52/5.79 ( ( member_nat @ X4 @ A2 )
% 5.52/5.79 & ! [Xa: nat] :
% 5.52/5.79 ( ( member_nat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal
% 5.52/5.79 thf(fact_3415_finite__has__minimal,axiom,
% 5.52/5.79 ! [A2: set_int] :
% 5.52/5.79 ( ( finite_finite_int @ A2 )
% 5.52/5.79 => ( ( A2 != bot_bot_set_int )
% 5.52/5.79 => ? [X4: int] :
% 5.52/5.79 ( ( member_int @ X4 @ A2 )
% 5.52/5.79 & ! [Xa: int] :
% 5.52/5.79 ( ( member_int @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_int @ Xa @ X4 )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_minimal
% 5.52/5.79 thf(fact_3416_finite__has__maximal,axiom,
% 5.52/5.79 ! [A2: set_Extended_enat] :
% 5.52/5.79 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.79 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 5.52/5.79 => ? [X4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ X4 @ A2 )
% 5.52/5.79 & ! [Xa: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_le2932123472753598470d_enat @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal
% 5.52/5.79 thf(fact_3417_finite__has__maximal,axiom,
% 5.52/5.79 ! [A2: set_set_nat] :
% 5.52/5.79 ( ( finite1152437895449049373et_nat @ A2 )
% 5.52/5.79 => ( ( A2 != bot_bot_set_set_nat )
% 5.52/5.79 => ? [X4: set_nat] :
% 5.52/5.79 ( ( member_set_nat @ X4 @ A2 )
% 5.52/5.79 & ! [Xa: set_nat] :
% 5.52/5.79 ( ( member_set_nat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_set_nat @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal
% 5.52/5.79 thf(fact_3418_finite__has__maximal,axiom,
% 5.52/5.79 ! [A2: set_rat] :
% 5.52/5.79 ( ( finite_finite_rat @ A2 )
% 5.52/5.79 => ( ( A2 != bot_bot_set_rat )
% 5.52/5.79 => ? [X4: rat] :
% 5.52/5.79 ( ( member_rat @ X4 @ A2 )
% 5.52/5.79 & ! [Xa: rat] :
% 5.52/5.79 ( ( member_rat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_rat @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal
% 5.52/5.79 thf(fact_3419_finite__has__maximal,axiom,
% 5.52/5.79 ! [A2: set_num] :
% 5.52/5.79 ( ( finite_finite_num @ A2 )
% 5.52/5.79 => ( ( A2 != bot_bot_set_num )
% 5.52/5.79 => ? [X4: num] :
% 5.52/5.79 ( ( member_num @ X4 @ A2 )
% 5.52/5.79 & ! [Xa: num] :
% 5.52/5.79 ( ( member_num @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_num @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal
% 5.52/5.79 thf(fact_3420_finite__has__maximal,axiom,
% 5.52/5.79 ! [A2: set_nat] :
% 5.52/5.79 ( ( finite_finite_nat @ A2 )
% 5.52/5.79 => ( ( A2 != bot_bot_set_nat )
% 5.52/5.79 => ? [X4: nat] :
% 5.52/5.79 ( ( member_nat @ X4 @ A2 )
% 5.52/5.79 & ! [Xa: nat] :
% 5.52/5.79 ( ( member_nat @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal
% 5.52/5.79 thf(fact_3421_finite__has__maximal,axiom,
% 5.52/5.79 ! [A2: set_int] :
% 5.52/5.79 ( ( finite_finite_int @ A2 )
% 5.52/5.79 => ( ( A2 != bot_bot_set_int )
% 5.52/5.79 => ? [X4: int] :
% 5.52/5.79 ( ( member_int @ X4 @ A2 )
% 5.52/5.79 & ! [Xa: int] :
% 5.52/5.79 ( ( member_int @ Xa @ A2 )
% 5.52/5.79 => ( ( ord_less_eq_int @ X4 @ Xa )
% 5.52/5.79 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_has_maximal
% 5.52/5.79 thf(fact_3422_arcosh__1,axiom,
% 5.52/5.79 ( ( arcosh_real @ one_one_real )
% 5.52/5.79 = zero_zero_real ) ).
% 5.52/5.79
% 5.52/5.79 % arcosh_1
% 5.52/5.79 thf(fact_3423_finite__nth__roots,axiom,
% 5.52/5.79 ! [N: nat,C: complex] :
% 5.52/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.79 => ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [Z2: complex] :
% 5.52/5.79 ( ( power_power_complex @ Z2 @ N )
% 5.52/5.79 = C ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % finite_nth_roots
% 5.52/5.79 thf(fact_3424_product__nth,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_num,Ys: list_num] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_num @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 5.52/5.79 => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs2 @ Ys ) @ N )
% 5.52/5.79 = ( product_Pair_num_num @ ( nth_num @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % product_nth
% 5.52/5.79 thf(fact_3425_product__nth,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_int,Ys: list_int] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_int @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.52/5.79 => ( ( nth_Pr4439495888332055232nt_int @ ( product_int_int @ Xs2 @ Ys ) @ N )
% 5.52/5.79 = ( product_Pair_int_int @ ( nth_int @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % product_nth
% 5.52/5.79 thf(fact_3426_product__nth,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.52/5.79 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N )
% 5.52/5.79 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % product_nth
% 5.52/5.79 thf(fact_3427_product__nth,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.52/5.79 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N )
% 5.52/5.79 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % product_nth
% 5.52/5.79 thf(fact_3428_product__nth,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.52/5.79 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N )
% 5.52/5.79 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % product_nth
% 5.52/5.79 thf(fact_3429_product__nth,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.52/5.79 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N )
% 5.52/5.79 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % product_nth
% 5.52/5.79 thf(fact_3430_product__nth,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_o,Ys: list_o] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.52/5.79 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N )
% 5.52/5.79 = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % product_nth
% 5.52/5.79 thf(fact_3431_product__nth,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_o,Ys: list_nat] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.52/5.79 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N )
% 5.52/5.79 = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % product_nth
% 5.52/5.79 thf(fact_3432_product__nth,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_nat,Ys: list_num] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 5.52/5.79 => ( ( nth_Pr8326237132889035090at_num @ ( product_nat_num @ Xs2 @ Ys ) @ N )
% 5.52/5.79 = ( product_Pair_nat_num @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % product_nth
% 5.52/5.79 thf(fact_3433_product__nth,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.52/5.79 => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) @ N )
% 5.52/5.79 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % product_nth
% 5.52/5.79 thf(fact_3434_prod_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_real,X2: real > complex,Y2: real > complex] :
% 5.52/5.79 ( ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [I4: real] :
% 5.52/5.79 ( ( member_real @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != one_one_complex ) ) ) )
% 5.52/5.79 => ( ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [I4: real] :
% 5.52/5.79 ( ( member_real @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != one_one_complex ) ) ) )
% 5.52/5.79 => ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [I4: real] :
% 5.52/5.79 ( ( member_real @ I4 @ I5 )
% 5.52/5.79 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != one_one_complex ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % prod.finite_Collect_op
% 5.52/5.79 thf(fact_3435_prod_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_nat,X2: nat > complex,Y2: nat > complex] :
% 5.52/5.79 ( ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [I4: nat] :
% 5.52/5.79 ( ( member_nat @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != one_one_complex ) ) ) )
% 5.52/5.79 => ( ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [I4: nat] :
% 5.52/5.79 ( ( member_nat @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != one_one_complex ) ) ) )
% 5.52/5.79 => ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [I4: nat] :
% 5.52/5.79 ( ( member_nat @ I4 @ I5 )
% 5.52/5.79 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != one_one_complex ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % prod.finite_Collect_op
% 5.52/5.79 thf(fact_3436_prod_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_int,X2: int > complex,Y2: int > complex] :
% 5.52/5.79 ( ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( member_int @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != one_one_complex ) ) ) )
% 5.52/5.79 => ( ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( member_int @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != one_one_complex ) ) ) )
% 5.52/5.79 => ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( member_int @ I4 @ I5 )
% 5.52/5.79 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != one_one_complex ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % prod.finite_Collect_op
% 5.52/5.79 thf(fact_3437_prod_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_complex,X2: complex > complex,Y2: complex > complex] :
% 5.52/5.79 ( ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [I4: complex] :
% 5.52/5.79 ( ( member_complex @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != one_one_complex ) ) ) )
% 5.52/5.79 => ( ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [I4: complex] :
% 5.52/5.79 ( ( member_complex @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != one_one_complex ) ) ) )
% 5.52/5.79 => ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [I4: complex] :
% 5.52/5.79 ( ( member_complex @ I4 @ I5 )
% 5.52/5.79 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != one_one_complex ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % prod.finite_Collect_op
% 5.52/5.79 thf(fact_3438_prod_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_Extended_enat,X2: extended_enat > complex,Y2: extended_enat > complex] :
% 5.52/5.79 ( ( finite4001608067531595151d_enat
% 5.52/5.79 @ ( collec4429806609662206161d_enat
% 5.52/5.79 @ ^ [I4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != one_one_complex ) ) ) )
% 5.52/5.79 => ( ( finite4001608067531595151d_enat
% 5.52/5.79 @ ( collec4429806609662206161d_enat
% 5.52/5.79 @ ^ [I4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != one_one_complex ) ) ) )
% 5.52/5.79 => ( finite4001608067531595151d_enat
% 5.52/5.79 @ ( collec4429806609662206161d_enat
% 5.52/5.79 @ ^ [I4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ I4 @ I5 )
% 5.52/5.79 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != one_one_complex ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % prod.finite_Collect_op
% 5.52/5.79 thf(fact_3439_prod_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_real,X2: real > real,Y2: real > real] :
% 5.52/5.79 ( ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [I4: real] :
% 5.52/5.79 ( ( member_real @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != one_one_real ) ) ) )
% 5.52/5.79 => ( ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [I4: real] :
% 5.52/5.79 ( ( member_real @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != one_one_real ) ) ) )
% 5.52/5.79 => ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [I4: real] :
% 5.52/5.79 ( ( member_real @ I4 @ I5 )
% 5.52/5.79 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != one_one_real ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % prod.finite_Collect_op
% 5.52/5.79 thf(fact_3440_prod_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_nat,X2: nat > real,Y2: nat > real] :
% 5.52/5.79 ( ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [I4: nat] :
% 5.52/5.79 ( ( member_nat @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != one_one_real ) ) ) )
% 5.52/5.79 => ( ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [I4: nat] :
% 5.52/5.79 ( ( member_nat @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != one_one_real ) ) ) )
% 5.52/5.79 => ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [I4: nat] :
% 5.52/5.79 ( ( member_nat @ I4 @ I5 )
% 5.52/5.79 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != one_one_real ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % prod.finite_Collect_op
% 5.52/5.79 thf(fact_3441_prod_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_int,X2: int > real,Y2: int > real] :
% 5.52/5.79 ( ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( member_int @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != one_one_real ) ) ) )
% 5.52/5.79 => ( ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( member_int @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != one_one_real ) ) ) )
% 5.52/5.79 => ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( member_int @ I4 @ I5 )
% 5.52/5.79 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != one_one_real ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % prod.finite_Collect_op
% 5.52/5.79 thf(fact_3442_prod_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_complex,X2: complex > real,Y2: complex > real] :
% 5.52/5.79 ( ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [I4: complex] :
% 5.52/5.79 ( ( member_complex @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != one_one_real ) ) ) )
% 5.52/5.79 => ( ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [I4: complex] :
% 5.52/5.79 ( ( member_complex @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != one_one_real ) ) ) )
% 5.52/5.79 => ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [I4: complex] :
% 5.52/5.79 ( ( member_complex @ I4 @ I5 )
% 5.52/5.79 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != one_one_real ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % prod.finite_Collect_op
% 5.52/5.79 thf(fact_3443_prod_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_Extended_enat,X2: extended_enat > real,Y2: extended_enat > real] :
% 5.52/5.79 ( ( finite4001608067531595151d_enat
% 5.52/5.79 @ ( collec4429806609662206161d_enat
% 5.52/5.79 @ ^ [I4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != one_one_real ) ) ) )
% 5.52/5.79 => ( ( finite4001608067531595151d_enat
% 5.52/5.79 @ ( collec4429806609662206161d_enat
% 5.52/5.79 @ ^ [I4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != one_one_real ) ) ) )
% 5.52/5.79 => ( finite4001608067531595151d_enat
% 5.52/5.79 @ ( collec4429806609662206161d_enat
% 5.52/5.79 @ ^ [I4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ I4 @ I5 )
% 5.52/5.79 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != one_one_real ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % prod.finite_Collect_op
% 5.52/5.79 thf(fact_3444_sum_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_real,X2: real > complex,Y2: real > complex] :
% 5.52/5.79 ( ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [I4: real] :
% 5.52/5.79 ( ( member_real @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != zero_zero_complex ) ) ) )
% 5.52/5.79 => ( ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [I4: real] :
% 5.52/5.79 ( ( member_real @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != zero_zero_complex ) ) ) )
% 5.52/5.79 => ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [I4: real] :
% 5.52/5.79 ( ( member_real @ I4 @ I5 )
% 5.52/5.79 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != zero_zero_complex ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % sum.finite_Collect_op
% 5.52/5.79 thf(fact_3445_sum_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_nat,X2: nat > complex,Y2: nat > complex] :
% 5.52/5.79 ( ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [I4: nat] :
% 5.52/5.79 ( ( member_nat @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != zero_zero_complex ) ) ) )
% 5.52/5.79 => ( ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [I4: nat] :
% 5.52/5.79 ( ( member_nat @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != zero_zero_complex ) ) ) )
% 5.52/5.79 => ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [I4: nat] :
% 5.52/5.79 ( ( member_nat @ I4 @ I5 )
% 5.52/5.79 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != zero_zero_complex ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % sum.finite_Collect_op
% 5.52/5.79 thf(fact_3446_sum_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_int,X2: int > complex,Y2: int > complex] :
% 5.52/5.79 ( ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( member_int @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != zero_zero_complex ) ) ) )
% 5.52/5.79 => ( ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( member_int @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != zero_zero_complex ) ) ) )
% 5.52/5.79 => ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( member_int @ I4 @ I5 )
% 5.52/5.79 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != zero_zero_complex ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % sum.finite_Collect_op
% 5.52/5.79 thf(fact_3447_sum_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_complex,X2: complex > complex,Y2: complex > complex] :
% 5.52/5.79 ( ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [I4: complex] :
% 5.52/5.79 ( ( member_complex @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != zero_zero_complex ) ) ) )
% 5.52/5.79 => ( ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [I4: complex] :
% 5.52/5.79 ( ( member_complex @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != zero_zero_complex ) ) ) )
% 5.52/5.79 => ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [I4: complex] :
% 5.52/5.79 ( ( member_complex @ I4 @ I5 )
% 5.52/5.79 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != zero_zero_complex ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % sum.finite_Collect_op
% 5.52/5.79 thf(fact_3448_sum_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_Extended_enat,X2: extended_enat > complex,Y2: extended_enat > complex] :
% 5.52/5.79 ( ( finite4001608067531595151d_enat
% 5.52/5.79 @ ( collec4429806609662206161d_enat
% 5.52/5.79 @ ^ [I4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != zero_zero_complex ) ) ) )
% 5.52/5.79 => ( ( finite4001608067531595151d_enat
% 5.52/5.79 @ ( collec4429806609662206161d_enat
% 5.52/5.79 @ ^ [I4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != zero_zero_complex ) ) ) )
% 5.52/5.79 => ( finite4001608067531595151d_enat
% 5.52/5.79 @ ( collec4429806609662206161d_enat
% 5.52/5.79 @ ^ [I4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ I4 @ I5 )
% 5.52/5.79 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != zero_zero_complex ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % sum.finite_Collect_op
% 5.52/5.79 thf(fact_3449_sum_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_real,X2: real > real,Y2: real > real] :
% 5.52/5.79 ( ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [I4: real] :
% 5.52/5.79 ( ( member_real @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != zero_zero_real ) ) ) )
% 5.52/5.79 => ( ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [I4: real] :
% 5.52/5.79 ( ( member_real @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != zero_zero_real ) ) ) )
% 5.52/5.79 => ( finite_finite_real
% 5.52/5.79 @ ( collect_real
% 5.52/5.79 @ ^ [I4: real] :
% 5.52/5.79 ( ( member_real @ I4 @ I5 )
% 5.52/5.79 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % sum.finite_Collect_op
% 5.52/5.79 thf(fact_3450_sum_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_nat,X2: nat > real,Y2: nat > real] :
% 5.52/5.79 ( ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [I4: nat] :
% 5.52/5.79 ( ( member_nat @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != zero_zero_real ) ) ) )
% 5.52/5.79 => ( ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [I4: nat] :
% 5.52/5.79 ( ( member_nat @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != zero_zero_real ) ) ) )
% 5.52/5.79 => ( finite_finite_nat
% 5.52/5.79 @ ( collect_nat
% 5.52/5.79 @ ^ [I4: nat] :
% 5.52/5.79 ( ( member_nat @ I4 @ I5 )
% 5.52/5.79 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % sum.finite_Collect_op
% 5.52/5.79 thf(fact_3451_sum_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_int,X2: int > real,Y2: int > real] :
% 5.52/5.79 ( ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( member_int @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != zero_zero_real ) ) ) )
% 5.52/5.79 => ( ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( member_int @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != zero_zero_real ) ) ) )
% 5.52/5.79 => ( finite_finite_int
% 5.52/5.79 @ ( collect_int
% 5.52/5.79 @ ^ [I4: int] :
% 5.52/5.79 ( ( member_int @ I4 @ I5 )
% 5.52/5.79 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % sum.finite_Collect_op
% 5.52/5.79 thf(fact_3452_sum_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_complex,X2: complex > real,Y2: complex > real] :
% 5.52/5.79 ( ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [I4: complex] :
% 5.52/5.79 ( ( member_complex @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != zero_zero_real ) ) ) )
% 5.52/5.79 => ( ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [I4: complex] :
% 5.52/5.79 ( ( member_complex @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != zero_zero_real ) ) ) )
% 5.52/5.79 => ( finite3207457112153483333omplex
% 5.52/5.79 @ ( collect_complex
% 5.52/5.79 @ ^ [I4: complex] :
% 5.52/5.79 ( ( member_complex @ I4 @ I5 )
% 5.52/5.79 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % sum.finite_Collect_op
% 5.52/5.79 thf(fact_3453_sum_Ofinite__Collect__op,axiom,
% 5.52/5.79 ! [I5: set_Extended_enat,X2: extended_enat > real,Y2: extended_enat > real] :
% 5.52/5.79 ( ( finite4001608067531595151d_enat
% 5.52/5.79 @ ( collec4429806609662206161d_enat
% 5.52/5.79 @ ^ [I4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ I4 @ I5 )
% 5.52/5.79 & ( ( X2 @ I4 )
% 5.52/5.79 != zero_zero_real ) ) ) )
% 5.52/5.79 => ( ( finite4001608067531595151d_enat
% 5.52/5.79 @ ( collec4429806609662206161d_enat
% 5.52/5.79 @ ^ [I4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ I4 @ I5 )
% 5.52/5.79 & ( ( Y2 @ I4 )
% 5.52/5.79 != zero_zero_real ) ) ) )
% 5.52/5.79 => ( finite4001608067531595151d_enat
% 5.52/5.79 @ ( collec4429806609662206161d_enat
% 5.52/5.79 @ ^ [I4: extended_enat] :
% 5.52/5.79 ( ( member_Extended_enat @ I4 @ I5 )
% 5.52/5.79 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.52/5.79 != zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % sum.finite_Collect_op
% 5.52/5.79 thf(fact_3454_dbl__inc__simps_I3_J,axiom,
% 5.52/5.79 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.52/5.79 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_simps(3)
% 5.52/5.79 thf(fact_3455_dbl__inc__simps_I3_J,axiom,
% 5.52/5.79 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.52/5.79 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_simps(3)
% 5.52/5.79 thf(fact_3456_dbl__inc__simps_I3_J,axiom,
% 5.52/5.79 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.52/5.79 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_simps(3)
% 5.52/5.79 thf(fact_3457_dbl__inc__simps_I3_J,axiom,
% 5.52/5.79 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.52/5.79 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_simps(3)
% 5.52/5.79 thf(fact_3458_VEBT__internal_Oheight_Osimps_I1_J,axiom,
% 5.52/5.79 ! [A: $o,B: $o] :
% 5.52/5.79 ( ( vEBT_VEBT_height @ ( vEBT_Leaf @ A @ B ) )
% 5.52/5.79 = zero_zero_nat ) ).
% 5.52/5.79
% 5.52/5.79 % VEBT_internal.height.simps(1)
% 5.52/5.79 thf(fact_3459_dbl__inc__simps_I2_J,axiom,
% 5.52/5.79 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.52/5.79 = one_one_complex ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_simps(2)
% 5.52/5.79 thf(fact_3460_dbl__inc__simps_I2_J,axiom,
% 5.52/5.79 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.52/5.79 = one_one_real ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_simps(2)
% 5.52/5.79 thf(fact_3461_dbl__inc__simps_I2_J,axiom,
% 5.52/5.79 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.52/5.79 = one_one_rat ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_simps(2)
% 5.52/5.79 thf(fact_3462_dbl__inc__simps_I2_J,axiom,
% 5.52/5.79 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.52/5.79 = one_one_int ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_simps(2)
% 5.52/5.79 thf(fact_3463_dbl__inc__simps_I5_J,axiom,
% 5.52/5.79 ! [K: num] :
% 5.52/5.79 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.52/5.79 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_simps(5)
% 5.52/5.79 thf(fact_3464_dbl__inc__simps_I5_J,axiom,
% 5.52/5.79 ! [K: num] :
% 5.52/5.79 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.52/5.79 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_simps(5)
% 5.52/5.79 thf(fact_3465_dbl__inc__simps_I5_J,axiom,
% 5.52/5.79 ! [K: num] :
% 5.52/5.79 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.52/5.79 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_simps(5)
% 5.52/5.79 thf(fact_3466_dbl__inc__simps_I5_J,axiom,
% 5.52/5.79 ! [K: num] :
% 5.52/5.79 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.52/5.79 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_simps(5)
% 5.52/5.79 thf(fact_3467_length__product,axiom,
% 5.52/5.79 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.52/5.79 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 5.52/5.79 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % length_product
% 5.52/5.79 thf(fact_3468_length__product,axiom,
% 5.52/5.79 ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.52/5.79 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 5.52/5.79 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % length_product
% 5.52/5.79 thf(fact_3469_length__product,axiom,
% 5.52/5.79 ! [Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.52/5.79 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) )
% 5.52/5.79 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % length_product
% 5.52/5.79 thf(fact_3470_length__product,axiom,
% 5.52/5.79 ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.52/5.79 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 5.52/5.79 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % length_product
% 5.52/5.79 thf(fact_3471_length__product,axiom,
% 5.52/5.79 ! [Xs2: list_o,Ys: list_o] :
% 5.52/5.79 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 5.52/5.79 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % length_product
% 5.52/5.79 thf(fact_3472_length__product,axiom,
% 5.52/5.79 ! [Xs2: list_o,Ys: list_nat] :
% 5.52/5.79 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs2 @ Ys ) )
% 5.52/5.79 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % length_product
% 5.52/5.79 thf(fact_3473_length__product,axiom,
% 5.52/5.79 ! [Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.52/5.79 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) )
% 5.52/5.79 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % length_product
% 5.52/5.79 thf(fact_3474_length__product,axiom,
% 5.52/5.79 ! [Xs2: list_nat,Ys: list_o] :
% 5.52/5.79 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs2 @ Ys ) )
% 5.52/5.79 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % length_product
% 5.52/5.79 thf(fact_3475_length__product,axiom,
% 5.52/5.79 ! [Xs2: list_nat,Ys: list_nat] :
% 5.52/5.79 ( ( size_s5460976970255530739at_nat @ ( product_nat_nat @ Xs2 @ Ys ) )
% 5.52/5.79 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % length_product
% 5.52/5.79 thf(fact_3476_dbl__inc__def,axiom,
% 5.52/5.79 ( neg_nu8295874005876285629c_real
% 5.52/5.79 = ( ^ [X: real] : ( plus_plus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_def
% 5.52/5.79 thf(fact_3477_dbl__inc__def,axiom,
% 5.52/5.79 ( neg_nu5219082963157363817nc_rat
% 5.52/5.79 = ( ^ [X: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_def
% 5.52/5.79 thf(fact_3478_dbl__inc__def,axiom,
% 5.52/5.79 ( neg_nu5851722552734809277nc_int
% 5.52/5.79 = ( ^ [X: int] : ( plus_plus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_def
% 5.52/5.79 thf(fact_3479_dbl__inc__def,axiom,
% 5.52/5.79 ( neg_nu8557863876264182079omplex
% 5.52/5.79 = ( ^ [X: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_inc_def
% 5.52/5.79 thf(fact_3480_VEBT__internal_Oheight_Ocases,axiom,
% 5.52/5.79 ! [X2: vEBT_VEBT] :
% 5.52/5.79 ( ! [A3: $o,B2: $o] :
% 5.52/5.79 ( X2
% 5.52/5.79 != ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.79 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.79 ( X2
% 5.52/5.79 != ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % VEBT_internal.height.cases
% 5.52/5.79 thf(fact_3481_divmod__BitM__2__eq,axiom,
% 5.52/5.79 ! [M: num] :
% 5.52/5.79 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.52/5.79 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.52/5.79
% 5.52/5.79 % divmod_BitM_2_eq
% 5.52/5.79 thf(fact_3482_insert__simp__excp,axiom,
% 5.52/5.79 ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X2: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.52/5.79 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.52/5.79 => ( ( ord_less_nat @ X2 @ Mi )
% 5.52/5.79 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.52/5.79 => ( ( X2 != Ma )
% 5.52/5.79 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.52/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X2 @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % insert_simp_excp
% 5.52/5.79 thf(fact_3483_insert__simp__norm,axiom,
% 5.52/5.79 ! [X2: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.52/5.79 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.52/5.79 => ( ( ord_less_nat @ Mi @ X2 )
% 5.52/5.79 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.52/5.79 => ( ( X2 != Ma )
% 5.52/5.79 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.52/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X2 @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % insert_simp_norm
% 5.52/5.79 thf(fact_3484_gcd__nat__induct,axiom,
% 5.52/5.79 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.52/5.79 ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 5.52/5.79 => ( ! [M4: nat,N2: nat] :
% 5.52/5.79 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.52/5.79 => ( ( P @ N2 @ ( modulo_modulo_nat @ M4 @ N2 ) )
% 5.52/5.79 => ( P @ M4 @ N2 ) ) )
% 5.52/5.79 => ( P @ M @ N ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % gcd_nat_induct
% 5.52/5.79 thf(fact_3485_concat__bit__Suc,axiom,
% 5.52/5.79 ! [N: nat,K: int,L: int] :
% 5.52/5.79 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 5.52/5.79 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % concat_bit_Suc
% 5.52/5.79 thf(fact_3486_dbl__simps_I3_J,axiom,
% 5.52/5.79 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.52/5.79 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_simps(3)
% 5.52/5.79 thf(fact_3487_dbl__simps_I3_J,axiom,
% 5.52/5.79 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.52/5.79 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_simps(3)
% 5.52/5.79 thf(fact_3488_dbl__simps_I3_J,axiom,
% 5.52/5.79 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.52/5.79 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_simps(3)
% 5.52/5.79 thf(fact_3489_dbl__simps_I3_J,axiom,
% 5.52/5.79 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.52/5.79 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_simps(3)
% 5.52/5.79 thf(fact_3490_length__list__update,axiom,
% 5.52/5.79 ! [Xs2: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT] :
% 5.52/5.79 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) )
% 5.52/5.79 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % length_list_update
% 5.52/5.79 thf(fact_3491_length__list__update,axiom,
% 5.52/5.79 ! [Xs2: list_o,I: nat,X2: $o] :
% 5.52/5.79 ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I @ X2 ) )
% 5.52/5.79 = ( size_size_list_o @ Xs2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % length_list_update
% 5.52/5.79 thf(fact_3492_length__list__update,axiom,
% 5.52/5.79 ! [Xs2: list_nat,I: nat,X2: nat] :
% 5.52/5.79 ( ( size_size_list_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) )
% 5.52/5.79 = ( size_size_list_nat @ Xs2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % length_list_update
% 5.52/5.79 thf(fact_3493_max__Suc__Suc,axiom,
% 5.52/5.79 ! [M: nat,N: nat] :
% 5.52/5.79 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.52/5.79 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_Suc_Suc
% 5.52/5.79 thf(fact_3494_max__0R,axiom,
% 5.52/5.79 ! [N: nat] :
% 5.52/5.79 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.52/5.79 = N ) ).
% 5.52/5.79
% 5.52/5.79 % max_0R
% 5.52/5.79 thf(fact_3495_max__0L,axiom,
% 5.52/5.79 ! [N: nat] :
% 5.52/5.79 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.52/5.79 = N ) ).
% 5.52/5.79
% 5.52/5.79 % max_0L
% 5.52/5.79 thf(fact_3496_max__nat_Oright__neutral,axiom,
% 5.52/5.79 ! [A: nat] :
% 5.52/5.79 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.52/5.79 = A ) ).
% 5.52/5.79
% 5.52/5.79 % max_nat.right_neutral
% 5.52/5.79 thf(fact_3497_max__nat_Oneutr__eq__iff,axiom,
% 5.52/5.79 ! [A: nat,B: nat] :
% 5.52/5.79 ( ( zero_zero_nat
% 5.52/5.79 = ( ord_max_nat @ A @ B ) )
% 5.52/5.79 = ( ( A = zero_zero_nat )
% 5.52/5.79 & ( B = zero_zero_nat ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_nat.neutr_eq_iff
% 5.52/5.79 thf(fact_3498_max__nat_Oleft__neutral,axiom,
% 5.52/5.79 ! [A: nat] :
% 5.52/5.79 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.52/5.79 = A ) ).
% 5.52/5.79
% 5.52/5.79 % max_nat.left_neutral
% 5.52/5.79 thf(fact_3499_max__nat_Oeq__neutr__iff,axiom,
% 5.52/5.79 ! [A: nat,B: nat] :
% 5.52/5.79 ( ( ( ord_max_nat @ A @ B )
% 5.52/5.79 = zero_zero_nat )
% 5.52/5.79 = ( ( A = zero_zero_nat )
% 5.52/5.79 & ( B = zero_zero_nat ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_nat.eq_neutr_iff
% 5.52/5.79 thf(fact_3500_list__update__id,axiom,
% 5.52/5.79 ! [Xs2: list_nat,I: nat] :
% 5.52/5.79 ( ( list_update_nat @ Xs2 @ I @ ( nth_nat @ Xs2 @ I ) )
% 5.52/5.79 = Xs2 ) ).
% 5.52/5.79
% 5.52/5.79 % list_update_id
% 5.52/5.79 thf(fact_3501_list__update__id,axiom,
% 5.52/5.79 ! [Xs2: list_VEBT_VEBT,I: nat] :
% 5.52/5.79 ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 5.52/5.79 = Xs2 ) ).
% 5.52/5.79
% 5.52/5.79 % list_update_id
% 5.52/5.79 thf(fact_3502_nth__list__update__neq,axiom,
% 5.52/5.79 ! [I: nat,J: nat,Xs2: list_nat,X2: nat] :
% 5.52/5.79 ( ( I != J )
% 5.52/5.79 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) @ J )
% 5.52/5.79 = ( nth_nat @ Xs2 @ J ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % nth_list_update_neq
% 5.52/5.79 thf(fact_3503_nth__list__update__neq,axiom,
% 5.52/5.79 ! [I: nat,J: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.52/5.79 ( ( I != J )
% 5.52/5.79 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ J )
% 5.52/5.79 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % nth_list_update_neq
% 5.52/5.79 thf(fact_3504_concat__bit__0,axiom,
% 5.52/5.79 ! [K: int,L: int] :
% 5.52/5.79 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 5.52/5.79 = L ) ).
% 5.52/5.79
% 5.52/5.79 % concat_bit_0
% 5.52/5.79 thf(fact_3505_dbl__simps_I2_J,axiom,
% 5.52/5.79 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.52/5.79 = zero_zero_real ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_simps(2)
% 5.52/5.79 thf(fact_3506_dbl__simps_I2_J,axiom,
% 5.52/5.79 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.52/5.79 = zero_zero_rat ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_simps(2)
% 5.52/5.79 thf(fact_3507_dbl__simps_I2_J,axiom,
% 5.52/5.79 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.52/5.79 = zero_zero_int ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_simps(2)
% 5.52/5.79 thf(fact_3508_max__number__of_I1_J,axiom,
% 5.52/5.79 ! [U: num,V: num] :
% 5.52/5.79 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.52/5.79 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.52/5.79 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.52/5.79 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.52/5.79 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.52/5.79 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_number_of(1)
% 5.52/5.79 thf(fact_3509_max__number__of_I1_J,axiom,
% 5.52/5.79 ! [U: num,V: num] :
% 5.52/5.79 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.52/5.79 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.52/5.79 = ( numeral_numeral_real @ V ) ) )
% 5.52/5.79 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.52/5.79 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.52/5.79 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_number_of(1)
% 5.52/5.79 thf(fact_3510_max__number__of_I1_J,axiom,
% 5.52/5.79 ! [U: num,V: num] :
% 5.52/5.79 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.52/5.79 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.52/5.79 = ( numeral_numeral_rat @ V ) ) )
% 5.52/5.79 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.52/5.79 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.52/5.79 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_number_of(1)
% 5.52/5.79 thf(fact_3511_max__number__of_I1_J,axiom,
% 5.52/5.79 ! [U: num,V: num] :
% 5.52/5.79 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.52/5.79 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.52/5.79 = ( numeral_numeral_nat @ V ) ) )
% 5.52/5.79 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.52/5.79 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.52/5.79 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_number_of(1)
% 5.52/5.79 thf(fact_3512_max__number__of_I1_J,axiom,
% 5.52/5.79 ! [U: num,V: num] :
% 5.52/5.79 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.79 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.79 = ( numeral_numeral_int @ V ) ) )
% 5.52/5.79 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.79 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.79 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_number_of(1)
% 5.52/5.79 thf(fact_3513_max__0__1_I4_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X2 ) @ zero_z5237406670263579293d_enat )
% 5.52/5.79 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(4)
% 5.52/5.79 thf(fact_3514_max__0__1_I4_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_real @ ( numeral_numeral_real @ X2 ) @ zero_zero_real )
% 5.52/5.79 = ( numeral_numeral_real @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(4)
% 5.52/5.79 thf(fact_3515_max__0__1_I4_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_rat @ ( numeral_numeral_rat @ X2 ) @ zero_zero_rat )
% 5.52/5.79 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(4)
% 5.52/5.79 thf(fact_3516_max__0__1_I4_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_nat @ ( numeral_numeral_nat @ X2 ) @ zero_zero_nat )
% 5.52/5.79 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(4)
% 5.52/5.79 thf(fact_3517_max__0__1_I4_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_int @ ( numeral_numeral_int @ X2 ) @ zero_zero_int )
% 5.52/5.79 = ( numeral_numeral_int @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(4)
% 5.52/5.79 thf(fact_3518_max__0__1_I3_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X2 ) )
% 5.52/5.79 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(3)
% 5.52/5.79 thf(fact_3519_max__0__1_I3_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X2 ) )
% 5.52/5.79 = ( numeral_numeral_real @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(3)
% 5.52/5.79 thf(fact_3520_max__0__1_I3_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.52/5.79 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(3)
% 5.52/5.79 thf(fact_3521_max__0__1_I3_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.52/5.79 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(3)
% 5.52/5.79 thf(fact_3522_max__0__1_I3_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X2 ) )
% 5.52/5.79 = ( numeral_numeral_int @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(3)
% 5.52/5.79 thf(fact_3523_max__0__1_I2_J,axiom,
% 5.52/5.79 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.52/5.79 = one_one_real ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(2)
% 5.52/5.79 thf(fact_3524_max__0__1_I2_J,axiom,
% 5.52/5.79 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.52/5.79 = one_one_rat ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(2)
% 5.52/5.79 thf(fact_3525_max__0__1_I2_J,axiom,
% 5.52/5.79 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.52/5.79 = one_one_nat ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(2)
% 5.52/5.79 thf(fact_3526_max__0__1_I2_J,axiom,
% 5.52/5.79 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 5.52/5.79 = one_on7984719198319812577d_enat ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(2)
% 5.52/5.79 thf(fact_3527_max__0__1_I2_J,axiom,
% 5.52/5.79 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.52/5.79 = one_one_int ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(2)
% 5.52/5.79 thf(fact_3528_max__0__1_I1_J,axiom,
% 5.52/5.79 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.52/5.79 = one_one_real ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(1)
% 5.52/5.79 thf(fact_3529_max__0__1_I1_J,axiom,
% 5.52/5.79 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.52/5.79 = one_one_rat ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(1)
% 5.52/5.79 thf(fact_3530_max__0__1_I1_J,axiom,
% 5.52/5.79 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.52/5.79 = one_one_nat ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(1)
% 5.52/5.79 thf(fact_3531_max__0__1_I1_J,axiom,
% 5.52/5.79 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 5.52/5.79 = one_on7984719198319812577d_enat ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(1)
% 5.52/5.79 thf(fact_3532_max__0__1_I1_J,axiom,
% 5.52/5.79 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.52/5.79 = one_one_int ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(1)
% 5.52/5.79 thf(fact_3533_max__0__1_I5_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X2 ) )
% 5.52/5.79 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(5)
% 5.52/5.79 thf(fact_3534_max__0__1_I5_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 5.52/5.79 = ( numeral_numeral_real @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(5)
% 5.52/5.79 thf(fact_3535_max__0__1_I5_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.52/5.79 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(5)
% 5.52/5.79 thf(fact_3536_max__0__1_I5_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.52/5.79 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(5)
% 5.52/5.79 thf(fact_3537_max__0__1_I5_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 5.52/5.79 = ( numeral_numeral_int @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(5)
% 5.52/5.79 thf(fact_3538_max__0__1_I6_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X2 ) @ one_on7984719198319812577d_enat )
% 5.52/5.79 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(6)
% 5.52/5.79 thf(fact_3539_max__0__1_I6_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_real @ ( numeral_numeral_real @ X2 ) @ one_one_real )
% 5.52/5.79 = ( numeral_numeral_real @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(6)
% 5.52/5.79 thf(fact_3540_max__0__1_I6_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat )
% 5.52/5.79 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(6)
% 5.52/5.79 thf(fact_3541_max__0__1_I6_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat )
% 5.52/5.79 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(6)
% 5.52/5.79 thf(fact_3542_max__0__1_I6_J,axiom,
% 5.52/5.79 ! [X2: num] :
% 5.52/5.79 ( ( ord_max_int @ ( numeral_numeral_int @ X2 ) @ one_one_int )
% 5.52/5.79 = ( numeral_numeral_int @ X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_0_1(6)
% 5.52/5.79 thf(fact_3543_list__update__beyond,axiom,
% 5.52/5.79 ! [Xs2: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT] :
% 5.52/5.79 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I )
% 5.52/5.79 => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 )
% 5.52/5.79 = Xs2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % list_update_beyond
% 5.52/5.79 thf(fact_3544_list__update__beyond,axiom,
% 5.52/5.79 ! [Xs2: list_o,I: nat,X2: $o] :
% 5.52/5.79 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I )
% 5.52/5.79 => ( ( list_update_o @ Xs2 @ I @ X2 )
% 5.52/5.79 = Xs2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % list_update_beyond
% 5.52/5.79 thf(fact_3545_list__update__beyond,axiom,
% 5.52/5.79 ! [Xs2: list_nat,I: nat,X2: nat] :
% 5.52/5.79 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I )
% 5.52/5.79 => ( ( list_update_nat @ Xs2 @ I @ X2 )
% 5.52/5.79 = Xs2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % list_update_beyond
% 5.52/5.79 thf(fact_3546_concat__bit__nonnegative__iff,axiom,
% 5.52/5.79 ! [N: nat,K: int,L: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 5.52/5.79 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 5.52/5.79
% 5.52/5.79 % concat_bit_nonnegative_iff
% 5.52/5.79 thf(fact_3547_concat__bit__negative__iff,axiom,
% 5.52/5.79 ! [N: nat,K: int,L: int] :
% 5.52/5.79 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 5.52/5.79 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 5.52/5.79
% 5.52/5.79 % concat_bit_negative_iff
% 5.52/5.79 thf(fact_3548_dbl__simps_I5_J,axiom,
% 5.52/5.79 ! [K: num] :
% 5.52/5.79 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.52/5.79 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_simps(5)
% 5.52/5.79 thf(fact_3549_dbl__simps_I5_J,axiom,
% 5.52/5.79 ! [K: num] :
% 5.52/5.79 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.52/5.79 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_simps(5)
% 5.52/5.79 thf(fact_3550_dbl__simps_I5_J,axiom,
% 5.52/5.79 ! [K: num] :
% 5.52/5.79 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 5.52/5.79 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_simps(5)
% 5.52/5.79 thf(fact_3551_dbl__simps_I5_J,axiom,
% 5.52/5.79 ! [K: num] :
% 5.52/5.79 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.52/5.79 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_simps(5)
% 5.52/5.79 thf(fact_3552_nth__list__update__eq,axiom,
% 5.52/5.79 ! [I: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.52/5.79 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.52/5.79 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ I )
% 5.52/5.79 = X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % nth_list_update_eq
% 5.52/5.79 thf(fact_3553_nth__list__update__eq,axiom,
% 5.52/5.79 ! [I: nat,Xs2: list_o,X2: $o] :
% 5.52/5.79 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.52/5.79 => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X2 ) @ I )
% 5.52/5.79 = X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % nth_list_update_eq
% 5.52/5.79 thf(fact_3554_nth__list__update__eq,axiom,
% 5.52/5.79 ! [I: nat,Xs2: list_nat,X2: nat] :
% 5.52/5.79 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.52/5.79 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) @ I )
% 5.52/5.79 = X2 ) ) ).
% 5.52/5.79
% 5.52/5.79 % nth_list_update_eq
% 5.52/5.79 thf(fact_3555_set__swap,axiom,
% 5.52/5.79 ! [I: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 5.52/5.79 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.52/5.79 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.52/5.79 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I ) ) )
% 5.52/5.79 = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % set_swap
% 5.52/5.79 thf(fact_3556_set__swap,axiom,
% 5.52/5.79 ! [I: nat,Xs2: list_o,J: nat] :
% 5.52/5.79 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.52/5.79 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 5.52/5.79 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I ) ) )
% 5.52/5.79 = ( set_o2 @ Xs2 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % set_swap
% 5.52/5.79 thf(fact_3557_set__swap,axiom,
% 5.52/5.79 ! [I: nat,Xs2: list_nat,J: nat] :
% 5.52/5.79 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.52/5.79 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 5.52/5.79 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I ) ) )
% 5.52/5.79 = ( set_nat2 @ Xs2 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % set_swap
% 5.52/5.79 thf(fact_3558_max__add__distrib__right,axiom,
% 5.52/5.79 ! [X2: real,Y2: real,Z: real] :
% 5.52/5.79 ( ( plus_plus_real @ X2 @ ( ord_max_real @ Y2 @ Z ) )
% 5.52/5.79 = ( ord_max_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( plus_plus_real @ X2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_add_distrib_right
% 5.52/5.79 thf(fact_3559_max__add__distrib__right,axiom,
% 5.52/5.79 ! [X2: rat,Y2: rat,Z: rat] :
% 5.52/5.79 ( ( plus_plus_rat @ X2 @ ( ord_max_rat @ Y2 @ Z ) )
% 5.52/5.79 = ( ord_max_rat @ ( plus_plus_rat @ X2 @ Y2 ) @ ( plus_plus_rat @ X2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_add_distrib_right
% 5.52/5.79 thf(fact_3560_max__add__distrib__right,axiom,
% 5.52/5.79 ! [X2: nat,Y2: nat,Z: nat] :
% 5.52/5.79 ( ( plus_plus_nat @ X2 @ ( ord_max_nat @ Y2 @ Z ) )
% 5.52/5.79 = ( ord_max_nat @ ( plus_plus_nat @ X2 @ Y2 ) @ ( plus_plus_nat @ X2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_add_distrib_right
% 5.52/5.79 thf(fact_3561_max__add__distrib__right,axiom,
% 5.52/5.79 ! [X2: int,Y2: int,Z: int] :
% 5.52/5.79 ( ( plus_plus_int @ X2 @ ( ord_max_int @ Y2 @ Z ) )
% 5.52/5.79 = ( ord_max_int @ ( plus_plus_int @ X2 @ Y2 ) @ ( plus_plus_int @ X2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_add_distrib_right
% 5.52/5.79 thf(fact_3562_max__add__distrib__left,axiom,
% 5.52/5.79 ! [X2: real,Y2: real,Z: real] :
% 5.52/5.79 ( ( plus_plus_real @ ( ord_max_real @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ord_max_real @ ( plus_plus_real @ X2 @ Z ) @ ( plus_plus_real @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_add_distrib_left
% 5.52/5.79 thf(fact_3563_max__add__distrib__left,axiom,
% 5.52/5.79 ! [X2: rat,Y2: rat,Z: rat] :
% 5.52/5.79 ( ( plus_plus_rat @ ( ord_max_rat @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ord_max_rat @ ( plus_plus_rat @ X2 @ Z ) @ ( plus_plus_rat @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_add_distrib_left
% 5.52/5.79 thf(fact_3564_max__add__distrib__left,axiom,
% 5.52/5.79 ! [X2: nat,Y2: nat,Z: nat] :
% 5.52/5.79 ( ( plus_plus_nat @ ( ord_max_nat @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ord_max_nat @ ( plus_plus_nat @ X2 @ Z ) @ ( plus_plus_nat @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_add_distrib_left
% 5.52/5.79 thf(fact_3565_max__add__distrib__left,axiom,
% 5.52/5.79 ! [X2: int,Y2: int,Z: int] :
% 5.52/5.79 ( ( plus_plus_int @ ( ord_max_int @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ord_max_int @ ( plus_plus_int @ X2 @ Z ) @ ( plus_plus_int @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_add_distrib_left
% 5.52/5.79 thf(fact_3566_max__diff__distrib__left,axiom,
% 5.52/5.79 ! [X2: real,Y2: real,Z: real] :
% 5.52/5.79 ( ( minus_minus_real @ ( ord_max_real @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ord_max_real @ ( minus_minus_real @ X2 @ Z ) @ ( minus_minus_real @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_diff_distrib_left
% 5.52/5.79 thf(fact_3567_max__diff__distrib__left,axiom,
% 5.52/5.79 ! [X2: rat,Y2: rat,Z: rat] :
% 5.52/5.79 ( ( minus_minus_rat @ ( ord_max_rat @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ord_max_rat @ ( minus_minus_rat @ X2 @ Z ) @ ( minus_minus_rat @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_diff_distrib_left
% 5.52/5.79 thf(fact_3568_max__diff__distrib__left,axiom,
% 5.52/5.79 ! [X2: int,Y2: int,Z: int] :
% 5.52/5.79 ( ( minus_minus_int @ ( ord_max_int @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ord_max_int @ ( minus_minus_int @ X2 @ Z ) @ ( minus_minus_int @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_diff_distrib_left
% 5.52/5.79 thf(fact_3569_nat__add__max__right,axiom,
% 5.52/5.79 ! [M: nat,N: nat,Q2: nat] :
% 5.52/5.79 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.52/5.79 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % nat_add_max_right
% 5.52/5.79 thf(fact_3570_nat__add__max__left,axiom,
% 5.52/5.79 ! [M: nat,N: nat,Q2: nat] :
% 5.52/5.79 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.52/5.79 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % nat_add_max_left
% 5.52/5.79 thf(fact_3571_nat__mult__max__right,axiom,
% 5.52/5.79 ! [M: nat,N: nat,Q2: nat] :
% 5.52/5.79 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.52/5.79 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % nat_mult_max_right
% 5.52/5.79 thf(fact_3572_nat__mult__max__left,axiom,
% 5.52/5.79 ! [M: nat,N: nat,Q2: nat] :
% 5.52/5.79 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.52/5.79 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % nat_mult_max_left
% 5.52/5.79 thf(fact_3573_semiring__norm_I26_J,axiom,
% 5.52/5.79 ( ( bitM @ one )
% 5.52/5.79 = one ) ).
% 5.52/5.79
% 5.52/5.79 % semiring_norm(26)
% 5.52/5.79 thf(fact_3574_max__def__raw,axiom,
% 5.52/5.79 ( ord_ma741700101516333627d_enat
% 5.52/5.79 = ( ^ [A4: extended_enat,B3: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_def_raw
% 5.52/5.79 thf(fact_3575_max__def__raw,axiom,
% 5.52/5.79 ( ord_max_set_nat
% 5.52/5.79 = ( ^ [A4: set_nat,B3: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_def_raw
% 5.52/5.79 thf(fact_3576_max__def__raw,axiom,
% 5.52/5.79 ( ord_max_rat
% 5.52/5.79 = ( ^ [A4: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_def_raw
% 5.52/5.79 thf(fact_3577_max__def__raw,axiom,
% 5.52/5.79 ( ord_max_num
% 5.52/5.79 = ( ^ [A4: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_def_raw
% 5.52/5.79 thf(fact_3578_max__def__raw,axiom,
% 5.52/5.79 ( ord_max_nat
% 5.52/5.79 = ( ^ [A4: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_def_raw
% 5.52/5.79 thf(fact_3579_max__def__raw,axiom,
% 5.52/5.79 ( ord_max_int
% 5.52/5.79 = ( ^ [A4: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_def_raw
% 5.52/5.79 thf(fact_3580_concat__bit__assoc,axiom,
% 5.52/5.79 ! [N: nat,K: int,M: nat,L: int,R: int] :
% 5.52/5.79 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L @ R ) )
% 5.52/5.79 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L ) @ R ) ) ).
% 5.52/5.79
% 5.52/5.79 % concat_bit_assoc
% 5.52/5.79 thf(fact_3581_nat__minus__add__max,axiom,
% 5.52/5.79 ! [N: nat,M: nat] :
% 5.52/5.79 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 5.52/5.79 = ( ord_max_nat @ N @ M ) ) ).
% 5.52/5.79
% 5.52/5.79 % nat_minus_add_max
% 5.52/5.79 thf(fact_3582_dbl__def,axiom,
% 5.52/5.79 ( neg_numeral_dbl_real
% 5.52/5.79 = ( ^ [X: real] : ( plus_plus_real @ X @ X ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_def
% 5.52/5.79 thf(fact_3583_dbl__def,axiom,
% 5.52/5.79 ( neg_numeral_dbl_rat
% 5.52/5.79 = ( ^ [X: rat] : ( plus_plus_rat @ X @ X ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_def
% 5.52/5.79 thf(fact_3584_dbl__def,axiom,
% 5.52/5.79 ( neg_numeral_dbl_int
% 5.52/5.79 = ( ^ [X: int] : ( plus_plus_int @ X @ X ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_def
% 5.52/5.79 thf(fact_3585_dbl__def,axiom,
% 5.52/5.79 ( neg_nu7009210354673126013omplex
% 5.52/5.79 = ( ^ [X: complex] : ( plus_plus_complex @ X @ X ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % dbl_def
% 5.52/5.79 thf(fact_3586_semiring__norm_I27_J,axiom,
% 5.52/5.79 ! [N: num] :
% 5.52/5.79 ( ( bitM @ ( bit0 @ N ) )
% 5.52/5.79 = ( bit1 @ ( bitM @ N ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % semiring_norm(27)
% 5.52/5.79 thf(fact_3587_semiring__norm_I28_J,axiom,
% 5.52/5.79 ! [N: num] :
% 5.52/5.79 ( ( bitM @ ( bit1 @ N ) )
% 5.52/5.79 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % semiring_norm(28)
% 5.52/5.79 thf(fact_3588_set__update__memI,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_option_nat,X2: option_nat] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 5.52/5.79 => ( member_option_nat @ X2 @ ( set_option_nat2 @ ( list_u3411377215356412978on_nat @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % set_update_memI
% 5.52/5.79 thf(fact_3589_set__update__memI,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_real,X2: real] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.52/5.79 => ( member_real @ X2 @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % set_update_memI
% 5.52/5.79 thf(fact_3590_set__update__memI,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_set_nat_rat,X2: set_nat_rat] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( size_s3959913991096427681at_rat @ Xs2 ) )
% 5.52/5.79 => ( member_set_nat_rat @ X2 @ ( set_set_nat_rat2 @ ( list_u886106648575569423at_rat @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % set_update_memI
% 5.52/5.79 thf(fact_3591_set__update__memI,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_int,X2: int] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.52/5.79 => ( member_int @ X2 @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % set_update_memI
% 5.52/5.79 thf(fact_3592_set__update__memI,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.52/5.79 => ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % set_update_memI
% 5.52/5.79 thf(fact_3593_set__update__memI,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_o,X2: $o] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.52/5.79 => ( member_o @ X2 @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % set_update_memI
% 5.52/5.79 thf(fact_3594_set__update__memI,axiom,
% 5.52/5.79 ! [N: nat,Xs2: list_nat,X2: nat] :
% 5.52/5.79 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.52/5.79 => ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % set_update_memI
% 5.52/5.79 thf(fact_3595_list__update__same__conv,axiom,
% 5.52/5.79 ! [I: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.52/5.79 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.52/5.79 => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 )
% 5.52/5.79 = Xs2 )
% 5.52/5.79 = ( ( nth_VEBT_VEBT @ Xs2 @ I )
% 5.52/5.79 = X2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % list_update_same_conv
% 5.52/5.79 thf(fact_3596_list__update__same__conv,axiom,
% 5.52/5.79 ! [I: nat,Xs2: list_o,X2: $o] :
% 5.52/5.79 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.52/5.79 => ( ( ( list_update_o @ Xs2 @ I @ X2 )
% 5.52/5.79 = Xs2 )
% 5.52/5.79 = ( ( nth_o @ Xs2 @ I )
% 5.52/5.79 = X2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % list_update_same_conv
% 5.52/5.79 thf(fact_3597_list__update__same__conv,axiom,
% 5.52/5.79 ! [I: nat,Xs2: list_nat,X2: nat] :
% 5.52/5.79 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.52/5.79 => ( ( ( list_update_nat @ Xs2 @ I @ X2 )
% 5.52/5.79 = Xs2 )
% 5.52/5.79 = ( ( nth_nat @ Xs2 @ I )
% 5.52/5.79 = X2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % list_update_same_conv
% 5.52/5.79 thf(fact_3598_nth__list__update,axiom,
% 5.52/5.79 ! [I: nat,Xs2: list_VEBT_VEBT,J: nat,X2: vEBT_VEBT] :
% 5.52/5.79 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.52/5.79 => ( ( ( I = J )
% 5.52/5.79 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ J )
% 5.52/5.79 = X2 ) )
% 5.52/5.79 & ( ( I != J )
% 5.52/5.79 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ J )
% 5.52/5.79 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % nth_list_update
% 5.52/5.79 thf(fact_3599_nth__list__update,axiom,
% 5.52/5.79 ! [I: nat,Xs2: list_o,X2: $o,J: nat] :
% 5.52/5.79 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.52/5.79 => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X2 ) @ J )
% 5.52/5.79 = ( ( ( I = J )
% 5.52/5.79 => X2 )
% 5.52/5.79 & ( ( I != J )
% 5.52/5.79 => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % nth_list_update
% 5.52/5.79 thf(fact_3600_nth__list__update,axiom,
% 5.52/5.79 ! [I: nat,Xs2: list_nat,J: nat,X2: nat] :
% 5.52/5.79 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.52/5.79 => ( ( ( I = J )
% 5.52/5.79 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) @ J )
% 5.52/5.79 = X2 ) )
% 5.52/5.79 & ( ( I != J )
% 5.52/5.79 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) @ J )
% 5.52/5.79 = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % nth_list_update
% 5.52/5.79 thf(fact_3601_eval__nat__numeral_I2_J,axiom,
% 5.52/5.79 ! [N: num] :
% 5.52/5.79 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.52/5.79 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % eval_nat_numeral(2)
% 5.52/5.79 thf(fact_3602_one__plus__BitM,axiom,
% 5.52/5.79 ! [N: num] :
% 5.52/5.79 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.52/5.79 = ( bit0 @ N ) ) ).
% 5.52/5.79
% 5.52/5.79 % one_plus_BitM
% 5.52/5.79 thf(fact_3603_BitM__plus__one,axiom,
% 5.52/5.79 ! [N: num] :
% 5.52/5.79 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.52/5.79 = ( bit0 @ N ) ) ).
% 5.52/5.79
% 5.52/5.79 % BitM_plus_one
% 5.52/5.79 thf(fact_3604_numeral__BitM,axiom,
% 5.52/5.79 ! [N: num] :
% 5.52/5.79 ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 5.52/5.79 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 5.52/5.79
% 5.52/5.79 % numeral_BitM
% 5.52/5.79 thf(fact_3605_numeral__BitM,axiom,
% 5.52/5.79 ! [N: num] :
% 5.52/5.79 ( ( numeral_numeral_real @ ( bitM @ N ) )
% 5.52/5.79 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 5.52/5.79
% 5.52/5.79 % numeral_BitM
% 5.52/5.79 thf(fact_3606_numeral__BitM,axiom,
% 5.52/5.79 ! [N: num] :
% 5.52/5.79 ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 5.52/5.79 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 5.52/5.79
% 5.52/5.79 % numeral_BitM
% 5.52/5.79 thf(fact_3607_numeral__BitM,axiom,
% 5.52/5.79 ! [N: num] :
% 5.52/5.79 ( ( numeral_numeral_int @ ( bitM @ N ) )
% 5.52/5.79 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 5.52/5.79
% 5.52/5.79 % numeral_BitM
% 5.52/5.79 thf(fact_3608_Euclid__induct,axiom,
% 5.52/5.79 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.52/5.79 ( ! [A3: nat,B2: nat] :
% 5.52/5.79 ( ( P @ A3 @ B2 )
% 5.52/5.79 = ( P @ B2 @ A3 ) )
% 5.52/5.79 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 5.52/5.79 => ( ! [A3: nat,B2: nat] :
% 5.52/5.79 ( ( P @ A3 @ B2 )
% 5.52/5.79 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B2 ) ) )
% 5.52/5.79 => ( P @ A @ B ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % Euclid_induct
% 5.52/5.79 thf(fact_3609_vebt__insert_Osimps_I5_J,axiom,
% 5.52/5.79 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.52/5.79 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.52/5.79 = ( if_VEBT_VEBT
% 5.52/5.79 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.52/5.79 & ~ ( ( X2 = Mi )
% 5.52/5.79 | ( X2 = Ma ) ) )
% 5.52/5.79 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ X2 @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.52/5.79 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % vebt_insert.simps(5)
% 5.52/5.79 thf(fact_3610_vebt__insert_Oelims,axiom,
% 5.52/5.79 ! [X2: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 5.52/5.79 ( ( ( vEBT_vebt_insert @ X2 @ Xa2 )
% 5.52/5.79 = Y2 )
% 5.52/5.79 => ( ! [A3: $o,B2: $o] :
% 5.52/5.79 ( ( X2
% 5.52/5.79 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.79 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.79 => ( Y2
% 5.52/5.79 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 5.52/5.79 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.79 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.79 => ( Y2
% 5.52/5.79 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.52/5.79 & ( ( Xa2 != one_one_nat )
% 5.52/5.79 => ( Y2
% 5.52/5.79 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ) ) )
% 5.52/5.79 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.79 ( ( X2
% 5.52/5.79 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.52/5.79 => ( Y2
% 5.52/5.79 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) ) )
% 5.52/5.79 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.79 ( ( X2
% 5.52/5.79 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.52/5.79 => ( Y2
% 5.52/5.79 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) ) )
% 5.52/5.79 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.79 ( ( X2
% 5.52/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.79 => ( Y2
% 5.52/5.79 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) ) )
% 5.52/5.79 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.79 ( ( X2
% 5.52/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.79 => ( Y2
% 5.52/5.79 != ( if_VEBT_VEBT
% 5.52/5.79 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.79 & ~ ( ( Xa2 = Mi2 )
% 5.52/5.79 | ( Xa2 = Ma2 ) ) )
% 5.52/5.79 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.52/5.79 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % vebt_insert.elims
% 5.52/5.79 thf(fact_3611_vebt__insert_Opelims,axiom,
% 5.52/5.79 ! [X2: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 5.52/5.79 ( ( ( vEBT_vebt_insert @ X2 @ Xa2 )
% 5.52/5.79 = Y2 )
% 5.52/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.79 => ( ! [A3: $o,B2: $o] :
% 5.52/5.79 ( ( X2
% 5.52/5.79 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.79 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.79 => ( Y2
% 5.52/5.79 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 5.52/5.79 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.79 => ( ( ( Xa2 = one_one_nat )
% 5.52/5.79 => ( Y2
% 5.52/5.79 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.52/5.79 & ( ( Xa2 != one_one_nat )
% 5.52/5.79 => ( Y2
% 5.52/5.79 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ) )
% 5.52/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.52/5.79 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.79 ( ( X2
% 5.52/5.79 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.52/5.79 => ( ( Y2
% 5.52/5.79 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.52/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.52/5.79 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.52/5.79 ( ( X2
% 5.52/5.79 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.52/5.79 => ( ( Y2
% 5.52/5.79 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.52/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.52/5.79 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.79 ( ( X2
% 5.52/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.79 => ( ( Y2
% 5.52/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 5.52/5.79 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.79 ( ( X2
% 5.52/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.52/5.79 => ( ( Y2
% 5.52/5.79 = ( if_VEBT_VEBT
% 5.52/5.79 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.52/5.79 & ~ ( ( Xa2 = Mi2 )
% 5.52/5.79 | ( Xa2 = Ma2 ) ) )
% 5.52/5.79 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.52/5.79 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) ) )
% 5.52/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % vebt_insert.pelims
% 5.52/5.79 thf(fact_3612_max_Oabsorb3,axiom,
% 5.52/5.79 ! [B: extended_enat,A: extended_enat] :
% 5.52/5.79 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.52/5.79 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.52/5.79 = A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb3
% 5.52/5.79 thf(fact_3613_max_Oabsorb3,axiom,
% 5.52/5.79 ! [B: real,A: real] :
% 5.52/5.79 ( ( ord_less_real @ B @ A )
% 5.52/5.79 => ( ( ord_max_real @ A @ B )
% 5.52/5.79 = A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb3
% 5.52/5.79 thf(fact_3614_max_Oabsorb3,axiom,
% 5.52/5.79 ! [B: rat,A: rat] :
% 5.52/5.79 ( ( ord_less_rat @ B @ A )
% 5.52/5.79 => ( ( ord_max_rat @ A @ B )
% 5.52/5.79 = A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb3
% 5.52/5.79 thf(fact_3615_max_Oabsorb3,axiom,
% 5.52/5.79 ! [B: num,A: num] :
% 5.52/5.79 ( ( ord_less_num @ B @ A )
% 5.52/5.79 => ( ( ord_max_num @ A @ B )
% 5.52/5.79 = A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb3
% 5.52/5.79 thf(fact_3616_max_Oabsorb3,axiom,
% 5.52/5.79 ! [B: nat,A: nat] :
% 5.52/5.79 ( ( ord_less_nat @ B @ A )
% 5.52/5.79 => ( ( ord_max_nat @ A @ B )
% 5.52/5.79 = A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb3
% 5.52/5.79 thf(fact_3617_max_Oabsorb3,axiom,
% 5.52/5.79 ! [B: int,A: int] :
% 5.52/5.79 ( ( ord_less_int @ B @ A )
% 5.52/5.79 => ( ( ord_max_int @ A @ B )
% 5.52/5.79 = A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb3
% 5.52/5.79 thf(fact_3618_max_Oabsorb4,axiom,
% 5.52/5.79 ! [A: extended_enat,B: extended_enat] :
% 5.52/5.79 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.52/5.79 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.52/5.79 = B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb4
% 5.52/5.79 thf(fact_3619_max_Oabsorb4,axiom,
% 5.52/5.79 ! [A: real,B: real] :
% 5.52/5.79 ( ( ord_less_real @ A @ B )
% 5.52/5.79 => ( ( ord_max_real @ A @ B )
% 5.52/5.79 = B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb4
% 5.52/5.79 thf(fact_3620_max_Oabsorb4,axiom,
% 5.52/5.79 ! [A: rat,B: rat] :
% 5.52/5.79 ( ( ord_less_rat @ A @ B )
% 5.52/5.79 => ( ( ord_max_rat @ A @ B )
% 5.52/5.79 = B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb4
% 5.52/5.79 thf(fact_3621_max_Oabsorb4,axiom,
% 5.52/5.79 ! [A: num,B: num] :
% 5.52/5.79 ( ( ord_less_num @ A @ B )
% 5.52/5.79 => ( ( ord_max_num @ A @ B )
% 5.52/5.79 = B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb4
% 5.52/5.79 thf(fact_3622_max_Oabsorb4,axiom,
% 5.52/5.79 ! [A: nat,B: nat] :
% 5.52/5.79 ( ( ord_less_nat @ A @ B )
% 5.52/5.79 => ( ( ord_max_nat @ A @ B )
% 5.52/5.79 = B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb4
% 5.52/5.79 thf(fact_3623_max_Oabsorb4,axiom,
% 5.52/5.79 ! [A: int,B: int] :
% 5.52/5.79 ( ( ord_less_int @ A @ B )
% 5.52/5.79 => ( ( ord_max_int @ A @ B )
% 5.52/5.79 = B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb4
% 5.52/5.79 thf(fact_3624_max__less__iff__conj,axiom,
% 5.52/5.79 ! [X2: extended_enat,Y2: extended_enat,Z: extended_enat] :
% 5.52/5.79 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 5.52/5.79 & ( ord_le72135733267957522d_enat @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_less_iff_conj
% 5.52/5.79 thf(fact_3625_max__less__iff__conj,axiom,
% 5.52/5.79 ! [X2: real,Y2: real,Z: real] :
% 5.52/5.79 ( ( ord_less_real @ ( ord_max_real @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ( ord_less_real @ X2 @ Z )
% 5.52/5.79 & ( ord_less_real @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_less_iff_conj
% 5.52/5.79 thf(fact_3626_max__less__iff__conj,axiom,
% 5.52/5.79 ! [X2: rat,Y2: rat,Z: rat] :
% 5.52/5.79 ( ( ord_less_rat @ ( ord_max_rat @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ( ord_less_rat @ X2 @ Z )
% 5.52/5.79 & ( ord_less_rat @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_less_iff_conj
% 5.52/5.79 thf(fact_3627_max__less__iff__conj,axiom,
% 5.52/5.79 ! [X2: num,Y2: num,Z: num] :
% 5.52/5.79 ( ( ord_less_num @ ( ord_max_num @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ( ord_less_num @ X2 @ Z )
% 5.52/5.79 & ( ord_less_num @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_less_iff_conj
% 5.52/5.79 thf(fact_3628_max__less__iff__conj,axiom,
% 5.52/5.79 ! [X2: nat,Y2: nat,Z: nat] :
% 5.52/5.79 ( ( ord_less_nat @ ( ord_max_nat @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ( ord_less_nat @ X2 @ Z )
% 5.52/5.79 & ( ord_less_nat @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_less_iff_conj
% 5.52/5.79 thf(fact_3629_max__less__iff__conj,axiom,
% 5.52/5.79 ! [X2: int,Y2: int,Z: int] :
% 5.52/5.79 ( ( ord_less_int @ ( ord_max_int @ X2 @ Y2 ) @ Z )
% 5.52/5.79 = ( ( ord_less_int @ X2 @ Z )
% 5.52/5.79 & ( ord_less_int @ Y2 @ Z ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max_less_iff_conj
% 5.52/5.79 thf(fact_3630_max_Oabsorb1,axiom,
% 5.52/5.79 ! [B: extended_enat,A: extended_enat] :
% 5.52/5.79 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.52/5.79 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.52/5.79 = A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb1
% 5.52/5.79 thf(fact_3631_max_Oabsorb1,axiom,
% 5.52/5.79 ! [B: rat,A: rat] :
% 5.52/5.79 ( ( ord_less_eq_rat @ B @ A )
% 5.52/5.79 => ( ( ord_max_rat @ A @ B )
% 5.52/5.79 = A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb1
% 5.52/5.79 thf(fact_3632_max_Oabsorb1,axiom,
% 5.52/5.79 ! [B: num,A: num] :
% 5.52/5.79 ( ( ord_less_eq_num @ B @ A )
% 5.52/5.79 => ( ( ord_max_num @ A @ B )
% 5.52/5.79 = A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb1
% 5.52/5.79 thf(fact_3633_max_Oabsorb1,axiom,
% 5.52/5.79 ! [B: nat,A: nat] :
% 5.52/5.79 ( ( ord_less_eq_nat @ B @ A )
% 5.52/5.79 => ( ( ord_max_nat @ A @ B )
% 5.52/5.79 = A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb1
% 5.52/5.79 thf(fact_3634_max_Oabsorb1,axiom,
% 5.52/5.79 ! [B: int,A: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ B @ A )
% 5.52/5.79 => ( ( ord_max_int @ A @ B )
% 5.52/5.79 = A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb1
% 5.52/5.79 thf(fact_3635_max_Oabsorb2,axiom,
% 5.52/5.79 ! [A: extended_enat,B: extended_enat] :
% 5.52/5.79 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.52/5.79 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.52/5.79 = B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb2
% 5.52/5.79 thf(fact_3636_max_Oabsorb2,axiom,
% 5.52/5.79 ! [A: rat,B: rat] :
% 5.52/5.79 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.79 => ( ( ord_max_rat @ A @ B )
% 5.52/5.79 = B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb2
% 5.52/5.79 thf(fact_3637_max_Oabsorb2,axiom,
% 5.52/5.79 ! [A: num,B: num] :
% 5.52/5.79 ( ( ord_less_eq_num @ A @ B )
% 5.52/5.79 => ( ( ord_max_num @ A @ B )
% 5.52/5.79 = B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb2
% 5.52/5.79 thf(fact_3638_max_Oabsorb2,axiom,
% 5.52/5.79 ! [A: nat,B: nat] :
% 5.52/5.79 ( ( ord_less_eq_nat @ A @ B )
% 5.52/5.79 => ( ( ord_max_nat @ A @ B )
% 5.52/5.79 = B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb2
% 5.52/5.79 thf(fact_3639_max_Oabsorb2,axiom,
% 5.52/5.79 ! [A: int,B: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ A @ B )
% 5.52/5.79 => ( ( ord_max_int @ A @ B )
% 5.52/5.79 = B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb2
% 5.52/5.79 thf(fact_3640_max_Obounded__iff,axiom,
% 5.52/5.79 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.52/5.79 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.52/5.79 = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.52/5.79 & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.bounded_iff
% 5.52/5.79 thf(fact_3641_max_Obounded__iff,axiom,
% 5.52/5.79 ! [B: rat,C: rat,A: rat] :
% 5.52/5.79 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.52/5.79 = ( ( ord_less_eq_rat @ B @ A )
% 5.52/5.79 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.bounded_iff
% 5.52/5.79 thf(fact_3642_max_Obounded__iff,axiom,
% 5.52/5.79 ! [B: num,C: num,A: num] :
% 5.52/5.79 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.52/5.79 = ( ( ord_less_eq_num @ B @ A )
% 5.52/5.79 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.bounded_iff
% 5.52/5.79 thf(fact_3643_max_Obounded__iff,axiom,
% 5.52/5.79 ! [B: nat,C: nat,A: nat] :
% 5.52/5.79 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.52/5.79 = ( ( ord_less_eq_nat @ B @ A )
% 5.52/5.79 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.bounded_iff
% 5.52/5.79 thf(fact_3644_max_Obounded__iff,axiom,
% 5.52/5.79 ! [B: int,C: int,A: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.52/5.79 = ( ( ord_less_eq_int @ B @ A )
% 5.52/5.79 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.bounded_iff
% 5.52/5.79 thf(fact_3645_max__enat__simps_I3_J,axiom,
% 5.52/5.79 ! [Q2: extended_enat] :
% 5.52/5.79 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.52/5.79 = Q2 ) ).
% 5.52/5.79
% 5.52/5.79 % max_enat_simps(3)
% 5.52/5.79 thf(fact_3646_max__enat__simps_I2_J,axiom,
% 5.52/5.79 ! [Q2: extended_enat] :
% 5.52/5.79 ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.52/5.79 = Q2 ) ).
% 5.52/5.79
% 5.52/5.79 % max_enat_simps(2)
% 5.52/5.79 thf(fact_3647_prod__decode__aux_Ocases,axiom,
% 5.52/5.79 ! [X2: product_prod_nat_nat] :
% 5.52/5.79 ~ ! [K3: nat,M4: nat] :
% 5.52/5.79 ( X2
% 5.52/5.79 != ( product_Pair_nat_nat @ K3 @ M4 ) ) ).
% 5.52/5.79
% 5.52/5.79 % prod_decode_aux.cases
% 5.52/5.79 thf(fact_3648_max_Omono,axiom,
% 5.52/5.79 ! [C: extended_enat,A: extended_enat,D2: extended_enat,B: extended_enat] :
% 5.52/5.79 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.52/5.79 => ( ( ord_le2932123472753598470d_enat @ D2 @ B )
% 5.52/5.79 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D2 ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.mono
% 5.52/5.79 thf(fact_3649_max_Omono,axiom,
% 5.52/5.79 ! [C: rat,A: rat,D2: rat,B: rat] :
% 5.52/5.79 ( ( ord_less_eq_rat @ C @ A )
% 5.52/5.79 => ( ( ord_less_eq_rat @ D2 @ B )
% 5.52/5.79 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D2 ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.mono
% 5.52/5.79 thf(fact_3650_max_Omono,axiom,
% 5.52/5.79 ! [C: num,A: num,D2: num,B: num] :
% 5.52/5.79 ( ( ord_less_eq_num @ C @ A )
% 5.52/5.79 => ( ( ord_less_eq_num @ D2 @ B )
% 5.52/5.79 => ( ord_less_eq_num @ ( ord_max_num @ C @ D2 ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.mono
% 5.52/5.79 thf(fact_3651_max_Omono,axiom,
% 5.52/5.79 ! [C: nat,A: nat,D2: nat,B: nat] :
% 5.52/5.79 ( ( ord_less_eq_nat @ C @ A )
% 5.52/5.79 => ( ( ord_less_eq_nat @ D2 @ B )
% 5.52/5.79 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D2 ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.mono
% 5.52/5.79 thf(fact_3652_max_Omono,axiom,
% 5.52/5.79 ! [C: int,A: int,D2: int,B: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ C @ A )
% 5.52/5.79 => ( ( ord_less_eq_int @ D2 @ B )
% 5.52/5.79 => ( ord_less_eq_int @ ( ord_max_int @ C @ D2 ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.mono
% 5.52/5.79 thf(fact_3653_max_OorderE,axiom,
% 5.52/5.79 ! [B: extended_enat,A: extended_enat] :
% 5.52/5.79 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.52/5.79 => ( A
% 5.52/5.79 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.orderE
% 5.52/5.79 thf(fact_3654_max_OorderE,axiom,
% 5.52/5.79 ! [B: rat,A: rat] :
% 5.52/5.79 ( ( ord_less_eq_rat @ B @ A )
% 5.52/5.79 => ( A
% 5.52/5.79 = ( ord_max_rat @ A @ B ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.orderE
% 5.52/5.79 thf(fact_3655_max_OorderE,axiom,
% 5.52/5.79 ! [B: num,A: num] :
% 5.52/5.79 ( ( ord_less_eq_num @ B @ A )
% 5.52/5.79 => ( A
% 5.52/5.79 = ( ord_max_num @ A @ B ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.orderE
% 5.52/5.79 thf(fact_3656_max_OorderE,axiom,
% 5.52/5.79 ! [B: nat,A: nat] :
% 5.52/5.79 ( ( ord_less_eq_nat @ B @ A )
% 5.52/5.79 => ( A
% 5.52/5.79 = ( ord_max_nat @ A @ B ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.orderE
% 5.52/5.79 thf(fact_3657_max_OorderE,axiom,
% 5.52/5.79 ! [B: int,A: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ B @ A )
% 5.52/5.79 => ( A
% 5.52/5.79 = ( ord_max_int @ A @ B ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.orderE
% 5.52/5.79 thf(fact_3658_max_OorderI,axiom,
% 5.52/5.79 ! [A: extended_enat,B: extended_enat] :
% 5.52/5.79 ( ( A
% 5.52/5.79 = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 5.52/5.79 => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.orderI
% 5.52/5.79 thf(fact_3659_max_OorderI,axiom,
% 5.52/5.79 ! [A: rat,B: rat] :
% 5.52/5.79 ( ( A
% 5.52/5.79 = ( ord_max_rat @ A @ B ) )
% 5.52/5.79 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.orderI
% 5.52/5.79 thf(fact_3660_max_OorderI,axiom,
% 5.52/5.79 ! [A: num,B: num] :
% 5.52/5.79 ( ( A
% 5.52/5.79 = ( ord_max_num @ A @ B ) )
% 5.52/5.79 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.orderI
% 5.52/5.79 thf(fact_3661_max_OorderI,axiom,
% 5.52/5.79 ! [A: nat,B: nat] :
% 5.52/5.79 ( ( A
% 5.52/5.79 = ( ord_max_nat @ A @ B ) )
% 5.52/5.79 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.orderI
% 5.52/5.79 thf(fact_3662_max_OorderI,axiom,
% 5.52/5.79 ! [A: int,B: int] :
% 5.52/5.79 ( ( A
% 5.52/5.79 = ( ord_max_int @ A @ B ) )
% 5.52/5.79 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.orderI
% 5.52/5.79 thf(fact_3663_max_OboundedE,axiom,
% 5.52/5.79 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.52/5.79 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.52/5.79 => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.52/5.79 => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.boundedE
% 5.52/5.79 thf(fact_3664_max_OboundedE,axiom,
% 5.52/5.79 ! [B: rat,C: rat,A: rat] :
% 5.52/5.79 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.52/5.79 => ~ ( ( ord_less_eq_rat @ B @ A )
% 5.52/5.79 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.boundedE
% 5.52/5.79 thf(fact_3665_max_OboundedE,axiom,
% 5.52/5.79 ! [B: num,C: num,A: num] :
% 5.52/5.79 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.52/5.79 => ~ ( ( ord_less_eq_num @ B @ A )
% 5.52/5.79 => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.boundedE
% 5.52/5.79 thf(fact_3666_max_OboundedE,axiom,
% 5.52/5.79 ! [B: nat,C: nat,A: nat] :
% 5.52/5.79 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.52/5.79 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.52/5.79 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.boundedE
% 5.52/5.79 thf(fact_3667_max_OboundedE,axiom,
% 5.52/5.79 ! [B: int,C: int,A: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.52/5.79 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.52/5.79 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.boundedE
% 5.52/5.79 thf(fact_3668_max_OboundedI,axiom,
% 5.52/5.79 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.52/5.79 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.52/5.79 => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.52/5.79 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.boundedI
% 5.52/5.79 thf(fact_3669_max_OboundedI,axiom,
% 5.52/5.79 ! [B: rat,A: rat,C: rat] :
% 5.52/5.79 ( ( ord_less_eq_rat @ B @ A )
% 5.52/5.79 => ( ( ord_less_eq_rat @ C @ A )
% 5.52/5.79 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.boundedI
% 5.52/5.79 thf(fact_3670_max_OboundedI,axiom,
% 5.52/5.79 ! [B: num,A: num,C: num] :
% 5.52/5.79 ( ( ord_less_eq_num @ B @ A )
% 5.52/5.79 => ( ( ord_less_eq_num @ C @ A )
% 5.52/5.79 => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.boundedI
% 5.52/5.79 thf(fact_3671_max_OboundedI,axiom,
% 5.52/5.79 ! [B: nat,A: nat,C: nat] :
% 5.52/5.79 ( ( ord_less_eq_nat @ B @ A )
% 5.52/5.79 => ( ( ord_less_eq_nat @ C @ A )
% 5.52/5.79 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.boundedI
% 5.52/5.79 thf(fact_3672_max_OboundedI,axiom,
% 5.52/5.79 ! [B: int,A: int,C: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ B @ A )
% 5.52/5.79 => ( ( ord_less_eq_int @ C @ A )
% 5.52/5.79 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.boundedI
% 5.52/5.79 thf(fact_3673_max_Oorder__iff,axiom,
% 5.52/5.79 ( ord_le2932123472753598470d_enat
% 5.52/5.79 = ( ^ [B3: extended_enat,A4: extended_enat] :
% 5.52/5.79 ( A4
% 5.52/5.79 = ( ord_ma741700101516333627d_enat @ A4 @ B3 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.order_iff
% 5.52/5.79 thf(fact_3674_max_Oorder__iff,axiom,
% 5.52/5.79 ( ord_less_eq_rat
% 5.52/5.79 = ( ^ [B3: rat,A4: rat] :
% 5.52/5.79 ( A4
% 5.52/5.79 = ( ord_max_rat @ A4 @ B3 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.order_iff
% 5.52/5.79 thf(fact_3675_max_Oorder__iff,axiom,
% 5.52/5.79 ( ord_less_eq_num
% 5.52/5.79 = ( ^ [B3: num,A4: num] :
% 5.52/5.79 ( A4
% 5.52/5.79 = ( ord_max_num @ A4 @ B3 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.order_iff
% 5.52/5.79 thf(fact_3676_max_Oorder__iff,axiom,
% 5.52/5.79 ( ord_less_eq_nat
% 5.52/5.79 = ( ^ [B3: nat,A4: nat] :
% 5.52/5.79 ( A4
% 5.52/5.79 = ( ord_max_nat @ A4 @ B3 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.order_iff
% 5.52/5.79 thf(fact_3677_max_Oorder__iff,axiom,
% 5.52/5.79 ( ord_less_eq_int
% 5.52/5.79 = ( ^ [B3: int,A4: int] :
% 5.52/5.79 ( A4
% 5.52/5.79 = ( ord_max_int @ A4 @ B3 ) ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.order_iff
% 5.52/5.79 thf(fact_3678_max_Ocobounded1,axiom,
% 5.52/5.79 ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.cobounded1
% 5.52/5.79 thf(fact_3679_max_Ocobounded1,axiom,
% 5.52/5.79 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.cobounded1
% 5.52/5.79 thf(fact_3680_max_Ocobounded1,axiom,
% 5.52/5.79 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.cobounded1
% 5.52/5.79 thf(fact_3681_max_Ocobounded1,axiom,
% 5.52/5.79 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.cobounded1
% 5.52/5.79 thf(fact_3682_max_Ocobounded1,axiom,
% 5.52/5.79 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.cobounded1
% 5.52/5.79 thf(fact_3683_max_Ocobounded2,axiom,
% 5.52/5.79 ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.cobounded2
% 5.52/5.79 thf(fact_3684_max_Ocobounded2,axiom,
% 5.52/5.79 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.cobounded2
% 5.52/5.79 thf(fact_3685_max_Ocobounded2,axiom,
% 5.52/5.79 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.cobounded2
% 5.52/5.79 thf(fact_3686_max_Ocobounded2,axiom,
% 5.52/5.79 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.cobounded2
% 5.52/5.79 thf(fact_3687_max_Ocobounded2,axiom,
% 5.52/5.79 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.cobounded2
% 5.52/5.79 thf(fact_3688_le__max__iff__disj,axiom,
% 5.52/5.79 ! [Z: extended_enat,X2: extended_enat,Y2: extended_enat] :
% 5.52/5.79 ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X2 @ Y2 ) )
% 5.52/5.79 = ( ( ord_le2932123472753598470d_enat @ Z @ X2 )
% 5.52/5.79 | ( ord_le2932123472753598470d_enat @ Z @ Y2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % le_max_iff_disj
% 5.52/5.79 thf(fact_3689_le__max__iff__disj,axiom,
% 5.52/5.79 ! [Z: rat,X2: rat,Y2: rat] :
% 5.52/5.79 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X2 @ Y2 ) )
% 5.52/5.79 = ( ( ord_less_eq_rat @ Z @ X2 )
% 5.52/5.79 | ( ord_less_eq_rat @ Z @ Y2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % le_max_iff_disj
% 5.52/5.79 thf(fact_3690_le__max__iff__disj,axiom,
% 5.52/5.79 ! [Z: num,X2: num,Y2: num] :
% 5.52/5.79 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X2 @ Y2 ) )
% 5.52/5.79 = ( ( ord_less_eq_num @ Z @ X2 )
% 5.52/5.79 | ( ord_less_eq_num @ Z @ Y2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % le_max_iff_disj
% 5.52/5.79 thf(fact_3691_le__max__iff__disj,axiom,
% 5.52/5.79 ! [Z: nat,X2: nat,Y2: nat] :
% 5.52/5.79 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.52/5.79 = ( ( ord_less_eq_nat @ Z @ X2 )
% 5.52/5.79 | ( ord_less_eq_nat @ Z @ Y2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % le_max_iff_disj
% 5.52/5.79 thf(fact_3692_le__max__iff__disj,axiom,
% 5.52/5.79 ! [Z: int,X2: int,Y2: int] :
% 5.52/5.79 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X2 @ Y2 ) )
% 5.52/5.79 = ( ( ord_less_eq_int @ Z @ X2 )
% 5.52/5.79 | ( ord_less_eq_int @ Z @ Y2 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % le_max_iff_disj
% 5.52/5.79 thf(fact_3693_max_Oabsorb__iff1,axiom,
% 5.52/5.79 ( ord_le2932123472753598470d_enat
% 5.52/5.79 = ( ^ [B3: extended_enat,A4: extended_enat] :
% 5.52/5.79 ( ( ord_ma741700101516333627d_enat @ A4 @ B3 )
% 5.52/5.79 = A4 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb_iff1
% 5.52/5.79 thf(fact_3694_max_Oabsorb__iff1,axiom,
% 5.52/5.79 ( ord_less_eq_rat
% 5.52/5.79 = ( ^ [B3: rat,A4: rat] :
% 5.52/5.79 ( ( ord_max_rat @ A4 @ B3 )
% 5.52/5.79 = A4 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb_iff1
% 5.52/5.79 thf(fact_3695_max_Oabsorb__iff1,axiom,
% 5.52/5.79 ( ord_less_eq_num
% 5.52/5.79 = ( ^ [B3: num,A4: num] :
% 5.52/5.79 ( ( ord_max_num @ A4 @ B3 )
% 5.52/5.79 = A4 ) ) ) ).
% 5.52/5.79
% 5.52/5.79 % max.absorb_iff1
% 5.52/5.79 thf(fact_3696_max_Oabsorb__iff1,axiom,
% 5.52/5.79 ( ord_less_eq_nat
% 5.52/5.79 = ( ^ [B3: nat,A4: nat] :
% 5.52/5.79 ( ( ord_max_nat @ A4 @ B3 )
% 5.52/5.79 = A4 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.absorb_iff1
% 5.52/5.80 thf(fact_3697_max_Oabsorb__iff1,axiom,
% 5.52/5.80 ( ord_less_eq_int
% 5.52/5.80 = ( ^ [B3: int,A4: int] :
% 5.52/5.80 ( ( ord_max_int @ A4 @ B3 )
% 5.52/5.80 = A4 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.absorb_iff1
% 5.52/5.80 thf(fact_3698_max_Oabsorb__iff2,axiom,
% 5.52/5.80 ( ord_le2932123472753598470d_enat
% 5.52/5.80 = ( ^ [A4: extended_enat,B3: extended_enat] :
% 5.52/5.80 ( ( ord_ma741700101516333627d_enat @ A4 @ B3 )
% 5.52/5.80 = B3 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.absorb_iff2
% 5.52/5.80 thf(fact_3699_max_Oabsorb__iff2,axiom,
% 5.52/5.80 ( ord_less_eq_rat
% 5.52/5.80 = ( ^ [A4: rat,B3: rat] :
% 5.52/5.80 ( ( ord_max_rat @ A4 @ B3 )
% 5.52/5.80 = B3 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.absorb_iff2
% 5.52/5.80 thf(fact_3700_max_Oabsorb__iff2,axiom,
% 5.52/5.80 ( ord_less_eq_num
% 5.52/5.80 = ( ^ [A4: num,B3: num] :
% 5.52/5.80 ( ( ord_max_num @ A4 @ B3 )
% 5.52/5.80 = B3 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.absorb_iff2
% 5.52/5.80 thf(fact_3701_max_Oabsorb__iff2,axiom,
% 5.52/5.80 ( ord_less_eq_nat
% 5.52/5.80 = ( ^ [A4: nat,B3: nat] :
% 5.52/5.80 ( ( ord_max_nat @ A4 @ B3 )
% 5.52/5.80 = B3 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.absorb_iff2
% 5.52/5.80 thf(fact_3702_max_Oabsorb__iff2,axiom,
% 5.52/5.80 ( ord_less_eq_int
% 5.52/5.80 = ( ^ [A4: int,B3: int] :
% 5.52/5.80 ( ( ord_max_int @ A4 @ B3 )
% 5.52/5.80 = B3 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.absorb_iff2
% 5.52/5.80 thf(fact_3703_max_OcoboundedI1,axiom,
% 5.52/5.80 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.52/5.80 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.52/5.80 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.coboundedI1
% 5.52/5.80 thf(fact_3704_max_OcoboundedI1,axiom,
% 5.52/5.80 ! [C: rat,A: rat,B: rat] :
% 5.52/5.80 ( ( ord_less_eq_rat @ C @ A )
% 5.52/5.80 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.coboundedI1
% 5.52/5.80 thf(fact_3705_max_OcoboundedI1,axiom,
% 5.52/5.80 ! [C: num,A: num,B: num] :
% 5.52/5.80 ( ( ord_less_eq_num @ C @ A )
% 5.52/5.80 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.coboundedI1
% 5.52/5.80 thf(fact_3706_max_OcoboundedI1,axiom,
% 5.52/5.80 ! [C: nat,A: nat,B: nat] :
% 5.52/5.80 ( ( ord_less_eq_nat @ C @ A )
% 5.52/5.80 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.coboundedI1
% 5.52/5.80 thf(fact_3707_max_OcoboundedI1,axiom,
% 5.52/5.80 ! [C: int,A: int,B: int] :
% 5.52/5.80 ( ( ord_less_eq_int @ C @ A )
% 5.52/5.80 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.coboundedI1
% 5.52/5.80 thf(fact_3708_max_OcoboundedI2,axiom,
% 5.52/5.80 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.52/5.80 ( ( ord_le2932123472753598470d_enat @ C @ B )
% 5.52/5.80 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.coboundedI2
% 5.52/5.80 thf(fact_3709_max_OcoboundedI2,axiom,
% 5.52/5.80 ! [C: rat,B: rat,A: rat] :
% 5.52/5.80 ( ( ord_less_eq_rat @ C @ B )
% 5.52/5.80 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.coboundedI2
% 5.52/5.80 thf(fact_3710_max_OcoboundedI2,axiom,
% 5.52/5.80 ! [C: num,B: num,A: num] :
% 5.52/5.80 ( ( ord_less_eq_num @ C @ B )
% 5.52/5.80 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.coboundedI2
% 5.52/5.80 thf(fact_3711_max_OcoboundedI2,axiom,
% 5.52/5.80 ! [C: nat,B: nat,A: nat] :
% 5.52/5.80 ( ( ord_less_eq_nat @ C @ B )
% 5.52/5.80 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.coboundedI2
% 5.52/5.80 thf(fact_3712_max_OcoboundedI2,axiom,
% 5.52/5.80 ! [C: int,B: int,A: int] :
% 5.52/5.80 ( ( ord_less_eq_int @ C @ B )
% 5.52/5.80 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.coboundedI2
% 5.52/5.80 thf(fact_3713_max_Ostrict__coboundedI2,axiom,
% 5.52/5.80 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.52/5.80 ( ( ord_le72135733267957522d_enat @ C @ B )
% 5.52/5.80 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_coboundedI2
% 5.52/5.80 thf(fact_3714_max_Ostrict__coboundedI2,axiom,
% 5.52/5.80 ! [C: real,B: real,A: real] :
% 5.52/5.80 ( ( ord_less_real @ C @ B )
% 5.52/5.80 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_coboundedI2
% 5.52/5.80 thf(fact_3715_max_Ostrict__coboundedI2,axiom,
% 5.52/5.80 ! [C: rat,B: rat,A: rat] :
% 5.52/5.80 ( ( ord_less_rat @ C @ B )
% 5.52/5.80 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_coboundedI2
% 5.52/5.80 thf(fact_3716_max_Ostrict__coboundedI2,axiom,
% 5.52/5.80 ! [C: num,B: num,A: num] :
% 5.52/5.80 ( ( ord_less_num @ C @ B )
% 5.52/5.80 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_coboundedI2
% 5.52/5.80 thf(fact_3717_max_Ostrict__coboundedI2,axiom,
% 5.52/5.80 ! [C: nat,B: nat,A: nat] :
% 5.52/5.80 ( ( ord_less_nat @ C @ B )
% 5.52/5.80 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_coboundedI2
% 5.52/5.80 thf(fact_3718_max_Ostrict__coboundedI2,axiom,
% 5.52/5.80 ! [C: int,B: int,A: int] :
% 5.52/5.80 ( ( ord_less_int @ C @ B )
% 5.52/5.80 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_coboundedI2
% 5.52/5.80 thf(fact_3719_max_Ostrict__coboundedI1,axiom,
% 5.52/5.80 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.52/5.80 ( ( ord_le72135733267957522d_enat @ C @ A )
% 5.52/5.80 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_coboundedI1
% 5.52/5.80 thf(fact_3720_max_Ostrict__coboundedI1,axiom,
% 5.52/5.80 ! [C: real,A: real,B: real] :
% 5.52/5.80 ( ( ord_less_real @ C @ A )
% 5.52/5.80 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_coboundedI1
% 5.52/5.80 thf(fact_3721_max_Ostrict__coboundedI1,axiom,
% 5.52/5.80 ! [C: rat,A: rat,B: rat] :
% 5.52/5.80 ( ( ord_less_rat @ C @ A )
% 5.52/5.80 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_coboundedI1
% 5.52/5.80 thf(fact_3722_max_Ostrict__coboundedI1,axiom,
% 5.52/5.80 ! [C: num,A: num,B: num] :
% 5.52/5.80 ( ( ord_less_num @ C @ A )
% 5.52/5.80 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_coboundedI1
% 5.52/5.80 thf(fact_3723_max_Ostrict__coboundedI1,axiom,
% 5.52/5.80 ! [C: nat,A: nat,B: nat] :
% 5.52/5.80 ( ( ord_less_nat @ C @ A )
% 5.52/5.80 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_coboundedI1
% 5.52/5.80 thf(fact_3724_max_Ostrict__coboundedI1,axiom,
% 5.52/5.80 ! [C: int,A: int,B: int] :
% 5.52/5.80 ( ( ord_less_int @ C @ A )
% 5.52/5.80 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_coboundedI1
% 5.52/5.80 thf(fact_3725_max_Ostrict__order__iff,axiom,
% 5.52/5.80 ( ord_le72135733267957522d_enat
% 5.52/5.80 = ( ^ [B3: extended_enat,A4: extended_enat] :
% 5.52/5.80 ( ( A4
% 5.52/5.80 = ( ord_ma741700101516333627d_enat @ A4 @ B3 ) )
% 5.52/5.80 & ( A4 != B3 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_order_iff
% 5.52/5.80 thf(fact_3726_max_Ostrict__order__iff,axiom,
% 5.52/5.80 ( ord_less_real
% 5.52/5.80 = ( ^ [B3: real,A4: real] :
% 5.52/5.80 ( ( A4
% 5.52/5.80 = ( ord_max_real @ A4 @ B3 ) )
% 5.52/5.80 & ( A4 != B3 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_order_iff
% 5.52/5.80 thf(fact_3727_max_Ostrict__order__iff,axiom,
% 5.52/5.80 ( ord_less_rat
% 5.52/5.80 = ( ^ [B3: rat,A4: rat] :
% 5.52/5.80 ( ( A4
% 5.52/5.80 = ( ord_max_rat @ A4 @ B3 ) )
% 5.52/5.80 & ( A4 != B3 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_order_iff
% 5.52/5.80 thf(fact_3728_max_Ostrict__order__iff,axiom,
% 5.52/5.80 ( ord_less_num
% 5.52/5.80 = ( ^ [B3: num,A4: num] :
% 5.52/5.80 ( ( A4
% 5.52/5.80 = ( ord_max_num @ A4 @ B3 ) )
% 5.52/5.80 & ( A4 != B3 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_order_iff
% 5.52/5.80 thf(fact_3729_max_Ostrict__order__iff,axiom,
% 5.52/5.80 ( ord_less_nat
% 5.52/5.80 = ( ^ [B3: nat,A4: nat] :
% 5.52/5.80 ( ( A4
% 5.52/5.80 = ( ord_max_nat @ A4 @ B3 ) )
% 5.52/5.80 & ( A4 != B3 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_order_iff
% 5.52/5.80 thf(fact_3730_max_Ostrict__order__iff,axiom,
% 5.52/5.80 ( ord_less_int
% 5.52/5.80 = ( ^ [B3: int,A4: int] :
% 5.52/5.80 ( ( A4
% 5.52/5.80 = ( ord_max_int @ A4 @ B3 ) )
% 5.52/5.80 & ( A4 != B3 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_order_iff
% 5.52/5.80 thf(fact_3731_max_Ostrict__boundedE,axiom,
% 5.52/5.80 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.52/5.80 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.52/5.80 => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.52/5.80 => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_boundedE
% 5.52/5.80 thf(fact_3732_max_Ostrict__boundedE,axiom,
% 5.52/5.80 ! [B: real,C: real,A: real] :
% 5.52/5.80 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 5.52/5.80 => ~ ( ( ord_less_real @ B @ A )
% 5.52/5.80 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_boundedE
% 5.52/5.80 thf(fact_3733_max_Ostrict__boundedE,axiom,
% 5.52/5.80 ! [B: rat,C: rat,A: rat] :
% 5.52/5.80 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.52/5.80 => ~ ( ( ord_less_rat @ B @ A )
% 5.52/5.80 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_boundedE
% 5.52/5.80 thf(fact_3734_max_Ostrict__boundedE,axiom,
% 5.52/5.80 ! [B: num,C: num,A: num] :
% 5.52/5.80 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 5.52/5.80 => ~ ( ( ord_less_num @ B @ A )
% 5.52/5.80 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_boundedE
% 5.52/5.80 thf(fact_3735_max_Ostrict__boundedE,axiom,
% 5.52/5.80 ! [B: nat,C: nat,A: nat] :
% 5.52/5.80 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.52/5.80 => ~ ( ( ord_less_nat @ B @ A )
% 5.52/5.80 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_boundedE
% 5.52/5.80 thf(fact_3736_max_Ostrict__boundedE,axiom,
% 5.52/5.80 ! [B: int,C: int,A: int] :
% 5.52/5.80 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 5.52/5.80 => ~ ( ( ord_less_int @ B @ A )
% 5.52/5.80 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % max.strict_boundedE
% 5.52/5.80 thf(fact_3737_less__max__iff__disj,axiom,
% 5.52/5.80 ! [Z: extended_enat,X2: extended_enat,Y2: extended_enat] :
% 5.52/5.80 ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X2 @ Y2 ) )
% 5.52/5.80 = ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 5.52/5.80 | ( ord_le72135733267957522d_enat @ Z @ Y2 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % less_max_iff_disj
% 5.52/5.80 thf(fact_3738_less__max__iff__disj,axiom,
% 5.52/5.80 ! [Z: real,X2: real,Y2: real] :
% 5.52/5.80 ( ( ord_less_real @ Z @ ( ord_max_real @ X2 @ Y2 ) )
% 5.52/5.80 = ( ( ord_less_real @ Z @ X2 )
% 5.52/5.80 | ( ord_less_real @ Z @ Y2 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % less_max_iff_disj
% 5.52/5.80 thf(fact_3739_less__max__iff__disj,axiom,
% 5.52/5.80 ! [Z: rat,X2: rat,Y2: rat] :
% 5.52/5.80 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X2 @ Y2 ) )
% 5.52/5.80 = ( ( ord_less_rat @ Z @ X2 )
% 5.52/5.80 | ( ord_less_rat @ Z @ Y2 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % less_max_iff_disj
% 5.52/5.80 thf(fact_3740_less__max__iff__disj,axiom,
% 5.52/5.80 ! [Z: num,X2: num,Y2: num] :
% 5.52/5.80 ( ( ord_less_num @ Z @ ( ord_max_num @ X2 @ Y2 ) )
% 5.52/5.80 = ( ( ord_less_num @ Z @ X2 )
% 5.52/5.80 | ( ord_less_num @ Z @ Y2 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % less_max_iff_disj
% 5.52/5.80 thf(fact_3741_less__max__iff__disj,axiom,
% 5.52/5.80 ! [Z: nat,X2: nat,Y2: nat] :
% 5.52/5.80 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.52/5.80 = ( ( ord_less_nat @ Z @ X2 )
% 5.52/5.80 | ( ord_less_nat @ Z @ Y2 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % less_max_iff_disj
% 5.52/5.80 thf(fact_3742_less__max__iff__disj,axiom,
% 5.52/5.80 ! [Z: int,X2: int,Y2: int] :
% 5.52/5.80 ( ( ord_less_int @ Z @ ( ord_max_int @ X2 @ Y2 ) )
% 5.52/5.80 = ( ( ord_less_int @ Z @ X2 )
% 5.52/5.80 | ( ord_less_int @ Z @ Y2 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % less_max_iff_disj
% 5.52/5.80 thf(fact_3743_triangle__def,axiom,
% 5.52/5.80 ( nat_triangle
% 5.52/5.80 = ( ^ [N3: nat] : ( divide_divide_nat @ ( times_times_nat @ N3 @ ( suc @ N3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % triangle_def
% 5.52/5.80 thf(fact_3744_even__succ__mod__exp,axiom,
% 5.52/5.80 ! [A: code_integer,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.80 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.80 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_succ_mod_exp
% 5.52/5.80 thf(fact_3745_even__succ__mod__exp,axiom,
% 5.52/5.80 ! [A: nat,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.80 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.80 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_succ_mod_exp
% 5.52/5.80 thf(fact_3746_even__succ__mod__exp,axiom,
% 5.52/5.80 ! [A: int,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.80 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.80 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_succ_mod_exp
% 5.52/5.80 thf(fact_3747_divmod__algorithm__code_I6_J,axiom,
% 5.52/5.80 ! [M: num,N: num] :
% 5.52/5.80 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.52/5.80 = ( produc2626176000494625587at_nat
% 5.52/5.80 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 5.52/5.80 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % divmod_algorithm_code(6)
% 5.52/5.80 thf(fact_3748_divmod__algorithm__code_I6_J,axiom,
% 5.52/5.80 ! [M: num,N: num] :
% 5.52/5.80 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.52/5.80 = ( produc4245557441103728435nt_int
% 5.52/5.80 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 5.52/5.80 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % divmod_algorithm_code(6)
% 5.52/5.80 thf(fact_3749_even__succ__div__exp,axiom,
% 5.52/5.80 ! [A: code_integer,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.80 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.80 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_succ_div_exp
% 5.52/5.80 thf(fact_3750_even__succ__div__exp,axiom,
% 5.52/5.80 ! [A: nat,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.80 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.80 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_succ_div_exp
% 5.52/5.80 thf(fact_3751_even__succ__div__exp,axiom,
% 5.52/5.80 ! [A: int,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.80 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.80 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_succ_div_exp
% 5.52/5.80 thf(fact_3752_option_Osize__gen_I2_J,axiom,
% 5.52/5.80 ! [X2: product_prod_nat_nat > nat,X23: product_prod_nat_nat] :
% 5.52/5.80 ( ( size_o8335143837870341156at_nat @ X2 @ ( some_P7363390416028606310at_nat @ X23 ) )
% 5.52/5.80 = ( plus_plus_nat @ ( X2 @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % option.size_gen(2)
% 5.52/5.80 thf(fact_3753_option_Osize__gen_I2_J,axiom,
% 5.52/5.80 ! [X2: nat > nat,X23: nat] :
% 5.52/5.80 ( ( size_option_nat @ X2 @ ( some_nat @ X23 ) )
% 5.52/5.80 = ( plus_plus_nat @ ( X2 @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % option.size_gen(2)
% 5.52/5.80 thf(fact_3754_option_Osize__gen_I2_J,axiom,
% 5.52/5.80 ! [X2: num > nat,X23: num] :
% 5.52/5.80 ( ( size_option_num @ X2 @ ( some_num @ X23 ) )
% 5.52/5.80 = ( plus_plus_nat @ ( X2 @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % option.size_gen(2)
% 5.52/5.80 thf(fact_3755_signed__take__bit__Suc,axiom,
% 5.52/5.80 ! [N: nat,A: int] :
% 5.52/5.80 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 5.52/5.80 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % signed_take_bit_Suc
% 5.52/5.80 thf(fact_3756_nat__dvd__1__iff__1,axiom,
% 5.52/5.80 ! [M: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.52/5.80 = ( M = one_one_nat ) ) ).
% 5.52/5.80
% 5.52/5.80 % nat_dvd_1_iff_1
% 5.52/5.80 thf(fact_3757_dvd__0__left__iff,axiom,
% 5.52/5.80 ! [A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.52/5.80 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_left_iff
% 5.52/5.80 thf(fact_3758_dvd__0__left__iff,axiom,
% 5.52/5.80 ! [A: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.52/5.80 = ( A = zero_zero_real ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_left_iff
% 5.52/5.80 thf(fact_3759_dvd__0__left__iff,axiom,
% 5.52/5.80 ! [A: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.52/5.80 = ( A = zero_zero_rat ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_left_iff
% 5.52/5.80 thf(fact_3760_dvd__0__left__iff,axiom,
% 5.52/5.80 ! [A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.52/5.80 = ( A = zero_zero_nat ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_left_iff
% 5.52/5.80 thf(fact_3761_dvd__0__left__iff,axiom,
% 5.52/5.80 ! [A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.52/5.80 = ( A = zero_zero_int ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_left_iff
% 5.52/5.80 thf(fact_3762_dvd__0__right,axiom,
% 5.52/5.80 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_right
% 5.52/5.80 thf(fact_3763_dvd__0__right,axiom,
% 5.52/5.80 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_right
% 5.52/5.80 thf(fact_3764_dvd__0__right,axiom,
% 5.52/5.80 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_right
% 5.52/5.80 thf(fact_3765_dvd__0__right,axiom,
% 5.52/5.80 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_right
% 5.52/5.80 thf(fact_3766_dvd__0__right,axiom,
% 5.52/5.80 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_right
% 5.52/5.80 thf(fact_3767_dvd__1__iff__1,axiom,
% 5.52/5.80 ! [M: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.52/5.80 = ( M
% 5.52/5.80 = ( suc @ zero_zero_nat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_1_iff_1
% 5.52/5.80 thf(fact_3768_dvd__1__left,axiom,
% 5.52/5.80 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_1_left
% 5.52/5.80 thf(fact_3769_dvd__add__triv__right__iff,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_triv_right_iff
% 5.52/5.80 thf(fact_3770_dvd__add__triv__right__iff,axiom,
% 5.52/5.80 ! [A: real,B: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.52/5.80 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_triv_right_iff
% 5.52/5.80 thf(fact_3771_dvd__add__triv__right__iff,axiom,
% 5.52/5.80 ! [A: rat,B: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.52/5.80 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_triv_right_iff
% 5.52/5.80 thf(fact_3772_dvd__add__triv__right__iff,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.52/5.80 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_triv_right_iff
% 5.52/5.80 thf(fact_3773_dvd__add__triv__right__iff,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.52/5.80 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_triv_right_iff
% 5.52/5.80 thf(fact_3774_dvd__add__triv__right__iff,axiom,
% 5.52/5.80 ! [A: complex,B: complex] :
% 5.52/5.80 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ A ) )
% 5.52/5.80 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_triv_right_iff
% 5.52/5.80 thf(fact_3775_dvd__add__triv__left__iff,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_triv_left_iff
% 5.52/5.80 thf(fact_3776_dvd__add__triv__left__iff,axiom,
% 5.52/5.80 ! [A: real,B: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.52/5.80 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_triv_left_iff
% 5.52/5.80 thf(fact_3777_dvd__add__triv__left__iff,axiom,
% 5.52/5.80 ! [A: rat,B: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.52/5.80 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_triv_left_iff
% 5.52/5.80 thf(fact_3778_dvd__add__triv__left__iff,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.52/5.80 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_triv_left_iff
% 5.52/5.80 thf(fact_3779_dvd__add__triv__left__iff,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.52/5.80 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_triv_left_iff
% 5.52/5.80 thf(fact_3780_dvd__add__triv__left__iff,axiom,
% 5.52/5.80 ! [A: complex,B: complex] :
% 5.52/5.80 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.52/5.80 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_triv_left_iff
% 5.52/5.80 thf(fact_3781_div__dvd__div,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_dvd_div
% 5.52/5.80 thf(fact_3782_div__dvd__div,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_nat @ A @ C )
% 5.52/5.80 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.52/5.80 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_dvd_div
% 5.52/5.80 thf(fact_3783_div__dvd__div,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_int @ A @ C )
% 5.52/5.80 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.52/5.80 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_dvd_div
% 5.52/5.80 thf(fact_3784_nat__mult__dvd__cancel__disj,axiom,
% 5.52/5.80 ! [K: nat,M: nat,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.52/5.80 = ( ( K = zero_zero_nat )
% 5.52/5.80 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % nat_mult_dvd_cancel_disj
% 5.52/5.80 thf(fact_3785_signed__take__bit__of__0,axiom,
% 5.52/5.80 ! [N: nat] :
% 5.52/5.80 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 5.52/5.80 = zero_zero_int ) ).
% 5.52/5.80
% 5.52/5.80 % signed_take_bit_of_0
% 5.52/5.80 thf(fact_3786_case__prod__conv,axiom,
% 5.52/5.80 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 5.52/5.80 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.52/5.80 = ( F @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % case_prod_conv
% 5.52/5.80 thf(fact_3787_case__prod__conv,axiom,
% 5.52/5.80 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 5.52/5.80 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.52/5.80 = ( F @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % case_prod_conv
% 5.52/5.80 thf(fact_3788_case__prod__conv,axiom,
% 5.52/5.80 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 5.52/5.80 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.52/5.80 = ( F @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % case_prod_conv
% 5.52/5.80 thf(fact_3789_case__prod__conv,axiom,
% 5.52/5.80 ! [F: int > int > $o,A: int,B: int] :
% 5.52/5.80 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.52/5.80 = ( F @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % case_prod_conv
% 5.52/5.80 thf(fact_3790_case__prod__conv,axiom,
% 5.52/5.80 ! [F: int > int > int,A: int,B: int] :
% 5.52/5.80 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.52/5.80 = ( F @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % case_prod_conv
% 5.52/5.80 thf(fact_3791_dvd__times__right__cancel__iff,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( A != zero_z3403309356797280102nteger )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_times_right_cancel_iff
% 5.52/5.80 thf(fact_3792_dvd__times__right__cancel__iff,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( A != zero_zero_nat )
% 5.52/5.80 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.52/5.80 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_times_right_cancel_iff
% 5.52/5.80 thf(fact_3793_dvd__times__right__cancel__iff,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( A != zero_zero_int )
% 5.52/5.80 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.52/5.80 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_times_right_cancel_iff
% 5.52/5.80 thf(fact_3794_dvd__times__left__cancel__iff,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( A != zero_z3403309356797280102nteger )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_times_left_cancel_iff
% 5.52/5.80 thf(fact_3795_dvd__times__left__cancel__iff,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( A != zero_zero_nat )
% 5.52/5.80 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.52/5.80 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_times_left_cancel_iff
% 5.52/5.80 thf(fact_3796_dvd__times__left__cancel__iff,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( A != zero_zero_int )
% 5.52/5.80 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.52/5.80 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_times_left_cancel_iff
% 5.52/5.80 thf(fact_3797_dvd__mult__cancel__right,axiom,
% 5.52/5.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.52/5.80 = ( ( C = zero_z3403309356797280102nteger )
% 5.52/5.80 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_cancel_right
% 5.52/5.80 thf(fact_3798_dvd__mult__cancel__right,axiom,
% 5.52/5.80 ! [A: real,C: real,B: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.52/5.80 = ( ( C = zero_zero_real )
% 5.52/5.80 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_cancel_right
% 5.52/5.80 thf(fact_3799_dvd__mult__cancel__right,axiom,
% 5.52/5.80 ! [A: rat,C: rat,B: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.52/5.80 = ( ( C = zero_zero_rat )
% 5.52/5.80 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_cancel_right
% 5.52/5.80 thf(fact_3800_dvd__mult__cancel__right,axiom,
% 5.52/5.80 ! [A: int,C: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.52/5.80 = ( ( C = zero_zero_int )
% 5.52/5.80 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_cancel_right
% 5.52/5.80 thf(fact_3801_dvd__mult__cancel__left,axiom,
% 5.52/5.80 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.52/5.80 = ( ( C = zero_z3403309356797280102nteger )
% 5.52/5.80 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_cancel_left
% 5.52/5.80 thf(fact_3802_dvd__mult__cancel__left,axiom,
% 5.52/5.80 ! [C: real,A: real,B: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.52/5.80 = ( ( C = zero_zero_real )
% 5.52/5.80 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_cancel_left
% 5.52/5.80 thf(fact_3803_dvd__mult__cancel__left,axiom,
% 5.52/5.80 ! [C: rat,A: rat,B: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.52/5.80 = ( ( C = zero_zero_rat )
% 5.52/5.80 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_cancel_left
% 5.52/5.80 thf(fact_3804_dvd__mult__cancel__left,axiom,
% 5.52/5.80 ! [C: int,A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.52/5.80 = ( ( C = zero_zero_int )
% 5.52/5.80 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_cancel_left
% 5.52/5.80 thf(fact_3805_unit__prod,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_prod
% 5.52/5.80 thf(fact_3806_unit__prod,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.80 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.80 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_prod
% 5.52/5.80 thf(fact_3807_unit__prod,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.80 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.80 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_prod
% 5.52/5.80 thf(fact_3808_dvd__add__times__triv__right__iff,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_times_triv_right_iff
% 5.52/5.80 thf(fact_3809_dvd__add__times__triv__right__iff,axiom,
% 5.52/5.80 ! [A: complex,B: complex,C: complex] :
% 5.52/5.80 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ ( times_times_complex @ C @ A ) ) )
% 5.52/5.80 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_times_triv_right_iff
% 5.52/5.80 thf(fact_3810_dvd__add__times__triv__right__iff,axiom,
% 5.52/5.80 ! [A: real,B: real,C: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.52/5.80 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_times_triv_right_iff
% 5.52/5.80 thf(fact_3811_dvd__add__times__triv__right__iff,axiom,
% 5.52/5.80 ! [A: rat,B: rat,C: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.52/5.80 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_times_triv_right_iff
% 5.52/5.80 thf(fact_3812_dvd__add__times__triv__right__iff,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.52/5.80 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_times_triv_right_iff
% 5.52/5.80 thf(fact_3813_dvd__add__times__triv__right__iff,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.52/5.80 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_times_triv_right_iff
% 5.52/5.80 thf(fact_3814_dvd__add__times__triv__left__iff,axiom,
% 5.52/5.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_times_triv_left_iff
% 5.52/5.80 thf(fact_3815_dvd__add__times__triv__left__iff,axiom,
% 5.52/5.80 ! [A: complex,C: complex,B: complex] :
% 5.52/5.80 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ ( times_times_complex @ C @ A ) @ B ) )
% 5.52/5.80 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_times_triv_left_iff
% 5.52/5.80 thf(fact_3816_dvd__add__times__triv__left__iff,axiom,
% 5.52/5.80 ! [A: real,C: real,B: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.52/5.80 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_times_triv_left_iff
% 5.52/5.80 thf(fact_3817_dvd__add__times__triv__left__iff,axiom,
% 5.52/5.80 ! [A: rat,C: rat,B: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.52/5.80 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_times_triv_left_iff
% 5.52/5.80 thf(fact_3818_dvd__add__times__triv__left__iff,axiom,
% 5.52/5.80 ! [A: nat,C: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.52/5.80 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_times_triv_left_iff
% 5.52/5.80 thf(fact_3819_dvd__add__times__triv__left__iff,axiom,
% 5.52/5.80 ! [A: int,C: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.52/5.80 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_times_triv_left_iff
% 5.52/5.80 thf(fact_3820_dvd__mult__div__cancel,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.80 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.52/5.80 = B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_div_cancel
% 5.52/5.80 thf(fact_3821_dvd__mult__div__cancel,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.80 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.52/5.80 = B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_div_cancel
% 5.52/5.80 thf(fact_3822_dvd__mult__div__cancel,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.52/5.80 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.52/5.80 = B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_div_cancel
% 5.52/5.80 thf(fact_3823_dvd__div__mult__self,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.80 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.52/5.80 = B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_mult_self
% 5.52/5.80 thf(fact_3824_dvd__div__mult__self,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.80 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.52/5.80 = B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_mult_self
% 5.52/5.80 thf(fact_3825_dvd__div__mult__self,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.52/5.80 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.52/5.80 = B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_mult_self
% 5.52/5.80 thf(fact_3826_unit__div__1__div__1,axiom,
% 5.52/5.80 ! [A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.80 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.52/5.80 = A ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_div_1_div_1
% 5.52/5.80 thf(fact_3827_unit__div__1__div__1,axiom,
% 5.52/5.80 ! [A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.80 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.52/5.80 = A ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_div_1_div_1
% 5.52/5.80 thf(fact_3828_unit__div__1__div__1,axiom,
% 5.52/5.80 ! [A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.80 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.52/5.80 = A ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_div_1_div_1
% 5.52/5.80 thf(fact_3829_unit__div__1__unit,axiom,
% 5.52/5.80 ! [A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_div_1_unit
% 5.52/5.80 thf(fact_3830_unit__div__1__unit,axiom,
% 5.52/5.80 ! [A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.80 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_div_1_unit
% 5.52/5.80 thf(fact_3831_unit__div__1__unit,axiom,
% 5.52/5.80 ! [A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.80 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_div_1_unit
% 5.52/5.80 thf(fact_3832_unit__div,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_div
% 5.52/5.80 thf(fact_3833_unit__div,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.80 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.80 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_div
% 5.52/5.80 thf(fact_3834_unit__div,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.80 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.80 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_div
% 5.52/5.80 thf(fact_3835_div__add,axiom,
% 5.52/5.80 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.52/5.80 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.52/5.80 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_add
% 5.52/5.80 thf(fact_3836_div__add,axiom,
% 5.52/5.80 ! [C: nat,A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_nat @ C @ B )
% 5.52/5.80 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.52/5.80 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_add
% 5.52/5.80 thf(fact_3837_div__add,axiom,
% 5.52/5.80 ! [C: int,A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_int @ C @ B )
% 5.52/5.80 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.52/5.80 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_add
% 5.52/5.80 thf(fact_3838_div__diff,axiom,
% 5.52/5.80 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.52/5.80 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.52/5.80 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_diff
% 5.52/5.80 thf(fact_3839_div__diff,axiom,
% 5.52/5.80 ! [C: int,A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_int @ C @ B )
% 5.52/5.80 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.52/5.80 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_diff
% 5.52/5.80 thf(fact_3840_dvd__imp__mod__0,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.80 => ( ( modulo364778990260209775nteger @ B @ A )
% 5.52/5.80 = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_imp_mod_0
% 5.52/5.80 thf(fact_3841_dvd__imp__mod__0,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.80 => ( ( modulo_modulo_nat @ B @ A )
% 5.52/5.80 = zero_zero_nat ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_imp_mod_0
% 5.52/5.80 thf(fact_3842_dvd__imp__mod__0,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.52/5.80 => ( ( modulo_modulo_int @ B @ A )
% 5.52/5.80 = zero_zero_int ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_imp_mod_0
% 5.52/5.80 thf(fact_3843_signed__take__bit__Suc__1,axiom,
% 5.52/5.80 ! [N: nat] :
% 5.52/5.80 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 5.52/5.80 = one_one_int ) ).
% 5.52/5.80
% 5.52/5.80 % signed_take_bit_Suc_1
% 5.52/5.80 thf(fact_3844_signed__take__bit__numeral__of__1,axiom,
% 5.52/5.80 ! [K: num] :
% 5.52/5.80 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.52/5.80 = one_one_int ) ).
% 5.52/5.80
% 5.52/5.80 % signed_take_bit_numeral_of_1
% 5.52/5.80 thf(fact_3845_triangle__Suc,axiom,
% 5.52/5.80 ! [N: nat] :
% 5.52/5.80 ( ( nat_triangle @ ( suc @ N ) )
% 5.52/5.80 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % triangle_Suc
% 5.52/5.80 thf(fact_3846_even__Suc__Suc__iff,axiom,
% 5.52/5.80 ! [N: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.52/5.80 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_Suc_Suc_iff
% 5.52/5.80 thf(fact_3847_even__Suc,axiom,
% 5.52/5.80 ! [N: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_Suc
% 5.52/5.80 thf(fact_3848_unit__div__mult__self,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.80 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.52/5.80 = B ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_div_mult_self
% 5.52/5.80 thf(fact_3849_unit__div__mult__self,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.80 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.52/5.80 = B ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_div_mult_self
% 5.52/5.80 thf(fact_3850_unit__div__mult__self,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.80 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.52/5.80 = B ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_div_mult_self
% 5.52/5.80 thf(fact_3851_unit__mult__div__div,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.80 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.52/5.80 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_mult_div_div
% 5.52/5.80 thf(fact_3852_unit__mult__div__div,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.80 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.52/5.80 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_mult_div_div
% 5.52/5.80 thf(fact_3853_unit__mult__div__div,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.80 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.52/5.80 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_mult_div_div
% 5.52/5.80 thf(fact_3854_pow__divides__pow__iff,axiom,
% 5.52/5.80 ! [N: nat,A: nat,B: nat] :
% 5.52/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.80 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.52/5.80 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % pow_divides_pow_iff
% 5.52/5.80 thf(fact_3855_pow__divides__pow__iff,axiom,
% 5.52/5.80 ! [N: nat,A: int,B: int] :
% 5.52/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.80 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.52/5.80 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % pow_divides_pow_iff
% 5.52/5.80 thf(fact_3856_even__mult__iff,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.52/5.80 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_mult_iff
% 5.52/5.80 thf(fact_3857_even__mult__iff,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.52/5.80 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_mult_iff
% 5.52/5.80 thf(fact_3858_even__mult__iff,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.52/5.80 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_mult_iff
% 5.52/5.80 thf(fact_3859_even__add,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.52/5.80 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_add
% 5.52/5.80 thf(fact_3860_even__add,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 5.52/5.80 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_add
% 5.52/5.80 thf(fact_3861_even__add,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 5.52/5.80 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_add
% 5.52/5.80 thf(fact_3862_odd__add,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 5.52/5.80 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.80 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % odd_add
% 5.52/5.80 thf(fact_3863_odd__add,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 5.52/5.80 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.80 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % odd_add
% 5.52/5.80 thf(fact_3864_odd__add,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 5.52/5.80 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.80 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % odd_add
% 5.52/5.80 thf(fact_3865_even__mod__2__iff,axiom,
% 5.52/5.80 ! [A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_mod_2_iff
% 5.52/5.80 thf(fact_3866_even__mod__2__iff,axiom,
% 5.52/5.80 ! [A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.80 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_mod_2_iff
% 5.52/5.80 thf(fact_3867_even__mod__2__iff,axiom,
% 5.52/5.80 ! [A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.52/5.80 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_mod_2_iff
% 5.52/5.80 thf(fact_3868_even__Suc__div__two,axiom,
% 5.52/5.80 ! [N: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.80 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.80 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_Suc_div_two
% 5.52/5.80 thf(fact_3869_odd__Suc__div__two,axiom,
% 5.52/5.80 ! [N: nat] :
% 5.52/5.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.80 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.80 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % odd_Suc_div_two
% 5.52/5.80 thf(fact_3870_signed__take__bit__Suc__bit0,axiom,
% 5.52/5.80 ! [N: nat,K: num] :
% 5.52/5.80 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.52/5.80 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % signed_take_bit_Suc_bit0
% 5.52/5.80 thf(fact_3871_dvd__numeral__simp,axiom,
% 5.52/5.80 ! [M: num,N: num] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 5.52/5.80 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_numeral_simp
% 5.52/5.80 thf(fact_3872_dvd__numeral__simp,axiom,
% 5.52/5.80 ! [M: num,N: num] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.52/5.80 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_numeral_simp
% 5.52/5.80 thf(fact_3873_dvd__numeral__simp,axiom,
% 5.52/5.80 ! [M: num,N: num] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.80 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_numeral_simp
% 5.52/5.80 thf(fact_3874_zero__le__power__eq__numeral,axiom,
% 5.52/5.80 ! [A: real,W: num] :
% 5.52/5.80 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.52/5.80 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % zero_le_power_eq_numeral
% 5.52/5.80 thf(fact_3875_zero__le__power__eq__numeral,axiom,
% 5.52/5.80 ! [A: rat,W: num] :
% 5.52/5.80 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.52/5.80 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % zero_le_power_eq_numeral
% 5.52/5.80 thf(fact_3876_zero__le__power__eq__numeral,axiom,
% 5.52/5.80 ! [A: int,W: num] :
% 5.52/5.80 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.52/5.80 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % zero_le_power_eq_numeral
% 5.52/5.80 thf(fact_3877_power__less__zero__eq__numeral,axiom,
% 5.52/5.80 ! [A: real,W: num] :
% 5.52/5.80 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.52/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % power_less_zero_eq_numeral
% 5.52/5.80 thf(fact_3878_power__less__zero__eq__numeral,axiom,
% 5.52/5.80 ! [A: rat,W: num] :
% 5.52/5.80 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.52/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % power_less_zero_eq_numeral
% 5.52/5.80 thf(fact_3879_power__less__zero__eq__numeral,axiom,
% 5.52/5.80 ! [A: int,W: num] :
% 5.52/5.80 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.52/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % power_less_zero_eq_numeral
% 5.52/5.80 thf(fact_3880_power__less__zero__eq,axiom,
% 5.52/5.80 ! [A: real,N: nat] :
% 5.52/5.80 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.52/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.80 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % power_less_zero_eq
% 5.52/5.80 thf(fact_3881_power__less__zero__eq,axiom,
% 5.52/5.80 ! [A: rat,N: nat] :
% 5.52/5.80 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.52/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.80 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % power_less_zero_eq
% 5.52/5.80 thf(fact_3882_power__less__zero__eq,axiom,
% 5.52/5.80 ! [A: int,N: nat] :
% 5.52/5.80 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.52/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.80 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % power_less_zero_eq
% 5.52/5.80 thf(fact_3883_even__plus__one__iff,axiom,
% 5.52/5.80 ! [A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_plus_one_iff
% 5.52/5.80 thf(fact_3884_even__plus__one__iff,axiom,
% 5.52/5.80 ! [A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_plus_one_iff
% 5.52/5.80 thf(fact_3885_even__plus__one__iff,axiom,
% 5.52/5.80 ! [A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_plus_one_iff
% 5.52/5.80 thf(fact_3886_even__diff,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_diff
% 5.52/5.80 thf(fact_3887_even__diff,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.52/5.80 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_diff
% 5.52/5.80 thf(fact_3888_odd__Suc__minus__one,axiom,
% 5.52/5.80 ! [N: nat] :
% 5.52/5.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.80 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.52/5.80 = N ) ) ).
% 5.52/5.80
% 5.52/5.80 % odd_Suc_minus_one
% 5.52/5.80 thf(fact_3889_even__diff__nat,axiom,
% 5.52/5.80 ! [M: nat,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.80 = ( ( ord_less_nat @ M @ N )
% 5.52/5.80 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_diff_nat
% 5.52/5.80 thf(fact_3890_zero__less__power__eq__numeral,axiom,
% 5.52/5.80 ! [A: real,W: num] :
% 5.52/5.80 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.52/5.80 = ( ( ( numeral_numeral_nat @ W )
% 5.52/5.80 = zero_zero_nat )
% 5.52/5.80 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( A != zero_zero_real ) )
% 5.52/5.80 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % zero_less_power_eq_numeral
% 5.52/5.80 thf(fact_3891_zero__less__power__eq__numeral,axiom,
% 5.52/5.80 ! [A: rat,W: num] :
% 5.52/5.80 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.52/5.80 = ( ( ( numeral_numeral_nat @ W )
% 5.52/5.80 = zero_zero_nat )
% 5.52/5.80 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( A != zero_zero_rat ) )
% 5.52/5.80 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % zero_less_power_eq_numeral
% 5.52/5.80 thf(fact_3892_zero__less__power__eq__numeral,axiom,
% 5.52/5.80 ! [A: int,W: num] :
% 5.52/5.80 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.52/5.80 = ( ( ( numeral_numeral_nat @ W )
% 5.52/5.80 = zero_zero_nat )
% 5.52/5.80 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( A != zero_zero_int ) )
% 5.52/5.80 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % zero_less_power_eq_numeral
% 5.52/5.80 thf(fact_3893_even__succ__div__2,axiom,
% 5.52/5.80 ! [A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.80 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_succ_div_2
% 5.52/5.80 thf(fact_3894_even__succ__div__2,axiom,
% 5.52/5.80 ! [A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.80 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_succ_div_2
% 5.52/5.80 thf(fact_3895_even__succ__div__2,axiom,
% 5.52/5.80 ! [A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.80 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_succ_div_2
% 5.52/5.80 thf(fact_3896_even__succ__div__two,axiom,
% 5.52/5.80 ! [A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.80 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_succ_div_two
% 5.52/5.80 thf(fact_3897_even__succ__div__two,axiom,
% 5.52/5.80 ! [A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.80 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_succ_div_two
% 5.52/5.80 thf(fact_3898_even__succ__div__two,axiom,
% 5.52/5.80 ! [A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.80 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_succ_div_two
% 5.52/5.80 thf(fact_3899_odd__succ__div__two,axiom,
% 5.52/5.80 ! [A: code_integer] :
% 5.52/5.80 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.80 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % odd_succ_div_two
% 5.52/5.80 thf(fact_3900_odd__succ__div__two,axiom,
% 5.52/5.80 ! [A: nat] :
% 5.52/5.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.80 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % odd_succ_div_two
% 5.52/5.80 thf(fact_3901_odd__succ__div__two,axiom,
% 5.52/5.80 ! [A: int] :
% 5.52/5.80 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.80 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % odd_succ_div_two
% 5.52/5.80 thf(fact_3902_even__power,axiom,
% 5.52/5.80 ! [A: code_integer,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.52/5.80 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_power
% 5.52/5.80 thf(fact_3903_even__power,axiom,
% 5.52/5.80 ! [A: nat,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 5.52/5.80 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_power
% 5.52/5.80 thf(fact_3904_even__power,axiom,
% 5.52/5.80 ! [A: int,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 5.52/5.80 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_power
% 5.52/5.80 thf(fact_3905_odd__two__times__div__two__nat,axiom,
% 5.52/5.80 ! [N: nat] :
% 5.52/5.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.80 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.80 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % odd_two_times_div_two_nat
% 5.52/5.80 thf(fact_3906_divmod__algorithm__code_I5_J,axiom,
% 5.52/5.80 ! [M: num,N: num] :
% 5.52/5.80 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.52/5.80 = ( produc2626176000494625587at_nat
% 5.52/5.80 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 5.52/5.80 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % divmod_algorithm_code(5)
% 5.52/5.80 thf(fact_3907_divmod__algorithm__code_I5_J,axiom,
% 5.52/5.80 ! [M: num,N: num] :
% 5.52/5.80 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.52/5.80 = ( produc4245557441103728435nt_int
% 5.52/5.80 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 5.52/5.80 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % divmod_algorithm_code(5)
% 5.52/5.80 thf(fact_3908_odd__two__times__div__two__succ,axiom,
% 5.52/5.80 ! [A: code_integer] :
% 5.52/5.80 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.52/5.80 = A ) ) ).
% 5.52/5.80
% 5.52/5.80 % odd_two_times_div_two_succ
% 5.52/5.80 thf(fact_3909_odd__two__times__div__two__succ,axiom,
% 5.52/5.80 ! [A: nat] :
% 5.52/5.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.52/5.80 = A ) ) ).
% 5.52/5.80
% 5.52/5.80 % odd_two_times_div_two_succ
% 5.52/5.80 thf(fact_3910_odd__two__times__div__two__succ,axiom,
% 5.52/5.80 ! [A: int] :
% 5.52/5.80 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.80 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.52/5.80 = A ) ) ).
% 5.52/5.80
% 5.52/5.80 % odd_two_times_div_two_succ
% 5.52/5.80 thf(fact_3911_power__le__zero__eq__numeral,axiom,
% 5.52/5.80 ! [A: real,W: num] :
% 5.52/5.80 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.52/5.80 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.52/5.80 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % power_le_zero_eq_numeral
% 5.52/5.80 thf(fact_3912_power__le__zero__eq__numeral,axiom,
% 5.52/5.80 ! [A: rat,W: num] :
% 5.52/5.80 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.52/5.80 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.52/5.80 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % power_le_zero_eq_numeral
% 5.52/5.80 thf(fact_3913_power__le__zero__eq__numeral,axiom,
% 5.52/5.80 ! [A: int,W: num] :
% 5.52/5.80 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.52/5.80 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.52/5.80 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.80 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % power_le_zero_eq_numeral
% 5.52/5.80 thf(fact_3914_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.52/5.80 ! [N: nat] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.52/5.80 = ( N = zero_zero_nat ) ) ).
% 5.52/5.80
% 5.52/5.80 % semiring_parity_class.even_mask_iff
% 5.52/5.80 thf(fact_3915_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.52/5.80 ! [N: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.52/5.80 = ( N = zero_zero_nat ) ) ).
% 5.52/5.80
% 5.52/5.80 % semiring_parity_class.even_mask_iff
% 5.52/5.80 thf(fact_3916_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.52/5.80 ! [N: nat] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.52/5.80 = ( N = zero_zero_nat ) ) ).
% 5.52/5.80
% 5.52/5.80 % semiring_parity_class.even_mask_iff
% 5.52/5.80 thf(fact_3917_signed__take__bit__Suc__bit1,axiom,
% 5.52/5.80 ! [N: nat,K: num] :
% 5.52/5.80 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.52/5.80 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.52/5.80
% 5.52/5.80 % signed_take_bit_Suc_bit1
% 5.52/5.80 thf(fact_3918_dvd__trans,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_nat @ B @ C )
% 5.52/5.80 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_trans
% 5.52/5.80 thf(fact_3919_dvd__trans,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_int @ B @ C )
% 5.52/5.80 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_trans
% 5.52/5.80 thf(fact_3920_dvd__trans,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ B @ C )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_trans
% 5.52/5.80 thf(fact_3921_dvd__refl,axiom,
% 5.52/5.80 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_refl
% 5.52/5.80 thf(fact_3922_dvd__refl,axiom,
% 5.52/5.80 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_refl
% 5.52/5.80 thf(fact_3923_dvd__refl,axiom,
% 5.52/5.80 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_refl
% 5.52/5.80 thf(fact_3924_dvd__0__left,axiom,
% 5.52/5.80 ! [A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.52/5.80 => ( A = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_left
% 5.52/5.80 thf(fact_3925_dvd__0__left,axiom,
% 5.52/5.80 ! [A: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.52/5.80 => ( A = zero_zero_real ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_left
% 5.52/5.80 thf(fact_3926_dvd__0__left,axiom,
% 5.52/5.80 ! [A: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.52/5.80 => ( A = zero_zero_rat ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_left
% 5.52/5.80 thf(fact_3927_dvd__0__left,axiom,
% 5.52/5.80 ! [A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.52/5.80 => ( A = zero_zero_nat ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_left
% 5.52/5.80 thf(fact_3928_dvd__0__left,axiom,
% 5.52/5.80 ! [A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.52/5.80 => ( A = zero_zero_int ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_0_left
% 5.52/5.80 thf(fact_3929_dvd__field__iff,axiom,
% 5.52/5.80 ( dvd_dvd_real
% 5.52/5.80 = ( ^ [A4: real,B3: real] :
% 5.52/5.80 ( ( A4 = zero_zero_real )
% 5.52/5.80 => ( B3 = zero_zero_real ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_field_iff
% 5.52/5.80 thf(fact_3930_dvd__field__iff,axiom,
% 5.52/5.80 ( dvd_dvd_rat
% 5.52/5.80 = ( ^ [A4: rat,B3: rat] :
% 5.52/5.80 ( ( A4 = zero_zero_rat )
% 5.52/5.80 => ( B3 = zero_zero_rat ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_field_iff
% 5.52/5.80 thf(fact_3931_division__decomp,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.52/5.80 => ? [B8: nat,C5: nat] :
% 5.52/5.80 ( ( A
% 5.52/5.80 = ( times_times_nat @ B8 @ C5 ) )
% 5.52/5.80 & ( dvd_dvd_nat @ B8 @ B )
% 5.52/5.80 & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % division_decomp
% 5.52/5.80 thf(fact_3932_division__decomp,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.52/5.80 => ? [B8: int,C5: int] :
% 5.52/5.80 ( ( A
% 5.52/5.80 = ( times_times_int @ B8 @ C5 ) )
% 5.52/5.80 & ( dvd_dvd_int @ B8 @ B )
% 5.52/5.80 & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % division_decomp
% 5.52/5.80 thf(fact_3933_dvd__productE,axiom,
% 5.52/5.80 ! [P6: nat,A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ P6 @ ( times_times_nat @ A @ B ) )
% 5.52/5.80 => ~ ! [X4: nat,Y3: nat] :
% 5.52/5.80 ( ( P6
% 5.52/5.80 = ( times_times_nat @ X4 @ Y3 ) )
% 5.52/5.80 => ( ( dvd_dvd_nat @ X4 @ A )
% 5.52/5.80 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_productE
% 5.52/5.80 thf(fact_3934_dvd__productE,axiom,
% 5.52/5.80 ! [P6: int,A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ P6 @ ( times_times_int @ A @ B ) )
% 5.52/5.80 => ~ ! [X4: int,Y3: int] :
% 5.52/5.80 ( ( P6
% 5.52/5.80 = ( times_times_int @ X4 @ Y3 ) )
% 5.52/5.80 => ( ( dvd_dvd_int @ X4 @ A )
% 5.52/5.80 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_productE
% 5.52/5.80 thf(fact_3935_dvd__triv__right,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_triv_right
% 5.52/5.80 thf(fact_3936_dvd__triv__right,axiom,
% 5.52/5.80 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_triv_right
% 5.52/5.80 thf(fact_3937_dvd__triv__right,axiom,
% 5.52/5.80 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_triv_right
% 5.52/5.80 thf(fact_3938_dvd__triv__right,axiom,
% 5.52/5.80 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_triv_right
% 5.52/5.80 thf(fact_3939_dvd__triv__right,axiom,
% 5.52/5.80 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_triv_right
% 5.52/5.80 thf(fact_3940_dvd__mult__right,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_right
% 5.52/5.80 thf(fact_3941_dvd__mult__right,axiom,
% 5.52/5.80 ! [A: real,B: real,C: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.52/5.80 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_right
% 5.52/5.80 thf(fact_3942_dvd__mult__right,axiom,
% 5.52/5.80 ! [A: rat,B: rat,C: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.52/5.80 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_right
% 5.52/5.80 thf(fact_3943_dvd__mult__right,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.52/5.80 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_right
% 5.52/5.80 thf(fact_3944_dvd__mult__right,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.52/5.80 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_right
% 5.52/5.80 thf(fact_3945_mult__dvd__mono,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mult_dvd_mono
% 5.52/5.80 thf(fact_3946_mult__dvd__mono,axiom,
% 5.52/5.80 ! [A: real,B: real,C: real,D2: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_real @ C @ D2 )
% 5.52/5.80 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mult_dvd_mono
% 5.52/5.80 thf(fact_3947_mult__dvd__mono,axiom,
% 5.52/5.80 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_rat @ C @ D2 )
% 5.52/5.80 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mult_dvd_mono
% 5.52/5.80 thf(fact_3948_mult__dvd__mono,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_nat @ C @ D2 )
% 5.52/5.80 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mult_dvd_mono
% 5.52/5.80 thf(fact_3949_mult__dvd__mono,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int,D2: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_int @ C @ D2 )
% 5.52/5.80 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mult_dvd_mono
% 5.52/5.80 thf(fact_3950_dvd__triv__left,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_triv_left
% 5.52/5.80 thf(fact_3951_dvd__triv__left,axiom,
% 5.52/5.80 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_triv_left
% 5.52/5.80 thf(fact_3952_dvd__triv__left,axiom,
% 5.52/5.80 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_triv_left
% 5.52/5.80 thf(fact_3953_dvd__triv__left,axiom,
% 5.52/5.80 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_triv_left
% 5.52/5.80 thf(fact_3954_dvd__triv__left,axiom,
% 5.52/5.80 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_triv_left
% 5.52/5.80 thf(fact_3955_dvd__mult__left,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_left
% 5.52/5.80 thf(fact_3956_dvd__mult__left,axiom,
% 5.52/5.80 ! [A: real,B: real,C: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.52/5.80 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_left
% 5.52/5.80 thf(fact_3957_dvd__mult__left,axiom,
% 5.52/5.80 ! [A: rat,B: rat,C: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.52/5.80 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_left
% 5.52/5.80 thf(fact_3958_dvd__mult__left,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.52/5.80 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_left
% 5.52/5.80 thf(fact_3959_dvd__mult__left,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.52/5.80 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_left
% 5.52/5.80 thf(fact_3960_dvd__mult2,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult2
% 5.52/5.80 thf(fact_3961_dvd__mult2,axiom,
% 5.52/5.80 ! [A: real,B: real,C: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ A @ B )
% 5.52/5.80 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult2
% 5.52/5.80 thf(fact_3962_dvd__mult2,axiom,
% 5.52/5.80 ! [A: rat,B: rat,C: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ A @ B )
% 5.52/5.80 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult2
% 5.52/5.80 thf(fact_3963_dvd__mult2,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.80 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult2
% 5.52/5.80 thf(fact_3964_dvd__mult2,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.52/5.80 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult2
% 5.52/5.80 thf(fact_3965_dvd__mult,axiom,
% 5.52/5.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult
% 5.52/5.80 thf(fact_3966_dvd__mult,axiom,
% 5.52/5.80 ! [A: real,C: real,B: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ A @ C )
% 5.52/5.80 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult
% 5.52/5.80 thf(fact_3967_dvd__mult,axiom,
% 5.52/5.80 ! [A: rat,C: rat,B: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ A @ C )
% 5.52/5.80 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult
% 5.52/5.80 thf(fact_3968_dvd__mult,axiom,
% 5.52/5.80 ! [A: nat,C: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ C )
% 5.52/5.80 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult
% 5.52/5.80 thf(fact_3969_dvd__mult,axiom,
% 5.52/5.80 ! [A: int,C: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ C )
% 5.52/5.80 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult
% 5.52/5.80 thf(fact_3970_dvd__def,axiom,
% 5.52/5.80 ( dvd_dvd_Code_integer
% 5.52/5.80 = ( ^ [B3: code_integer,A4: code_integer] :
% 5.52/5.80 ? [K2: code_integer] :
% 5.52/5.80 ( A4
% 5.52/5.80 = ( times_3573771949741848930nteger @ B3 @ K2 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_def
% 5.52/5.80 thf(fact_3971_dvd__def,axiom,
% 5.52/5.80 ( dvd_dvd_real
% 5.52/5.80 = ( ^ [B3: real,A4: real] :
% 5.52/5.80 ? [K2: real] :
% 5.52/5.80 ( A4
% 5.52/5.80 = ( times_times_real @ B3 @ K2 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_def
% 5.52/5.80 thf(fact_3972_dvd__def,axiom,
% 5.52/5.80 ( dvd_dvd_rat
% 5.52/5.80 = ( ^ [B3: rat,A4: rat] :
% 5.52/5.80 ? [K2: rat] :
% 5.52/5.80 ( A4
% 5.52/5.80 = ( times_times_rat @ B3 @ K2 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_def
% 5.52/5.80 thf(fact_3973_dvd__def,axiom,
% 5.52/5.80 ( dvd_dvd_nat
% 5.52/5.80 = ( ^ [B3: nat,A4: nat] :
% 5.52/5.80 ? [K2: nat] :
% 5.52/5.80 ( A4
% 5.52/5.80 = ( times_times_nat @ B3 @ K2 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_def
% 5.52/5.80 thf(fact_3974_dvd__def,axiom,
% 5.52/5.80 ( dvd_dvd_int
% 5.52/5.80 = ( ^ [B3: int,A4: int] :
% 5.52/5.80 ? [K2: int] :
% 5.52/5.80 ( A4
% 5.52/5.80 = ( times_times_int @ B3 @ K2 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_def
% 5.52/5.80 thf(fact_3975_dvdI,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.52/5.80 ( ( A
% 5.52/5.80 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvdI
% 5.52/5.80 thf(fact_3976_dvdI,axiom,
% 5.52/5.80 ! [A: real,B: real,K: real] :
% 5.52/5.80 ( ( A
% 5.52/5.80 = ( times_times_real @ B @ K ) )
% 5.52/5.80 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvdI
% 5.52/5.80 thf(fact_3977_dvdI,axiom,
% 5.52/5.80 ! [A: rat,B: rat,K: rat] :
% 5.52/5.80 ( ( A
% 5.52/5.80 = ( times_times_rat @ B @ K ) )
% 5.52/5.80 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvdI
% 5.52/5.80 thf(fact_3978_dvdI,axiom,
% 5.52/5.80 ! [A: nat,B: nat,K: nat] :
% 5.52/5.80 ( ( A
% 5.52/5.80 = ( times_times_nat @ B @ K ) )
% 5.52/5.80 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvdI
% 5.52/5.80 thf(fact_3979_dvdI,axiom,
% 5.52/5.80 ! [A: int,B: int,K: int] :
% 5.52/5.80 ( ( A
% 5.52/5.80 = ( times_times_int @ B @ K ) )
% 5.52/5.80 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvdI
% 5.52/5.80 thf(fact_3980_dvdE,axiom,
% 5.52/5.80 ! [B: code_integer,A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.52/5.80 => ~ ! [K3: code_integer] :
% 5.52/5.80 ( A
% 5.52/5.80 != ( times_3573771949741848930nteger @ B @ K3 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvdE
% 5.52/5.80 thf(fact_3981_dvdE,axiom,
% 5.52/5.80 ! [B: real,A: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ B @ A )
% 5.52/5.80 => ~ ! [K3: real] :
% 5.52/5.80 ( A
% 5.52/5.80 != ( times_times_real @ B @ K3 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvdE
% 5.52/5.80 thf(fact_3982_dvdE,axiom,
% 5.52/5.80 ! [B: rat,A: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ B @ A )
% 5.52/5.80 => ~ ! [K3: rat] :
% 5.52/5.80 ( A
% 5.52/5.80 != ( times_times_rat @ B @ K3 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvdE
% 5.52/5.80 thf(fact_3983_dvdE,axiom,
% 5.52/5.80 ! [B: nat,A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ B @ A )
% 5.52/5.80 => ~ ! [K3: nat] :
% 5.52/5.80 ( A
% 5.52/5.80 != ( times_times_nat @ B @ K3 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvdE
% 5.52/5.80 thf(fact_3984_dvdE,axiom,
% 5.52/5.80 ! [B: int,A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ B @ A )
% 5.52/5.80 => ~ ! [K3: int] :
% 5.52/5.80 ( A
% 5.52/5.80 != ( times_times_int @ B @ K3 ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvdE
% 5.52/5.80 thf(fact_3985_dvd__unit__imp__unit,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_unit_imp_unit
% 5.52/5.80 thf(fact_3986_dvd__unit__imp__unit,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.80 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_unit_imp_unit
% 5.52/5.80 thf(fact_3987_dvd__unit__imp__unit,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.80 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_unit_imp_unit
% 5.52/5.80 thf(fact_3988_unit__imp__dvd,axiom,
% 5.52/5.80 ! [B: code_integer,A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_imp_dvd
% 5.52/5.80 thf(fact_3989_unit__imp__dvd,axiom,
% 5.52/5.80 ! [B: nat,A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.80 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_imp_dvd
% 5.52/5.80 thf(fact_3990_unit__imp__dvd,axiom,
% 5.52/5.80 ! [B: int,A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.80 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_imp_dvd
% 5.52/5.80 thf(fact_3991_one__dvd,axiom,
% 5.52/5.80 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.52/5.80
% 5.52/5.80 % one_dvd
% 5.52/5.80 thf(fact_3992_one__dvd,axiom,
% 5.52/5.80 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.52/5.80
% 5.52/5.80 % one_dvd
% 5.52/5.80 thf(fact_3993_one__dvd,axiom,
% 5.52/5.80 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.52/5.80
% 5.52/5.80 % one_dvd
% 5.52/5.80 thf(fact_3994_one__dvd,axiom,
% 5.52/5.80 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.52/5.80
% 5.52/5.80 % one_dvd
% 5.52/5.80 thf(fact_3995_one__dvd,axiom,
% 5.52/5.80 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.52/5.80
% 5.52/5.80 % one_dvd
% 5.52/5.80 thf(fact_3996_one__dvd,axiom,
% 5.52/5.80 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.52/5.80
% 5.52/5.80 % one_dvd
% 5.52/5.80 thf(fact_3997_dvd__add__right__iff,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_right_iff
% 5.52/5.80 thf(fact_3998_dvd__add__right__iff,axiom,
% 5.52/5.80 ! [A: real,B: real,C: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_right_iff
% 5.52/5.80 thf(fact_3999_dvd__add__right__iff,axiom,
% 5.52/5.80 ! [A: rat,B: rat,C: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_right_iff
% 5.52/5.80 thf(fact_4000_dvd__add__right__iff,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_right_iff
% 5.52/5.80 thf(fact_4001_dvd__add__right__iff,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_right_iff
% 5.52/5.80 thf(fact_4002_dvd__add__right__iff,axiom,
% 5.52/5.80 ! [A: complex,B: complex,C: complex] :
% 5.52/5.80 ( ( dvd_dvd_complex @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_complex @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_right_iff
% 5.52/5.80 thf(fact_4003_dvd__add__left__iff,axiom,
% 5.52/5.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_left_iff
% 5.52/5.80 thf(fact_4004_dvd__add__left__iff,axiom,
% 5.52/5.80 ! [A: real,C: real,B: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ A @ C )
% 5.52/5.80 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_left_iff
% 5.52/5.80 thf(fact_4005_dvd__add__left__iff,axiom,
% 5.52/5.80 ! [A: rat,C: rat,B: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ A @ C )
% 5.52/5.80 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_left_iff
% 5.52/5.80 thf(fact_4006_dvd__add__left__iff,axiom,
% 5.52/5.80 ! [A: nat,C: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ C )
% 5.52/5.80 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_left_iff
% 5.52/5.80 thf(fact_4007_dvd__add__left__iff,axiom,
% 5.52/5.80 ! [A: int,C: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ C )
% 5.52/5.80 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_left_iff
% 5.52/5.80 thf(fact_4008_dvd__add__left__iff,axiom,
% 5.52/5.80 ! [A: complex,C: complex,B: complex] :
% 5.52/5.80 ( ( dvd_dvd_complex @ A @ C )
% 5.52/5.80 => ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add_left_iff
% 5.52/5.80 thf(fact_4009_dvd__add,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add
% 5.52/5.80 thf(fact_4010_dvd__add,axiom,
% 5.52/5.80 ! [A: real,B: real,C: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_real @ A @ C )
% 5.52/5.80 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add
% 5.52/5.80 thf(fact_4011_dvd__add,axiom,
% 5.52/5.80 ! [A: rat,B: rat,C: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_rat @ A @ C )
% 5.52/5.80 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add
% 5.52/5.80 thf(fact_4012_dvd__add,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_nat @ A @ C )
% 5.52/5.80 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add
% 5.52/5.80 thf(fact_4013_dvd__add,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_int @ A @ C )
% 5.52/5.80 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add
% 5.52/5.80 thf(fact_4014_dvd__add,axiom,
% 5.52/5.80 ! [A: complex,B: complex,C: complex] :
% 5.52/5.80 ( ( dvd_dvd_complex @ A @ B )
% 5.52/5.80 => ( ( dvd_dvd_complex @ A @ C )
% 5.52/5.80 => ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_add
% 5.52/5.80 thf(fact_4015_dvd__diff__commute,axiom,
% 5.52/5.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_diff_commute
% 5.52/5.80 thf(fact_4016_dvd__diff__commute,axiom,
% 5.52/5.80 ! [A: int,C: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.52/5.80 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_diff_commute
% 5.52/5.80 thf(fact_4017_dvd__diff,axiom,
% 5.52/5.80 ! [X2: code_integer,Y2: code_integer,Z: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ X2 @ Y2 )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ X2 @ Z )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ X2 @ ( minus_8373710615458151222nteger @ Y2 @ Z ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_diff
% 5.52/5.80 thf(fact_4018_dvd__diff,axiom,
% 5.52/5.80 ! [X2: complex,Y2: complex,Z: complex] :
% 5.52/5.80 ( ( dvd_dvd_complex @ X2 @ Y2 )
% 5.52/5.80 => ( ( dvd_dvd_complex @ X2 @ Z )
% 5.52/5.80 => ( dvd_dvd_complex @ X2 @ ( minus_minus_complex @ Y2 @ Z ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_diff
% 5.52/5.80 thf(fact_4019_dvd__diff,axiom,
% 5.52/5.80 ! [X2: real,Y2: real,Z: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ X2 @ Y2 )
% 5.52/5.80 => ( ( dvd_dvd_real @ X2 @ Z )
% 5.52/5.80 => ( dvd_dvd_real @ X2 @ ( minus_minus_real @ Y2 @ Z ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_diff
% 5.52/5.80 thf(fact_4020_dvd__diff,axiom,
% 5.52/5.80 ! [X2: rat,Y2: rat,Z: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ X2 @ Y2 )
% 5.52/5.80 => ( ( dvd_dvd_rat @ X2 @ Z )
% 5.52/5.80 => ( dvd_dvd_rat @ X2 @ ( minus_minus_rat @ Y2 @ Z ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_diff
% 5.52/5.80 thf(fact_4021_dvd__diff,axiom,
% 5.52/5.80 ! [X2: int,Y2: int,Z: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ X2 @ Y2 )
% 5.52/5.80 => ( ( dvd_dvd_int @ X2 @ Z )
% 5.52/5.80 => ( dvd_dvd_int @ X2 @ ( minus_minus_int @ Y2 @ Z ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_diff
% 5.52/5.80 thf(fact_4022_dvd__div__eq__iff,axiom,
% 5.52/5.80 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.52/5.80 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.52/5.80 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.52/5.80 = ( A = B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_iff
% 5.52/5.80 thf(fact_4023_dvd__div__eq__iff,axiom,
% 5.52/5.80 ! [C: complex,A: complex,B: complex] :
% 5.52/5.80 ( ( dvd_dvd_complex @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_complex @ C @ B )
% 5.52/5.80 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.52/5.80 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.52/5.80 = ( A = B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_iff
% 5.52/5.80 thf(fact_4024_dvd__div__eq__iff,axiom,
% 5.52/5.80 ! [C: real,A: real,B: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_real @ C @ B )
% 5.52/5.80 => ( ( ( divide_divide_real @ A @ C )
% 5.52/5.80 = ( divide_divide_real @ B @ C ) )
% 5.52/5.80 = ( A = B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_iff
% 5.52/5.80 thf(fact_4025_dvd__div__eq__iff,axiom,
% 5.52/5.80 ! [C: rat,A: rat,B: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_rat @ C @ B )
% 5.52/5.80 => ( ( ( divide_divide_rat @ A @ C )
% 5.52/5.80 = ( divide_divide_rat @ B @ C ) )
% 5.52/5.80 = ( A = B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_iff
% 5.52/5.80 thf(fact_4026_dvd__div__eq__iff,axiom,
% 5.52/5.80 ! [C: nat,A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_nat @ C @ B )
% 5.52/5.80 => ( ( ( divide_divide_nat @ A @ C )
% 5.52/5.80 = ( divide_divide_nat @ B @ C ) )
% 5.52/5.80 = ( A = B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_iff
% 5.52/5.80 thf(fact_4027_dvd__div__eq__iff,axiom,
% 5.52/5.80 ! [C: int,A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_int @ C @ B )
% 5.52/5.80 => ( ( ( divide_divide_int @ A @ C )
% 5.52/5.80 = ( divide_divide_int @ B @ C ) )
% 5.52/5.80 = ( A = B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_iff
% 5.52/5.80 thf(fact_4028_dvd__div__eq__cancel,axiom,
% 5.52/5.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.52/5.80 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.52/5.80 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.52/5.80 => ( A = B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_cancel
% 5.52/5.80 thf(fact_4029_dvd__div__eq__cancel,axiom,
% 5.52/5.80 ! [A: complex,C: complex,B: complex] :
% 5.52/5.80 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.52/5.80 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.52/5.80 => ( ( dvd_dvd_complex @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_complex @ C @ B )
% 5.52/5.80 => ( A = B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_cancel
% 5.52/5.80 thf(fact_4030_dvd__div__eq__cancel,axiom,
% 5.52/5.80 ! [A: real,C: real,B: real] :
% 5.52/5.80 ( ( ( divide_divide_real @ A @ C )
% 5.52/5.80 = ( divide_divide_real @ B @ C ) )
% 5.52/5.80 => ( ( dvd_dvd_real @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_real @ C @ B )
% 5.52/5.80 => ( A = B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_cancel
% 5.52/5.80 thf(fact_4031_dvd__div__eq__cancel,axiom,
% 5.52/5.80 ! [A: rat,C: rat,B: rat] :
% 5.52/5.80 ( ( ( divide_divide_rat @ A @ C )
% 5.52/5.80 = ( divide_divide_rat @ B @ C ) )
% 5.52/5.80 => ( ( dvd_dvd_rat @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_rat @ C @ B )
% 5.52/5.80 => ( A = B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_cancel
% 5.52/5.80 thf(fact_4032_dvd__div__eq__cancel,axiom,
% 5.52/5.80 ! [A: nat,C: nat,B: nat] :
% 5.52/5.80 ( ( ( divide_divide_nat @ A @ C )
% 5.52/5.80 = ( divide_divide_nat @ B @ C ) )
% 5.52/5.80 => ( ( dvd_dvd_nat @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_nat @ C @ B )
% 5.52/5.80 => ( A = B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_cancel
% 5.52/5.80 thf(fact_4033_dvd__div__eq__cancel,axiom,
% 5.52/5.80 ! [A: int,C: int,B: int] :
% 5.52/5.80 ( ( ( divide_divide_int @ A @ C )
% 5.52/5.80 = ( divide_divide_int @ B @ C ) )
% 5.52/5.80 => ( ( dvd_dvd_int @ C @ A )
% 5.52/5.80 => ( ( dvd_dvd_int @ C @ B )
% 5.52/5.80 => ( A = B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_cancel
% 5.52/5.80 thf(fact_4034_div__div__div__same,axiom,
% 5.52/5.80 ! [D2: code_integer,B: code_integer,A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ D2 @ B )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.52/5.80 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D2 ) @ ( divide6298287555418463151nteger @ B @ D2 ) )
% 5.52/5.80 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_div_div_same
% 5.52/5.80 thf(fact_4035_div__div__div__same,axiom,
% 5.52/5.80 ! [D2: nat,B: nat,A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ D2 @ B )
% 5.52/5.80 => ( ( dvd_dvd_nat @ B @ A )
% 5.52/5.80 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D2 ) @ ( divide_divide_nat @ B @ D2 ) )
% 5.52/5.80 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_div_div_same
% 5.52/5.80 thf(fact_4036_div__div__div__same,axiom,
% 5.52/5.80 ! [D2: int,B: int,A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ D2 @ B )
% 5.52/5.80 => ( ( dvd_dvd_int @ B @ A )
% 5.52/5.80 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D2 ) @ ( divide_divide_int @ B @ D2 ) )
% 5.52/5.80 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_div_div_same
% 5.52/5.80 thf(fact_4037_dvd__power__same,axiom,
% 5.52/5.80 ! [X2: code_integer,Y2: code_integer,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ X2 @ Y2 )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y2 @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_power_same
% 5.52/5.80 thf(fact_4038_dvd__power__same,axiom,
% 5.52/5.80 ! [X2: nat,Y2: nat,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ X2 @ Y2 )
% 5.52/5.80 => ( dvd_dvd_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y2 @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_power_same
% 5.52/5.80 thf(fact_4039_dvd__power__same,axiom,
% 5.52/5.80 ! [X2: real,Y2: real,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_real @ X2 @ Y2 )
% 5.52/5.80 => ( dvd_dvd_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y2 @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_power_same
% 5.52/5.80 thf(fact_4040_dvd__power__same,axiom,
% 5.52/5.80 ! [X2: int,Y2: int,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_int @ X2 @ Y2 )
% 5.52/5.80 => ( dvd_dvd_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y2 @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_power_same
% 5.52/5.80 thf(fact_4041_dvd__power__same,axiom,
% 5.52/5.80 ! [X2: complex,Y2: complex,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_complex @ X2 @ Y2 )
% 5.52/5.80 => ( dvd_dvd_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y2 @ N ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_power_same
% 5.52/5.80 thf(fact_4042_old_Oprod_Ocase,axiom,
% 5.52/5.80 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X23: nat] :
% 5.52/5.80 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X23 ) )
% 5.52/5.80 = ( F @ X1 @ X23 ) ) ).
% 5.52/5.80
% 5.52/5.80 % old.prod.case
% 5.52/5.80 thf(fact_4043_old_Oprod_Ocase,axiom,
% 5.52/5.80 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X23: nat] :
% 5.52/5.80 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X23 ) )
% 5.52/5.80 = ( F @ X1 @ X23 ) ) ).
% 5.52/5.80
% 5.52/5.80 % old.prod.case
% 5.52/5.80 thf(fact_4044_old_Oprod_Ocase,axiom,
% 5.52/5.80 ! [F: int > int > product_prod_int_int,X1: int,X23: int] :
% 5.52/5.80 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X23 ) )
% 5.52/5.80 = ( F @ X1 @ X23 ) ) ).
% 5.52/5.80
% 5.52/5.80 % old.prod.case
% 5.52/5.80 thf(fact_4045_old_Oprod_Ocase,axiom,
% 5.52/5.80 ! [F: int > int > $o,X1: int,X23: int] :
% 5.52/5.80 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X23 ) )
% 5.52/5.80 = ( F @ X1 @ X23 ) ) ).
% 5.52/5.80
% 5.52/5.80 % old.prod.case
% 5.52/5.80 thf(fact_4046_old_Oprod_Ocase,axiom,
% 5.52/5.80 ! [F: int > int > int,X1: int,X23: int] :
% 5.52/5.80 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X23 ) )
% 5.52/5.80 = ( F @ X1 @ X23 ) ) ).
% 5.52/5.80
% 5.52/5.80 % old.prod.case
% 5.52/5.80 thf(fact_4047_mod__mod__cancel,axiom,
% 5.52/5.80 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.52/5.80 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 5.52/5.80 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mod_mod_cancel
% 5.52/5.80 thf(fact_4048_mod__mod__cancel,axiom,
% 5.52/5.80 ! [C: nat,B: nat,A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ C @ B )
% 5.52/5.80 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 5.52/5.80 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mod_mod_cancel
% 5.52/5.80 thf(fact_4049_mod__mod__cancel,axiom,
% 5.52/5.80 ! [C: int,B: int,A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ C @ B )
% 5.52/5.80 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 5.52/5.80 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mod_mod_cancel
% 5.52/5.80 thf(fact_4050_dvd__mod,axiom,
% 5.52/5.80 ! [K: code_integer,M: code_integer,N: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ K @ N )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mod
% 5.52/5.80 thf(fact_4051_dvd__mod,axiom,
% 5.52/5.80 ! [K: nat,M: nat,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ K @ M )
% 5.52/5.80 => ( ( dvd_dvd_nat @ K @ N )
% 5.52/5.80 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mod
% 5.52/5.80 thf(fact_4052_dvd__mod,axiom,
% 5.52/5.80 ! [K: int,M: int,N: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ K @ M )
% 5.52/5.80 => ( ( dvd_dvd_int @ K @ N )
% 5.52/5.80 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mod
% 5.52/5.80 thf(fact_4053_dvd__mod__imp__dvd,axiom,
% 5.52/5.80 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mod_imp_dvd
% 5.52/5.80 thf(fact_4054_dvd__mod__imp__dvd,axiom,
% 5.52/5.80 ! [C: nat,A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.52/5.80 => ( ( dvd_dvd_nat @ C @ B )
% 5.52/5.80 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mod_imp_dvd
% 5.52/5.80 thf(fact_4055_dvd__mod__imp__dvd,axiom,
% 5.52/5.80 ! [C: int,A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.52/5.80 => ( ( dvd_dvd_int @ C @ B )
% 5.52/5.80 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mod_imp_dvd
% 5.52/5.80 thf(fact_4056_dvd__mod__iff,axiom,
% 5.52/5.80 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mod_iff
% 5.52/5.80 thf(fact_4057_dvd__mod__iff,axiom,
% 5.52/5.80 ! [C: nat,B: nat,A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ C @ B )
% 5.52/5.80 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.52/5.80 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mod_iff
% 5.52/5.80 thf(fact_4058_dvd__mod__iff,axiom,
% 5.52/5.80 ! [C: int,B: int,A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ C @ B )
% 5.52/5.80 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.52/5.80 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mod_iff
% 5.52/5.80 thf(fact_4059_signed__take__bit__mult,axiom,
% 5.52/5.80 ! [N: nat,K: int,L: int] :
% 5.52/5.80 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.52/5.80 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % signed_take_bit_mult
% 5.52/5.80 thf(fact_4060_signed__take__bit__add,axiom,
% 5.52/5.80 ! [N: nat,K: int,L: int] :
% 5.52/5.80 ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.52/5.80 = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % signed_take_bit_add
% 5.52/5.80 thf(fact_4061_dvd__diff__nat,axiom,
% 5.52/5.80 ! [K: nat,M: nat,N: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ K @ M )
% 5.52/5.80 => ( ( dvd_dvd_nat @ K @ N )
% 5.52/5.80 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_diff_nat
% 5.52/5.80 thf(fact_4062_signed__take__bit__diff,axiom,
% 5.52/5.80 ! [N: nat,K: int,L: int] :
% 5.52/5.80 ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.52/5.80 = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % signed_take_bit_diff
% 5.52/5.80 thf(fact_4063_subset__divisors__dvd,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( ord_less_eq_set_int
% 5.52/5.80 @ ( collect_int
% 5.52/5.80 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.52/5.80 @ ( collect_int
% 5.52/5.80 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.52/5.80 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % subset_divisors_dvd
% 5.52/5.80 thf(fact_4064_subset__divisors__dvd,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( ord_le7084787975880047091nteger
% 5.52/5.80 @ ( collect_Code_integer
% 5.52/5.80 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 5.52/5.80 @ ( collect_Code_integer
% 5.52/5.80 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % subset_divisors_dvd
% 5.52/5.80 thf(fact_4065_subset__divisors__dvd,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( ord_less_eq_set_nat
% 5.52/5.80 @ ( collect_nat
% 5.52/5.80 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.52/5.80 @ ( collect_nat
% 5.52/5.80 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.52/5.80 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.52/5.80
% 5.52/5.80 % subset_divisors_dvd
% 5.52/5.80 thf(fact_4066_cond__case__prod__eta,axiom,
% 5.52/5.80 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.52/5.80 ( ! [X4: nat,Y3: nat] :
% 5.52/5.80 ( ( F @ X4 @ Y3 )
% 5.52/5.80 = ( G @ ( product_Pair_nat_nat @ X4 @ Y3 ) ) )
% 5.52/5.80 => ( ( produc27273713700761075at_nat @ F )
% 5.52/5.80 = G ) ) ).
% 5.52/5.80
% 5.52/5.80 % cond_case_prod_eta
% 5.52/5.80 thf(fact_4067_cond__case__prod__eta,axiom,
% 5.52/5.80 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.52/5.80 ( ! [X4: nat,Y3: nat] :
% 5.52/5.80 ( ( F @ X4 @ Y3 )
% 5.52/5.80 = ( G @ ( product_Pair_nat_nat @ X4 @ Y3 ) ) )
% 5.52/5.80 => ( ( produc8739625826339149834_nat_o @ F )
% 5.52/5.80 = G ) ) ).
% 5.52/5.80
% 5.52/5.80 % cond_case_prod_eta
% 5.52/5.80 thf(fact_4068_cond__case__prod__eta,axiom,
% 5.52/5.80 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 5.52/5.80 ( ! [X4: int,Y3: int] :
% 5.52/5.80 ( ( F @ X4 @ Y3 )
% 5.52/5.80 = ( G @ ( product_Pair_int_int @ X4 @ Y3 ) ) )
% 5.52/5.80 => ( ( produc4245557441103728435nt_int @ F )
% 5.52/5.80 = G ) ) ).
% 5.52/5.80
% 5.52/5.80 % cond_case_prod_eta
% 5.52/5.80 thf(fact_4069_cond__case__prod__eta,axiom,
% 5.52/5.80 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 5.52/5.80 ( ! [X4: int,Y3: int] :
% 5.52/5.80 ( ( F @ X4 @ Y3 )
% 5.52/5.80 = ( G @ ( product_Pair_int_int @ X4 @ Y3 ) ) )
% 5.52/5.80 => ( ( produc4947309494688390418_int_o @ F )
% 5.52/5.80 = G ) ) ).
% 5.52/5.80
% 5.52/5.80 % cond_case_prod_eta
% 5.52/5.80 thf(fact_4070_cond__case__prod__eta,axiom,
% 5.52/5.80 ! [F: int > int > int,G: product_prod_int_int > int] :
% 5.52/5.80 ( ! [X4: int,Y3: int] :
% 5.52/5.80 ( ( F @ X4 @ Y3 )
% 5.52/5.80 = ( G @ ( product_Pair_int_int @ X4 @ Y3 ) ) )
% 5.52/5.80 => ( ( produc8211389475949308722nt_int @ F )
% 5.52/5.80 = G ) ) ).
% 5.52/5.80
% 5.52/5.80 % cond_case_prod_eta
% 5.52/5.80 thf(fact_4071_case__prod__eta,axiom,
% 5.52/5.80 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.52/5.80 ( ( produc27273713700761075at_nat
% 5.52/5.80 @ ^ [X: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X @ Y ) ) )
% 5.52/5.80 = F ) ).
% 5.52/5.80
% 5.52/5.80 % case_prod_eta
% 5.52/5.80 thf(fact_4072_case__prod__eta,axiom,
% 5.52/5.80 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.52/5.80 ( ( produc8739625826339149834_nat_o
% 5.52/5.80 @ ^ [X: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X @ Y ) ) )
% 5.52/5.80 = F ) ).
% 5.52/5.80
% 5.52/5.80 % case_prod_eta
% 5.52/5.80 thf(fact_4073_case__prod__eta,axiom,
% 5.52/5.80 ! [F: product_prod_int_int > product_prod_int_int] :
% 5.52/5.80 ( ( produc4245557441103728435nt_int
% 5.52/5.80 @ ^ [X: int,Y: int] : ( F @ ( product_Pair_int_int @ X @ Y ) ) )
% 5.52/5.80 = F ) ).
% 5.52/5.80
% 5.52/5.80 % case_prod_eta
% 5.52/5.80 thf(fact_4074_case__prod__eta,axiom,
% 5.52/5.80 ! [F: product_prod_int_int > $o] :
% 5.52/5.80 ( ( produc4947309494688390418_int_o
% 5.52/5.80 @ ^ [X: int,Y: int] : ( F @ ( product_Pair_int_int @ X @ Y ) ) )
% 5.52/5.80 = F ) ).
% 5.52/5.80
% 5.52/5.80 % case_prod_eta
% 5.52/5.80 thf(fact_4075_case__prod__eta,axiom,
% 5.52/5.80 ! [F: product_prod_int_int > int] :
% 5.52/5.80 ( ( produc8211389475949308722nt_int
% 5.52/5.80 @ ^ [X: int,Y: int] : ( F @ ( product_Pair_int_int @ X @ Y ) ) )
% 5.52/5.80 = F ) ).
% 5.52/5.80
% 5.52/5.80 % case_prod_eta
% 5.52/5.80 thf(fact_4076_case__prodE2,axiom,
% 5.52/5.80 ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.52/5.80 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 5.52/5.80 => ~ ! [X4: nat,Y3: nat] :
% 5.52/5.80 ( ( Z
% 5.52/5.80 = ( product_Pair_nat_nat @ X4 @ Y3 ) )
% 5.52/5.80 => ~ ( Q @ ( P @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % case_prodE2
% 5.52/5.80 thf(fact_4077_case__prodE2,axiom,
% 5.52/5.80 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 5.52/5.80 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 5.52/5.80 => ~ ! [X4: nat,Y3: nat] :
% 5.52/5.80 ( ( Z
% 5.52/5.80 = ( product_Pair_nat_nat @ X4 @ Y3 ) )
% 5.52/5.80 => ~ ( Q @ ( P @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % case_prodE2
% 5.52/5.80 thf(fact_4078_case__prodE2,axiom,
% 5.52/5.80 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 5.52/5.80 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 5.52/5.80 => ~ ! [X4: int,Y3: int] :
% 5.52/5.80 ( ( Z
% 5.52/5.80 = ( product_Pair_int_int @ X4 @ Y3 ) )
% 5.52/5.80 => ~ ( Q @ ( P @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % case_prodE2
% 5.52/5.80 thf(fact_4079_case__prodE2,axiom,
% 5.52/5.80 ! [Q: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 5.52/5.80 ( ( Q @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 5.52/5.80 => ~ ! [X4: int,Y3: int] :
% 5.52/5.80 ( ( Z
% 5.52/5.80 = ( product_Pair_int_int @ X4 @ Y3 ) )
% 5.52/5.80 => ~ ( Q @ ( P @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % case_prodE2
% 5.52/5.80 thf(fact_4080_case__prodE2,axiom,
% 5.52/5.80 ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 5.52/5.80 ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 5.52/5.80 => ~ ! [X4: int,Y3: int] :
% 5.52/5.80 ( ( Z
% 5.52/5.80 = ( product_Pair_int_int @ X4 @ Y3 ) )
% 5.52/5.80 => ~ ( Q @ ( P @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % case_prodE2
% 5.52/5.80 thf(fact_4081_strict__subset__divisors__dvd,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( ord_less_set_nat
% 5.52/5.80 @ ( collect_nat
% 5.52/5.80 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.52/5.80 @ ( collect_nat
% 5.52/5.80 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.52/5.80 = ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.80 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % strict_subset_divisors_dvd
% 5.52/5.80 thf(fact_4082_strict__subset__divisors__dvd,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( ord_less_set_int
% 5.52/5.80 @ ( collect_int
% 5.52/5.80 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.52/5.80 @ ( collect_int
% 5.52/5.80 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.52/5.80 = ( ( dvd_dvd_int @ A @ B )
% 5.52/5.80 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % strict_subset_divisors_dvd
% 5.52/5.80 thf(fact_4083_strict__subset__divisors__dvd,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( ord_le1307284697595431911nteger
% 5.52/5.80 @ ( collect_Code_integer
% 5.52/5.80 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 5.52/5.80 @ ( collect_Code_integer
% 5.52/5.80 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 5.52/5.80 = ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.80 & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % strict_subset_divisors_dvd
% 5.52/5.80 thf(fact_4084_even__signed__take__bit__iff,axiom,
% 5.52/5.80 ! [M: nat,A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_signed_take_bit_iff
% 5.52/5.80 thf(fact_4085_even__signed__take__bit__iff,axiom,
% 5.52/5.80 ! [M: nat,A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.52/5.80 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.52/5.80
% 5.52/5.80 % even_signed_take_bit_iff
% 5.52/5.80 thf(fact_4086_not__is__unit__0,axiom,
% 5.52/5.80 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.52/5.80
% 5.52/5.80 % not_is_unit_0
% 5.52/5.80 thf(fact_4087_not__is__unit__0,axiom,
% 5.52/5.80 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.52/5.80
% 5.52/5.80 % not_is_unit_0
% 5.52/5.80 thf(fact_4088_not__is__unit__0,axiom,
% 5.52/5.80 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.52/5.80
% 5.52/5.80 % not_is_unit_0
% 5.52/5.80 thf(fact_4089_pinf_I9_J,axiom,
% 5.52/5.80 ! [D2: code_integer,S: code_integer] :
% 5.52/5.80 ? [Z3: code_integer] :
% 5.52/5.80 ! [X6: code_integer] :
% 5.52/5.80 ( ( ord_le6747313008572928689nteger @ Z3 @ X6 )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X6 @ S ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % pinf(9)
% 5.52/5.80 thf(fact_4090_pinf_I9_J,axiom,
% 5.52/5.80 ! [D2: real,S: real] :
% 5.52/5.80 ? [Z3: real] :
% 5.52/5.80 ! [X6: real] :
% 5.52/5.80 ( ( ord_less_real @ Z3 @ X6 )
% 5.52/5.80 => ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X6 @ S ) )
% 5.52/5.80 = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X6 @ S ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % pinf(9)
% 5.52/5.80 thf(fact_4091_pinf_I9_J,axiom,
% 5.52/5.80 ! [D2: rat,S: rat] :
% 5.52/5.80 ? [Z3: rat] :
% 5.52/5.80 ! [X6: rat] :
% 5.52/5.80 ( ( ord_less_rat @ Z3 @ X6 )
% 5.52/5.80 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S ) )
% 5.52/5.80 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % pinf(9)
% 5.52/5.80 thf(fact_4092_pinf_I9_J,axiom,
% 5.52/5.80 ! [D2: nat,S: nat] :
% 5.52/5.80 ? [Z3: nat] :
% 5.52/5.80 ! [X6: nat] :
% 5.52/5.80 ( ( ord_less_nat @ Z3 @ X6 )
% 5.52/5.80 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S ) )
% 5.52/5.80 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % pinf(9)
% 5.52/5.80 thf(fact_4093_pinf_I9_J,axiom,
% 5.52/5.80 ! [D2: int,S: int] :
% 5.52/5.80 ? [Z3: int] :
% 5.52/5.80 ! [X6: int] :
% 5.52/5.80 ( ( ord_less_int @ Z3 @ X6 )
% 5.52/5.80 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S ) )
% 5.52/5.80 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % pinf(9)
% 5.52/5.80 thf(fact_4094_pinf_I10_J,axiom,
% 5.52/5.80 ! [D2: code_integer,S: code_integer] :
% 5.52/5.80 ? [Z3: code_integer] :
% 5.52/5.80 ! [X6: code_integer] :
% 5.52/5.80 ( ( ord_le6747313008572928689nteger @ Z3 @ X6 )
% 5.52/5.80 => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % pinf(10)
% 5.52/5.80 thf(fact_4095_pinf_I10_J,axiom,
% 5.52/5.80 ! [D2: real,S: real] :
% 5.52/5.80 ? [Z3: real] :
% 5.52/5.80 ! [X6: real] :
% 5.52/5.80 ( ( ord_less_real @ Z3 @ X6 )
% 5.52/5.80 => ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X6 @ S ) ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X6 @ S ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % pinf(10)
% 5.52/5.80 thf(fact_4096_pinf_I10_J,axiom,
% 5.52/5.80 ! [D2: rat,S: rat] :
% 5.52/5.80 ? [Z3: rat] :
% 5.52/5.80 ! [X6: rat] :
% 5.52/5.80 ( ( ord_less_rat @ Z3 @ X6 )
% 5.52/5.80 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S ) ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % pinf(10)
% 5.52/5.80 thf(fact_4097_pinf_I10_J,axiom,
% 5.52/5.80 ! [D2: nat,S: nat] :
% 5.52/5.80 ? [Z3: nat] :
% 5.52/5.80 ! [X6: nat] :
% 5.52/5.80 ( ( ord_less_nat @ Z3 @ X6 )
% 5.52/5.80 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S ) ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % pinf(10)
% 5.52/5.80 thf(fact_4098_pinf_I10_J,axiom,
% 5.52/5.80 ! [D2: int,S: int] :
% 5.52/5.80 ? [Z3: int] :
% 5.52/5.80 ! [X6: int] :
% 5.52/5.80 ( ( ord_less_int @ Z3 @ X6 )
% 5.52/5.80 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S ) ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % pinf(10)
% 5.52/5.80 thf(fact_4099_minf_I9_J,axiom,
% 5.52/5.80 ! [D2: code_integer,S: code_integer] :
% 5.52/5.80 ? [Z3: code_integer] :
% 5.52/5.80 ! [X6: code_integer] :
% 5.52/5.80 ( ( ord_le6747313008572928689nteger @ X6 @ Z3 )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X6 @ S ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % minf(9)
% 5.52/5.80 thf(fact_4100_minf_I9_J,axiom,
% 5.52/5.80 ! [D2: real,S: real] :
% 5.52/5.80 ? [Z3: real] :
% 5.52/5.80 ! [X6: real] :
% 5.52/5.80 ( ( ord_less_real @ X6 @ Z3 )
% 5.52/5.80 => ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X6 @ S ) )
% 5.52/5.80 = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X6 @ S ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % minf(9)
% 5.52/5.80 thf(fact_4101_minf_I9_J,axiom,
% 5.52/5.80 ! [D2: rat,S: rat] :
% 5.52/5.80 ? [Z3: rat] :
% 5.52/5.80 ! [X6: rat] :
% 5.52/5.80 ( ( ord_less_rat @ X6 @ Z3 )
% 5.52/5.80 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S ) )
% 5.52/5.80 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % minf(9)
% 5.52/5.80 thf(fact_4102_minf_I9_J,axiom,
% 5.52/5.80 ! [D2: nat,S: nat] :
% 5.52/5.80 ? [Z3: nat] :
% 5.52/5.80 ! [X6: nat] :
% 5.52/5.80 ( ( ord_less_nat @ X6 @ Z3 )
% 5.52/5.80 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S ) )
% 5.52/5.80 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % minf(9)
% 5.52/5.80 thf(fact_4103_minf_I9_J,axiom,
% 5.52/5.80 ! [D2: int,S: int] :
% 5.52/5.80 ? [Z3: int] :
% 5.52/5.80 ! [X6: int] :
% 5.52/5.80 ( ( ord_less_int @ X6 @ Z3 )
% 5.52/5.80 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S ) )
% 5.52/5.80 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % minf(9)
% 5.52/5.80 thf(fact_4104_minf_I10_J,axiom,
% 5.52/5.80 ! [D2: code_integer,S: code_integer] :
% 5.52/5.80 ? [Z3: code_integer] :
% 5.52/5.80 ! [X6: code_integer] :
% 5.52/5.80 ( ( ord_le6747313008572928689nteger @ X6 @ Z3 )
% 5.52/5.80 => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % minf(10)
% 5.52/5.80 thf(fact_4105_minf_I10_J,axiom,
% 5.52/5.80 ! [D2: real,S: real] :
% 5.52/5.80 ? [Z3: real] :
% 5.52/5.80 ! [X6: real] :
% 5.52/5.80 ( ( ord_less_real @ X6 @ Z3 )
% 5.52/5.80 => ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X6 @ S ) ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X6 @ S ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % minf(10)
% 5.52/5.80 thf(fact_4106_minf_I10_J,axiom,
% 5.52/5.80 ! [D2: rat,S: rat] :
% 5.52/5.80 ? [Z3: rat] :
% 5.52/5.80 ! [X6: rat] :
% 5.52/5.80 ( ( ord_less_rat @ X6 @ Z3 )
% 5.52/5.80 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S ) ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % minf(10)
% 5.52/5.80 thf(fact_4107_minf_I10_J,axiom,
% 5.52/5.80 ! [D2: nat,S: nat] :
% 5.52/5.80 ? [Z3: nat] :
% 5.52/5.80 ! [X6: nat] :
% 5.52/5.80 ( ( ord_less_nat @ X6 @ Z3 )
% 5.52/5.80 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S ) ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % minf(10)
% 5.52/5.80 thf(fact_4108_minf_I10_J,axiom,
% 5.52/5.80 ! [D2: int,S: int] :
% 5.52/5.80 ? [Z3: int] :
% 5.52/5.80 ! [X6: int] :
% 5.52/5.80 ( ( ord_less_int @ X6 @ Z3 )
% 5.52/5.80 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S ) ) )
% 5.52/5.80 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % minf(10)
% 5.52/5.80 thf(fact_4109_dvd__div__eq__0__iff,axiom,
% 5.52/5.80 ! [B: code_integer,A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.52/5.80 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.52/5.80 = zero_z3403309356797280102nteger )
% 5.52/5.80 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_0_iff
% 5.52/5.80 thf(fact_4110_dvd__div__eq__0__iff,axiom,
% 5.52/5.80 ! [B: complex,A: complex] :
% 5.52/5.80 ( ( dvd_dvd_complex @ B @ A )
% 5.52/5.80 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.52/5.80 = zero_zero_complex )
% 5.52/5.80 = ( A = zero_zero_complex ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_0_iff
% 5.52/5.80 thf(fact_4111_dvd__div__eq__0__iff,axiom,
% 5.52/5.80 ! [B: real,A: real] :
% 5.52/5.80 ( ( dvd_dvd_real @ B @ A )
% 5.52/5.80 => ( ( ( divide_divide_real @ A @ B )
% 5.52/5.80 = zero_zero_real )
% 5.52/5.80 = ( A = zero_zero_real ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_0_iff
% 5.52/5.80 thf(fact_4112_dvd__div__eq__0__iff,axiom,
% 5.52/5.80 ! [B: rat,A: rat] :
% 5.52/5.80 ( ( dvd_dvd_rat @ B @ A )
% 5.52/5.80 => ( ( ( divide_divide_rat @ A @ B )
% 5.52/5.80 = zero_zero_rat )
% 5.52/5.80 = ( A = zero_zero_rat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_0_iff
% 5.52/5.80 thf(fact_4113_dvd__div__eq__0__iff,axiom,
% 5.52/5.80 ! [B: nat,A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ B @ A )
% 5.52/5.80 => ( ( ( divide_divide_nat @ A @ B )
% 5.52/5.80 = zero_zero_nat )
% 5.52/5.80 = ( A = zero_zero_nat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_0_iff
% 5.52/5.80 thf(fact_4114_dvd__div__eq__0__iff,axiom,
% 5.52/5.80 ! [B: int,A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ B @ A )
% 5.52/5.80 => ( ( ( divide_divide_int @ A @ B )
% 5.52/5.80 = zero_zero_int )
% 5.52/5.80 = ( A = zero_zero_int ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_eq_0_iff
% 5.52/5.80 thf(fact_4115_unit__mult__right__cancel,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.80 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.52/5.80 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.52/5.80 = ( B = C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_mult_right_cancel
% 5.52/5.80 thf(fact_4116_unit__mult__right__cancel,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.80 => ( ( ( times_times_nat @ B @ A )
% 5.52/5.80 = ( times_times_nat @ C @ A ) )
% 5.52/5.80 = ( B = C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_mult_right_cancel
% 5.52/5.80 thf(fact_4117_unit__mult__right__cancel,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.80 => ( ( ( times_times_int @ B @ A )
% 5.52/5.80 = ( times_times_int @ C @ A ) )
% 5.52/5.80 = ( B = C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_mult_right_cancel
% 5.52/5.80 thf(fact_4118_unit__mult__left__cancel,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.80 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.52/5.80 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.52/5.80 = ( B = C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_mult_left_cancel
% 5.52/5.80 thf(fact_4119_unit__mult__left__cancel,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.80 => ( ( ( times_times_nat @ A @ B )
% 5.52/5.80 = ( times_times_nat @ A @ C ) )
% 5.52/5.80 = ( B = C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_mult_left_cancel
% 5.52/5.80 thf(fact_4120_unit__mult__left__cancel,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.80 => ( ( ( times_times_int @ A @ B )
% 5.52/5.80 = ( times_times_int @ A @ C ) )
% 5.52/5.80 = ( B = C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % unit_mult_left_cancel
% 5.52/5.80 thf(fact_4121_mult__unit__dvd__iff_H,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mult_unit_dvd_iff'
% 5.52/5.80 thf(fact_4122_mult__unit__dvd__iff_H,axiom,
% 5.52/5.80 ! [A: nat,B: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.80 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.52/5.80 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mult_unit_dvd_iff'
% 5.52/5.80 thf(fact_4123_mult__unit__dvd__iff_H,axiom,
% 5.52/5.80 ! [A: int,B: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.80 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.52/5.80 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mult_unit_dvd_iff'
% 5.52/5.80 thf(fact_4124_dvd__mult__unit__iff_H,axiom,
% 5.52/5.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_unit_iff'
% 5.52/5.80 thf(fact_4125_dvd__mult__unit__iff_H,axiom,
% 5.52/5.80 ! [B: nat,A: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.80 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_unit_iff'
% 5.52/5.80 thf(fact_4126_dvd__mult__unit__iff_H,axiom,
% 5.52/5.80 ! [B: int,A: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.80 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.52/5.80 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_unit_iff'
% 5.52/5.80 thf(fact_4127_mult__unit__dvd__iff,axiom,
% 5.52/5.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mult_unit_dvd_iff
% 5.52/5.80 thf(fact_4128_mult__unit__dvd__iff,axiom,
% 5.52/5.80 ! [B: nat,A: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.80 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.52/5.80 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mult_unit_dvd_iff
% 5.52/5.80 thf(fact_4129_mult__unit__dvd__iff,axiom,
% 5.52/5.80 ! [B: int,A: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.80 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.52/5.80 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % mult_unit_dvd_iff
% 5.52/5.80 thf(fact_4130_dvd__mult__unit__iff,axiom,
% 5.52/5.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.52/5.80 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_unit_iff
% 5.52/5.80 thf(fact_4131_dvd__mult__unit__iff,axiom,
% 5.52/5.80 ! [B: nat,A: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.80 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.52/5.80 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_unit_iff
% 5.52/5.80 thf(fact_4132_dvd__mult__unit__iff,axiom,
% 5.52/5.80 ! [B: int,A: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.80 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.52/5.80 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_unit_iff
% 5.52/5.80 thf(fact_4133_is__unit__mult__iff,axiom,
% 5.52/5.80 ! [A: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.52/5.80 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.80 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % is_unit_mult_iff
% 5.52/5.80 thf(fact_4134_is__unit__mult__iff,axiom,
% 5.52/5.80 ! [A: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.52/5.80 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.80 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % is_unit_mult_iff
% 5.52/5.80 thf(fact_4135_is__unit__mult__iff,axiom,
% 5.52/5.80 ! [A: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.52/5.80 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.80 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % is_unit_mult_iff
% 5.52/5.80 thf(fact_4136_div__mult__div__if__dvd,axiom,
% 5.52/5.80 ! [B: code_integer,A: code_integer,D2: code_integer,C: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ D2 @ C )
% 5.52/5.80 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D2 ) )
% 5.52/5.80 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_mult_div_if_dvd
% 5.52/5.80 thf(fact_4137_div__mult__div__if__dvd,axiom,
% 5.52/5.80 ! [B: nat,A: nat,D2: nat,C: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ B @ A )
% 5.52/5.80 => ( ( dvd_dvd_nat @ D2 @ C )
% 5.52/5.80 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D2 ) )
% 5.52/5.80 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_mult_div_if_dvd
% 5.52/5.80 thf(fact_4138_div__mult__div__if__dvd,axiom,
% 5.52/5.80 ! [B: int,A: int,D2: int,C: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ B @ A )
% 5.52/5.80 => ( ( dvd_dvd_int @ D2 @ C )
% 5.52/5.80 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D2 ) )
% 5.52/5.80 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_mult_div_if_dvd
% 5.52/5.80 thf(fact_4139_dvd__mult__imp__div,axiom,
% 5.52/5.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.52/5.80 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_imp_div
% 5.52/5.80 thf(fact_4140_dvd__mult__imp__div,axiom,
% 5.52/5.80 ! [A: nat,C: nat,B: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.52/5.80 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_imp_div
% 5.52/5.80 thf(fact_4141_dvd__mult__imp__div,axiom,
% 5.52/5.80 ! [A: int,C: int,B: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.52/5.80 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_mult_imp_div
% 5.52/5.80 thf(fact_4142_dvd__div__mult2__eq,axiom,
% 5.52/5.80 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.52/5.80 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.52/5.80 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_mult2_eq
% 5.52/5.80 thf(fact_4143_dvd__div__mult2__eq,axiom,
% 5.52/5.80 ! [B: nat,C: nat,A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.52/5.80 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.52/5.80 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_mult2_eq
% 5.52/5.80 thf(fact_4144_dvd__div__mult2__eq,axiom,
% 5.52/5.80 ! [B: int,C: int,A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.52/5.80 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.52/5.80 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % dvd_div_mult2_eq
% 5.52/5.80 thf(fact_4145_div__div__eq__right,axiom,
% 5.52/5.80 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.52/5.80 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.52/5.80 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.52/5.80 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_div_eq_right
% 5.52/5.80 thf(fact_4146_div__div__eq__right,axiom,
% 5.52/5.80 ! [C: nat,B: nat,A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ C @ B )
% 5.52/5.80 => ( ( dvd_dvd_nat @ B @ A )
% 5.52/5.80 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.52/5.80 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_div_eq_right
% 5.52/5.80 thf(fact_4147_div__div__eq__right,axiom,
% 5.52/5.80 ! [C: int,B: int,A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ C @ B )
% 5.52/5.80 => ( ( dvd_dvd_int @ B @ A )
% 5.52/5.80 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.52/5.80 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_div_eq_right
% 5.52/5.80 thf(fact_4148_div__mult__swap,axiom,
% 5.52/5.80 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.52/5.80 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.52/5.80 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.52/5.80 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_mult_swap
% 5.52/5.80 thf(fact_4149_div__mult__swap,axiom,
% 5.52/5.80 ! [C: nat,B: nat,A: nat] :
% 5.52/5.80 ( ( dvd_dvd_nat @ C @ B )
% 5.52/5.80 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.52/5.80 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.52/5.80
% 5.52/5.80 % div_mult_swap
% 5.52/5.80 thf(fact_4150_div__mult__swap,axiom,
% 5.52/5.80 ! [C: int,B: int,A: int] :
% 5.52/5.80 ( ( dvd_dvd_int @ C @ B )
% 5.52/5.80 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.52/5.80 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_mult_swap
% 5.52/5.81 thf(fact_4151_dvd__div__mult,axiom,
% 5.52/5.81 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.52/5.81 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.52/5.81 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_mult
% 5.52/5.81 thf(fact_4152_dvd__div__mult,axiom,
% 5.52/5.81 ! [C: nat,B: nat,A: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ C @ B )
% 5.52/5.81 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.52/5.81 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_mult
% 5.52/5.81 thf(fact_4153_dvd__div__mult,axiom,
% 5.52/5.81 ! [C: int,B: int,A: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ C @ B )
% 5.52/5.81 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.52/5.81 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_mult
% 5.52/5.81 thf(fact_4154_dvd__div__unit__iff,axiom,
% 5.52/5.81 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.52/5.81 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_unit_iff
% 5.52/5.81 thf(fact_4155_dvd__div__unit__iff,axiom,
% 5.52/5.81 ! [B: nat,A: nat,C: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.81 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.52/5.81 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_unit_iff
% 5.52/5.81 thf(fact_4156_dvd__div__unit__iff,axiom,
% 5.52/5.81 ! [B: int,A: int,C: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.81 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.52/5.81 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_unit_iff
% 5.52/5.81 thf(fact_4157_div__unit__dvd__iff,axiom,
% 5.52/5.81 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.52/5.81 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_unit_dvd_iff
% 5.52/5.81 thf(fact_4158_div__unit__dvd__iff,axiom,
% 5.52/5.81 ! [B: nat,A: nat,C: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.81 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.52/5.81 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_unit_dvd_iff
% 5.52/5.81 thf(fact_4159_div__unit__dvd__iff,axiom,
% 5.52/5.81 ! [B: int,A: int,C: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.81 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.52/5.81 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_unit_dvd_iff
% 5.52/5.81 thf(fact_4160_unit__div__cancel,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.81 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.52/5.81 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.52/5.81 = ( B = C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_div_cancel
% 5.52/5.81 thf(fact_4161_unit__div__cancel,axiom,
% 5.52/5.81 ! [A: nat,B: nat,C: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.81 => ( ( ( divide_divide_nat @ B @ A )
% 5.52/5.81 = ( divide_divide_nat @ C @ A ) )
% 5.52/5.81 = ( B = C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_div_cancel
% 5.52/5.81 thf(fact_4162_unit__div__cancel,axiom,
% 5.52/5.81 ! [A: int,B: int,C: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.81 => ( ( ( divide_divide_int @ B @ A )
% 5.52/5.81 = ( divide_divide_int @ C @ A ) )
% 5.52/5.81 = ( B = C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_div_cancel
% 5.52/5.81 thf(fact_4163_div__plus__div__distrib__dvd__right,axiom,
% 5.52/5.81 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.52/5.81 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.52/5.81 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_plus_div_distrib_dvd_right
% 5.52/5.81 thf(fact_4164_div__plus__div__distrib__dvd__right,axiom,
% 5.52/5.81 ! [C: nat,B: nat,A: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ C @ B )
% 5.52/5.81 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.52/5.81 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_plus_div_distrib_dvd_right
% 5.52/5.81 thf(fact_4165_div__plus__div__distrib__dvd__right,axiom,
% 5.52/5.81 ! [C: int,B: int,A: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ C @ B )
% 5.52/5.81 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.52/5.81 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_plus_div_distrib_dvd_right
% 5.52/5.81 thf(fact_4166_div__plus__div__distrib__dvd__left,axiom,
% 5.52/5.81 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.52/5.81 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.52/5.81 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_plus_div_distrib_dvd_left
% 5.52/5.81 thf(fact_4167_div__plus__div__distrib__dvd__left,axiom,
% 5.52/5.81 ! [C: nat,A: nat,B: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ C @ A )
% 5.52/5.81 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.52/5.81 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_plus_div_distrib_dvd_left
% 5.52/5.81 thf(fact_4168_div__plus__div__distrib__dvd__left,axiom,
% 5.52/5.81 ! [C: int,A: int,B: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ C @ A )
% 5.52/5.81 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.52/5.81 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_plus_div_distrib_dvd_left
% 5.52/5.81 thf(fact_4169_div__power,axiom,
% 5.52/5.81 ! [B: code_integer,A: code_integer,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.52/5.81 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 5.52/5.81 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_power
% 5.52/5.81 thf(fact_4170_div__power,axiom,
% 5.52/5.81 ! [B: nat,A: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ B @ A )
% 5.52/5.81 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 5.52/5.81 = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_power
% 5.52/5.81 thf(fact_4171_div__power,axiom,
% 5.52/5.81 ! [B: int,A: int,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_int @ B @ A )
% 5.52/5.81 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 5.52/5.81 = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_power
% 5.52/5.81 thf(fact_4172_mod__0__imp__dvd,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.52/5.81 = zero_z3403309356797280102nteger )
% 5.52/5.81 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_0_imp_dvd
% 5.52/5.81 thf(fact_4173_mod__0__imp__dvd,axiom,
% 5.52/5.81 ! [A: nat,B: nat] :
% 5.52/5.81 ( ( ( modulo_modulo_nat @ A @ B )
% 5.52/5.81 = zero_zero_nat )
% 5.52/5.81 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_0_imp_dvd
% 5.52/5.81 thf(fact_4174_mod__0__imp__dvd,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( ( modulo_modulo_int @ A @ B )
% 5.52/5.81 = zero_zero_int )
% 5.52/5.81 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_0_imp_dvd
% 5.52/5.81 thf(fact_4175_dvd__eq__mod__eq__0,axiom,
% 5.52/5.81 ( dvd_dvd_Code_integer
% 5.52/5.81 = ( ^ [A4: code_integer,B3: code_integer] :
% 5.52/5.81 ( ( modulo364778990260209775nteger @ B3 @ A4 )
% 5.52/5.81 = zero_z3403309356797280102nteger ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_eq_mod_eq_0
% 5.52/5.81 thf(fact_4176_dvd__eq__mod__eq__0,axiom,
% 5.52/5.81 ( dvd_dvd_nat
% 5.52/5.81 = ( ^ [A4: nat,B3: nat] :
% 5.52/5.81 ( ( modulo_modulo_nat @ B3 @ A4 )
% 5.52/5.81 = zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_eq_mod_eq_0
% 5.52/5.81 thf(fact_4177_dvd__eq__mod__eq__0,axiom,
% 5.52/5.81 ( dvd_dvd_int
% 5.52/5.81 = ( ^ [A4: int,B3: int] :
% 5.52/5.81 ( ( modulo_modulo_int @ B3 @ A4 )
% 5.52/5.81 = zero_zero_int ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_eq_mod_eq_0
% 5.52/5.81 thf(fact_4178_mod__eq__0__iff__dvd,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.52/5.81 = zero_z3403309356797280102nteger )
% 5.52/5.81 = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_eq_0_iff_dvd
% 5.52/5.81 thf(fact_4179_mod__eq__0__iff__dvd,axiom,
% 5.52/5.81 ! [A: nat,B: nat] :
% 5.52/5.81 ( ( ( modulo_modulo_nat @ A @ B )
% 5.52/5.81 = zero_zero_nat )
% 5.52/5.81 = ( dvd_dvd_nat @ B @ A ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_eq_0_iff_dvd
% 5.52/5.81 thf(fact_4180_mod__eq__0__iff__dvd,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( ( modulo_modulo_int @ A @ B )
% 5.52/5.81 = zero_zero_int )
% 5.52/5.81 = ( dvd_dvd_int @ B @ A ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_eq_0_iff_dvd
% 5.52/5.81 thf(fact_4181_dvd__power__le,axiom,
% 5.52/5.81 ! [X2: code_integer,Y2: code_integer,N: nat,M: nat] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ X2 @ Y2 )
% 5.52/5.81 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.81 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y2 @ M ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power_le
% 5.52/5.81 thf(fact_4182_dvd__power__le,axiom,
% 5.52/5.81 ! [X2: nat,Y2: nat,N: nat,M: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ X2 @ Y2 )
% 5.52/5.81 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.81 => ( dvd_dvd_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y2 @ M ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power_le
% 5.52/5.81 thf(fact_4183_dvd__power__le,axiom,
% 5.52/5.81 ! [X2: real,Y2: real,N: nat,M: nat] :
% 5.52/5.81 ( ( dvd_dvd_real @ X2 @ Y2 )
% 5.52/5.81 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.81 => ( dvd_dvd_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y2 @ M ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power_le
% 5.52/5.81 thf(fact_4184_dvd__power__le,axiom,
% 5.52/5.81 ! [X2: int,Y2: int,N: nat,M: nat] :
% 5.52/5.81 ( ( dvd_dvd_int @ X2 @ Y2 )
% 5.52/5.81 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.81 => ( dvd_dvd_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y2 @ M ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power_le
% 5.52/5.81 thf(fact_4185_dvd__power__le,axiom,
% 5.52/5.81 ! [X2: complex,Y2: complex,N: nat,M: nat] :
% 5.52/5.81 ( ( dvd_dvd_complex @ X2 @ Y2 )
% 5.52/5.81 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.81 => ( dvd_dvd_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y2 @ M ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power_le
% 5.52/5.81 thf(fact_4186_power__le__dvd,axiom,
% 5.52/5.81 ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 5.52/5.81 => ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % power_le_dvd
% 5.52/5.81 thf(fact_4187_power__le__dvd,axiom,
% 5.52/5.81 ! [A: nat,N: nat,B: nat,M: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 5.52/5.81 => ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % power_le_dvd
% 5.52/5.81 thf(fact_4188_power__le__dvd,axiom,
% 5.52/5.81 ! [A: real,N: nat,B: real,M: nat] :
% 5.52/5.81 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 5.52/5.81 => ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % power_le_dvd
% 5.52/5.81 thf(fact_4189_power__le__dvd,axiom,
% 5.52/5.81 ! [A: int,N: nat,B: int,M: nat] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 5.52/5.81 => ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % power_le_dvd
% 5.52/5.81 thf(fact_4190_power__le__dvd,axiom,
% 5.52/5.81 ! [A: complex,N: nat,B: complex,M: nat] :
% 5.52/5.81 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 5.52/5.81 => ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % power_le_dvd
% 5.52/5.81 thf(fact_4191_le__imp__power__dvd,axiom,
% 5.52/5.81 ! [M: nat,N: nat,A: code_integer] :
% 5.52/5.81 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % le_imp_power_dvd
% 5.52/5.81 thf(fact_4192_le__imp__power__dvd,axiom,
% 5.52/5.81 ! [M: nat,N: nat,A: nat] :
% 5.52/5.81 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % le_imp_power_dvd
% 5.52/5.81 thf(fact_4193_le__imp__power__dvd,axiom,
% 5.52/5.81 ! [M: nat,N: nat,A: real] :
% 5.52/5.81 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % le_imp_power_dvd
% 5.52/5.81 thf(fact_4194_le__imp__power__dvd,axiom,
% 5.52/5.81 ! [M: nat,N: nat,A: int] :
% 5.52/5.81 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % le_imp_power_dvd
% 5.52/5.81 thf(fact_4195_le__imp__power__dvd,axiom,
% 5.52/5.81 ! [M: nat,N: nat,A: complex] :
% 5.52/5.81 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % le_imp_power_dvd
% 5.52/5.81 thf(fact_4196_dvd__minus__mod,axiom,
% 5.52/5.81 ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_minus_mod
% 5.52/5.81 thf(fact_4197_dvd__minus__mod,axiom,
% 5.52/5.81 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_minus_mod
% 5.52/5.81 thf(fact_4198_dvd__minus__mod,axiom,
% 5.52/5.81 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_minus_mod
% 5.52/5.81 thf(fact_4199_mod__eq__dvd__iff,axiom,
% 5.52/5.81 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.52/5.81 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.52/5.81 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.52/5.81 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_eq_dvd_iff
% 5.52/5.81 thf(fact_4200_mod__eq__dvd__iff,axiom,
% 5.52/5.81 ! [A: int,C: int,B: int] :
% 5.52/5.81 ( ( ( modulo_modulo_int @ A @ C )
% 5.52/5.81 = ( modulo_modulo_int @ B @ C ) )
% 5.52/5.81 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_eq_dvd_iff
% 5.52/5.81 thf(fact_4201_dvd__pos__nat,axiom,
% 5.52/5.81 ! [N: nat,M: nat] :
% 5.52/5.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.81 => ( ( dvd_dvd_nat @ M @ N )
% 5.52/5.81 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_pos_nat
% 5.52/5.81 thf(fact_4202_nat__dvd__not__less,axiom,
% 5.52/5.81 ! [M: nat,N: nat] :
% 5.52/5.81 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.81 => ( ( ord_less_nat @ M @ N )
% 5.52/5.81 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % nat_dvd_not_less
% 5.52/5.81 thf(fact_4203_dvd__minus__self,axiom,
% 5.52/5.81 ! [M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 5.52/5.81 = ( ( ord_less_nat @ N @ M )
% 5.52/5.81 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_minus_self
% 5.52/5.81 thf(fact_4204_less__eq__dvd__minus,axiom,
% 5.52/5.81 ! [M: nat,N: nat] :
% 5.52/5.81 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 => ( ( dvd_dvd_nat @ M @ N )
% 5.52/5.81 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % less_eq_dvd_minus
% 5.52/5.81 thf(fact_4205_dvd__diffD1,axiom,
% 5.52/5.81 ! [K: nat,M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.81 => ( ( dvd_dvd_nat @ K @ M )
% 5.52/5.81 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.81 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_diffD1
% 5.52/5.81 thf(fact_4206_dvd__diffD,axiom,
% 5.52/5.81 ! [K: nat,M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.81 => ( ( dvd_dvd_nat @ K @ N )
% 5.52/5.81 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.81 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_diffD
% 5.52/5.81 thf(fact_4207_zdvd__not__zless,axiom,
% 5.52/5.81 ! [M: int,N: int] :
% 5.52/5.81 ( ( ord_less_int @ zero_zero_int @ M )
% 5.52/5.81 => ( ( ord_less_int @ M @ N )
% 5.52/5.81 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zdvd_not_zless
% 5.52/5.81 thf(fact_4208_bezout__lemma__nat,axiom,
% 5.52/5.81 ! [D2: nat,A: nat,B: nat,X2: nat,Y2: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ D2 @ A )
% 5.52/5.81 => ( ( dvd_dvd_nat @ D2 @ B )
% 5.52/5.81 => ( ( ( ( times_times_nat @ A @ X2 )
% 5.52/5.81 = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D2 ) )
% 5.52/5.81 | ( ( times_times_nat @ B @ X2 )
% 5.52/5.81 = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D2 ) ) )
% 5.52/5.81 => ? [X4: nat,Y3: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ D2 @ A )
% 5.52/5.81 & ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ A @ B ) )
% 5.52/5.81 & ( ( ( times_times_nat @ A @ X4 )
% 5.52/5.81 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D2 ) )
% 5.52/5.81 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X4 )
% 5.52/5.81 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D2 ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % bezout_lemma_nat
% 5.52/5.81 thf(fact_4209_bezout__add__nat,axiom,
% 5.52/5.81 ! [A: nat,B: nat] :
% 5.52/5.81 ? [D3: nat,X4: nat,Y3: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ D3 @ A )
% 5.52/5.81 & ( dvd_dvd_nat @ D3 @ B )
% 5.52/5.81 & ( ( ( times_times_nat @ A @ X4 )
% 5.52/5.81 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 5.52/5.81 | ( ( times_times_nat @ B @ X4 )
% 5.52/5.81 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % bezout_add_nat
% 5.52/5.81 thf(fact_4210_bezout1__nat,axiom,
% 5.52/5.81 ! [A: nat,B: nat] :
% 5.52/5.81 ? [D3: nat,X4: nat,Y3: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ D3 @ A )
% 5.52/5.81 & ( dvd_dvd_nat @ D3 @ B )
% 5.52/5.81 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.52/5.81 = D3 )
% 5.52/5.81 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.52/5.81 = D3 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % bezout1_nat
% 5.52/5.81 thf(fact_4211_unit__dvdE,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.81 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.52/5.81 => ! [C2: code_integer] :
% 5.52/5.81 ( B
% 5.52/5.81 != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_dvdE
% 5.52/5.81 thf(fact_4212_unit__dvdE,axiom,
% 5.52/5.81 ! [A: nat,B: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.81 => ~ ( ( A != zero_zero_nat )
% 5.52/5.81 => ! [C2: nat] :
% 5.52/5.81 ( B
% 5.52/5.81 != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_dvdE
% 5.52/5.81 thf(fact_4213_unit__dvdE,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.81 => ~ ( ( A != zero_zero_int )
% 5.52/5.81 => ! [C2: int] :
% 5.52/5.81 ( B
% 5.52/5.81 != ( times_times_int @ A @ C2 ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_dvdE
% 5.52/5.81 thf(fact_4214_unity__coeff__ex,axiom,
% 5.52/5.81 ! [P: code_integer > $o,L: code_integer] :
% 5.52/5.81 ( ( ? [X: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X ) ) )
% 5.52/5.81 = ( ? [X: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X @ zero_z3403309356797280102nteger ) )
% 5.52/5.81 & ( P @ X ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unity_coeff_ex
% 5.52/5.81 thf(fact_4215_unity__coeff__ex,axiom,
% 5.52/5.81 ! [P: complex > $o,L: complex] :
% 5.52/5.81 ( ( ? [X: complex] : ( P @ ( times_times_complex @ L @ X ) ) )
% 5.52/5.81 = ( ? [X: complex] :
% 5.52/5.81 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X @ zero_zero_complex ) )
% 5.52/5.81 & ( P @ X ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unity_coeff_ex
% 5.52/5.81 thf(fact_4216_unity__coeff__ex,axiom,
% 5.52/5.81 ! [P: real > $o,L: real] :
% 5.52/5.81 ( ( ? [X: real] : ( P @ ( times_times_real @ L @ X ) ) )
% 5.52/5.81 = ( ? [X: real] :
% 5.52/5.81 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X @ zero_zero_real ) )
% 5.52/5.81 & ( P @ X ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unity_coeff_ex
% 5.52/5.81 thf(fact_4217_unity__coeff__ex,axiom,
% 5.52/5.81 ! [P: rat > $o,L: rat] :
% 5.52/5.81 ( ( ? [X: rat] : ( P @ ( times_times_rat @ L @ X ) ) )
% 5.52/5.81 = ( ? [X: rat] :
% 5.52/5.81 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X @ zero_zero_rat ) )
% 5.52/5.81 & ( P @ X ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unity_coeff_ex
% 5.52/5.81 thf(fact_4218_unity__coeff__ex,axiom,
% 5.52/5.81 ! [P: nat > $o,L: nat] :
% 5.52/5.81 ( ( ? [X: nat] : ( P @ ( times_times_nat @ L @ X ) ) )
% 5.52/5.81 = ( ? [X: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X @ zero_zero_nat ) )
% 5.52/5.81 & ( P @ X ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unity_coeff_ex
% 5.52/5.81 thf(fact_4219_unity__coeff__ex,axiom,
% 5.52/5.81 ! [P: int > $o,L: int] :
% 5.52/5.81 ( ( ? [X: int] : ( P @ ( times_times_int @ L @ X ) ) )
% 5.52/5.81 = ( ? [X: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X @ zero_zero_int ) )
% 5.52/5.81 & ( P @ X ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unity_coeff_ex
% 5.52/5.81 thf(fact_4220_dvd__div__eq__mult,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.52/5.81 ( ( A != zero_z3403309356797280102nteger )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.81 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.52/5.81 = C )
% 5.52/5.81 = ( B
% 5.52/5.81 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_eq_mult
% 5.52/5.81 thf(fact_4221_dvd__div__eq__mult,axiom,
% 5.52/5.81 ! [A: nat,B: nat,C: nat] :
% 5.52/5.81 ( ( A != zero_zero_nat )
% 5.52/5.81 => ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.81 => ( ( ( divide_divide_nat @ B @ A )
% 5.52/5.81 = C )
% 5.52/5.81 = ( B
% 5.52/5.81 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_eq_mult
% 5.52/5.81 thf(fact_4222_dvd__div__eq__mult,axiom,
% 5.52/5.81 ! [A: int,B: int,C: int] :
% 5.52/5.81 ( ( A != zero_zero_int )
% 5.52/5.81 => ( ( dvd_dvd_int @ A @ B )
% 5.52/5.81 => ( ( ( divide_divide_int @ B @ A )
% 5.52/5.81 = C )
% 5.52/5.81 = ( B
% 5.52/5.81 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_eq_mult
% 5.52/5.81 thf(fact_4223_div__dvd__iff__mult,axiom,
% 5.52/5.81 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.52/5.81 ( ( B != zero_z3403309356797280102nteger )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.52/5.81 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_dvd_iff_mult
% 5.52/5.81 thf(fact_4224_div__dvd__iff__mult,axiom,
% 5.52/5.81 ! [B: nat,A: nat,C: nat] :
% 5.52/5.81 ( ( B != zero_zero_nat )
% 5.52/5.81 => ( ( dvd_dvd_nat @ B @ A )
% 5.52/5.81 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.52/5.81 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_dvd_iff_mult
% 5.52/5.81 thf(fact_4225_div__dvd__iff__mult,axiom,
% 5.52/5.81 ! [B: int,A: int,C: int] :
% 5.52/5.81 ( ( B != zero_zero_int )
% 5.52/5.81 => ( ( dvd_dvd_int @ B @ A )
% 5.52/5.81 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.52/5.81 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_dvd_iff_mult
% 5.52/5.81 thf(fact_4226_dvd__div__iff__mult,axiom,
% 5.52/5.81 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.52/5.81 ( ( C != zero_z3403309356797280102nteger )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.52/5.81 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_iff_mult
% 5.52/5.81 thf(fact_4227_dvd__div__iff__mult,axiom,
% 5.52/5.81 ! [C: nat,B: nat,A: nat] :
% 5.52/5.81 ( ( C != zero_zero_nat )
% 5.52/5.81 => ( ( dvd_dvd_nat @ C @ B )
% 5.52/5.81 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.52/5.81 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_iff_mult
% 5.52/5.81 thf(fact_4228_dvd__div__iff__mult,axiom,
% 5.52/5.81 ! [C: int,B: int,A: int] :
% 5.52/5.81 ( ( C != zero_zero_int )
% 5.52/5.81 => ( ( dvd_dvd_int @ C @ B )
% 5.52/5.81 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.52/5.81 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_iff_mult
% 5.52/5.81 thf(fact_4229_dvd__div__div__eq__mult,axiom,
% 5.52/5.81 ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 5.52/5.81 ( ( A != zero_z3403309356797280102nteger )
% 5.52/5.81 => ( ( C != zero_z3403309356797280102nteger )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 5.52/5.81 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.52/5.81 = ( divide6298287555418463151nteger @ D2 @ C ) )
% 5.52/5.81 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.52/5.81 = ( times_3573771949741848930nteger @ A @ D2 ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_div_eq_mult
% 5.52/5.81 thf(fact_4230_dvd__div__div__eq__mult,axiom,
% 5.52/5.81 ! [A: nat,C: nat,B: nat,D2: nat] :
% 5.52/5.81 ( ( A != zero_zero_nat )
% 5.52/5.81 => ( ( C != zero_zero_nat )
% 5.52/5.81 => ( ( dvd_dvd_nat @ A @ B )
% 5.52/5.81 => ( ( dvd_dvd_nat @ C @ D2 )
% 5.52/5.81 => ( ( ( divide_divide_nat @ B @ A )
% 5.52/5.81 = ( divide_divide_nat @ D2 @ C ) )
% 5.52/5.81 = ( ( times_times_nat @ B @ C )
% 5.52/5.81 = ( times_times_nat @ A @ D2 ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_div_eq_mult
% 5.52/5.81 thf(fact_4231_dvd__div__div__eq__mult,axiom,
% 5.52/5.81 ! [A: int,C: int,B: int,D2: int] :
% 5.52/5.81 ( ( A != zero_zero_int )
% 5.52/5.81 => ( ( C != zero_zero_int )
% 5.52/5.81 => ( ( dvd_dvd_int @ A @ B )
% 5.52/5.81 => ( ( dvd_dvd_int @ C @ D2 )
% 5.52/5.81 => ( ( ( divide_divide_int @ B @ A )
% 5.52/5.81 = ( divide_divide_int @ D2 @ C ) )
% 5.52/5.81 = ( ( times_times_int @ B @ C )
% 5.52/5.81 = ( times_times_int @ A @ D2 ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_div_div_eq_mult
% 5.52/5.81 thf(fact_4232_unit__div__eq__0__iff,axiom,
% 5.52/5.81 ! [B: code_integer,A: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.81 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.52/5.81 = zero_z3403309356797280102nteger )
% 5.52/5.81 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_div_eq_0_iff
% 5.52/5.81 thf(fact_4233_unit__div__eq__0__iff,axiom,
% 5.52/5.81 ! [B: nat,A: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.81 => ( ( ( divide_divide_nat @ A @ B )
% 5.52/5.81 = zero_zero_nat )
% 5.52/5.81 = ( A = zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_div_eq_0_iff
% 5.52/5.81 thf(fact_4234_unit__div__eq__0__iff,axiom,
% 5.52/5.81 ! [B: int,A: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.81 => ( ( ( divide_divide_int @ A @ B )
% 5.52/5.81 = zero_zero_int )
% 5.52/5.81 = ( A = zero_zero_int ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_div_eq_0_iff
% 5.52/5.81 thf(fact_4235_even__numeral,axiom,
% 5.52/5.81 ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_numeral
% 5.52/5.81 thf(fact_4236_even__numeral,axiom,
% 5.52/5.81 ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_numeral
% 5.52/5.81 thf(fact_4237_even__numeral,axiom,
% 5.52/5.81 ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_numeral
% 5.52/5.81 thf(fact_4238_inf__period_I3_J,axiom,
% 5.52/5.81 ! [D2: code_integer,D4: code_integer,T: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ D2 @ D4 )
% 5.52/5.81 => ! [X6: code_integer,K4: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X6 @ T ) )
% 5.52/5.81 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X6 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % inf_period(3)
% 5.52/5.81 thf(fact_4239_inf__period_I3_J,axiom,
% 5.52/5.81 ! [D2: complex,D4: complex,T: complex] :
% 5.52/5.81 ( ( dvd_dvd_complex @ D2 @ D4 )
% 5.52/5.81 => ! [X6: complex,K4: complex] :
% 5.52/5.81 ( ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ X6 @ T ) )
% 5.52/5.81 = ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ ( minus_minus_complex @ X6 @ ( times_times_complex @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % inf_period(3)
% 5.52/5.81 thf(fact_4240_inf__period_I3_J,axiom,
% 5.52/5.81 ! [D2: real,D4: real,T: real] :
% 5.52/5.81 ( ( dvd_dvd_real @ D2 @ D4 )
% 5.52/5.81 => ! [X6: real,K4: real] :
% 5.52/5.81 ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X6 @ T ) )
% 5.52/5.81 = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % inf_period(3)
% 5.52/5.81 thf(fact_4241_inf__period_I3_J,axiom,
% 5.52/5.81 ! [D2: rat,D4: rat,T: rat] :
% 5.52/5.81 ( ( dvd_dvd_rat @ D2 @ D4 )
% 5.52/5.81 => ! [X6: rat,K4: rat] :
% 5.52/5.81 ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ T ) )
% 5.52/5.81 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % inf_period(3)
% 5.52/5.81 thf(fact_4242_inf__period_I3_J,axiom,
% 5.52/5.81 ! [D2: int,D4: int,T: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ D2 @ D4 )
% 5.52/5.81 => ! [X6: int,K4: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ T ) )
% 5.52/5.81 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % inf_period(3)
% 5.52/5.81 thf(fact_4243_inf__period_I4_J,axiom,
% 5.52/5.81 ! [D2: code_integer,D4: code_integer,T: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ D2 @ D4 )
% 5.52/5.81 => ! [X6: code_integer,K4: code_integer] :
% 5.52/5.81 ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X6 @ T ) ) )
% 5.52/5.81 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X6 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % inf_period(4)
% 5.52/5.81 thf(fact_4244_inf__period_I4_J,axiom,
% 5.52/5.81 ! [D2: complex,D4: complex,T: complex] :
% 5.52/5.81 ( ( dvd_dvd_complex @ D2 @ D4 )
% 5.52/5.81 => ! [X6: complex,K4: complex] :
% 5.52/5.81 ( ( ~ ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ X6 @ T ) ) )
% 5.52/5.81 = ( ~ ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ ( minus_minus_complex @ X6 @ ( times_times_complex @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % inf_period(4)
% 5.52/5.81 thf(fact_4245_inf__period_I4_J,axiom,
% 5.52/5.81 ! [D2: real,D4: real,T: real] :
% 5.52/5.81 ( ( dvd_dvd_real @ D2 @ D4 )
% 5.52/5.81 => ! [X6: real,K4: real] :
% 5.52/5.81 ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X6 @ T ) ) )
% 5.52/5.81 = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % inf_period(4)
% 5.52/5.81 thf(fact_4246_inf__period_I4_J,axiom,
% 5.52/5.81 ! [D2: rat,D4: rat,T: rat] :
% 5.52/5.81 ( ( dvd_dvd_rat @ D2 @ D4 )
% 5.52/5.81 => ! [X6: rat,K4: rat] :
% 5.52/5.81 ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ T ) ) )
% 5.52/5.81 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % inf_period(4)
% 5.52/5.81 thf(fact_4247_inf__period_I4_J,axiom,
% 5.52/5.81 ! [D2: int,D4: int,T: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ D2 @ D4 )
% 5.52/5.81 => ! [X6: int,K4: int] :
% 5.52/5.81 ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ T ) ) )
% 5.52/5.81 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % inf_period(4)
% 5.52/5.81 thf(fact_4248_is__unit__div__mult2__eq,axiom,
% 5.52/5.81 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.52/5.81 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.52/5.81 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unit_div_mult2_eq
% 5.52/5.81 thf(fact_4249_is__unit__div__mult2__eq,axiom,
% 5.52/5.81 ! [B: nat,C: nat,A: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.81 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.52/5.81 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.52/5.81 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unit_div_mult2_eq
% 5.52/5.81 thf(fact_4250_is__unit__div__mult2__eq,axiom,
% 5.52/5.81 ! [B: int,C: int,A: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.81 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.52/5.81 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.52/5.81 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unit_div_mult2_eq
% 5.52/5.81 thf(fact_4251_unit__div__mult__swap,axiom,
% 5.52/5.81 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.52/5.81 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.52/5.81 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_div_mult_swap
% 5.52/5.81 thf(fact_4252_unit__div__mult__swap,axiom,
% 5.52/5.81 ! [C: nat,A: nat,B: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.52/5.81 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.52/5.81 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_div_mult_swap
% 5.52/5.81 thf(fact_4253_unit__div__mult__swap,axiom,
% 5.52/5.81 ! [C: int,A: int,B: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.52/5.81 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.52/5.81 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_div_mult_swap
% 5.52/5.81 thf(fact_4254_unit__div__commute,axiom,
% 5.52/5.81 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.81 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.52/5.81 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_div_commute
% 5.52/5.81 thf(fact_4255_unit__div__commute,axiom,
% 5.52/5.81 ! [B: nat,A: nat,C: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.81 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.52/5.81 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_div_commute
% 5.52/5.81 thf(fact_4256_unit__div__commute,axiom,
% 5.52/5.81 ! [B: int,A: int,C: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.81 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.52/5.81 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_div_commute
% 5.52/5.81 thf(fact_4257_div__mult__unit2,axiom,
% 5.52/5.81 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.52/5.81 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.52/5.81 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_mult_unit2
% 5.52/5.81 thf(fact_4258_div__mult__unit2,axiom,
% 5.52/5.81 ! [C: nat,B: nat,A: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.52/5.81 => ( ( dvd_dvd_nat @ B @ A )
% 5.52/5.81 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.52/5.81 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_mult_unit2
% 5.52/5.81 thf(fact_4259_div__mult__unit2,axiom,
% 5.52/5.81 ! [C: int,B: int,A: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.52/5.81 => ( ( dvd_dvd_int @ B @ A )
% 5.52/5.81 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.52/5.81 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_mult_unit2
% 5.52/5.81 thf(fact_4260_unit__eq__div2,axiom,
% 5.52/5.81 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.81 => ( ( A
% 5.52/5.81 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.52/5.81 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.52/5.81 = C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_eq_div2
% 5.52/5.81 thf(fact_4261_unit__eq__div2,axiom,
% 5.52/5.81 ! [B: nat,A: nat,C: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.81 => ( ( A
% 5.52/5.81 = ( divide_divide_nat @ C @ B ) )
% 5.52/5.81 = ( ( times_times_nat @ A @ B )
% 5.52/5.81 = C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_eq_div2
% 5.52/5.81 thf(fact_4262_unit__eq__div2,axiom,
% 5.52/5.81 ! [B: int,A: int,C: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.81 => ( ( A
% 5.52/5.81 = ( divide_divide_int @ C @ B ) )
% 5.52/5.81 = ( ( times_times_int @ A @ B )
% 5.52/5.81 = C ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_eq_div2
% 5.52/5.81 thf(fact_4263_unit__eq__div1,axiom,
% 5.52/5.81 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.81 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.52/5.81 = C )
% 5.52/5.81 = ( A
% 5.52/5.81 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_eq_div1
% 5.52/5.81 thf(fact_4264_unit__eq__div1,axiom,
% 5.52/5.81 ! [B: nat,A: nat,C: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.81 => ( ( ( divide_divide_nat @ A @ B )
% 5.52/5.81 = C )
% 5.52/5.81 = ( A
% 5.52/5.81 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_eq_div1
% 5.52/5.81 thf(fact_4265_unit__eq__div1,axiom,
% 5.52/5.81 ! [B: int,A: int,C: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.81 => ( ( ( divide_divide_int @ A @ B )
% 5.52/5.81 = C )
% 5.52/5.81 = ( A
% 5.52/5.81 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_eq_div1
% 5.52/5.81 thf(fact_4266_is__unit__power__iff,axiom,
% 5.52/5.81 ! [A: code_integer,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 5.52/5.81 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.81 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unit_power_iff
% 5.52/5.81 thf(fact_4267_is__unit__power__iff,axiom,
% 5.52/5.81 ! [A: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 5.52/5.81 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.81 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unit_power_iff
% 5.52/5.81 thf(fact_4268_is__unit__power__iff,axiom,
% 5.52/5.81 ! [A: int,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 5.52/5.81 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.81 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unit_power_iff
% 5.52/5.81 thf(fact_4269_unit__imp__mod__eq__0,axiom,
% 5.52/5.81 ! [B: code_integer,A: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.81 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.52/5.81 = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_imp_mod_eq_0
% 5.52/5.81 thf(fact_4270_unit__imp__mod__eq__0,axiom,
% 5.52/5.81 ! [B: nat,A: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.81 => ( ( modulo_modulo_nat @ A @ B )
% 5.52/5.81 = zero_zero_nat ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_imp_mod_eq_0
% 5.52/5.81 thf(fact_4271_unit__imp__mod__eq__0,axiom,
% 5.52/5.81 ! [B: int,A: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.81 => ( ( modulo_modulo_int @ A @ B )
% 5.52/5.81 = zero_zero_int ) ) ).
% 5.52/5.81
% 5.52/5.81 % unit_imp_mod_eq_0
% 5.52/5.81 thf(fact_4272_dvd__imp__le,axiom,
% 5.52/5.81 ! [K: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ K @ N )
% 5.52/5.81 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.81 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_imp_le
% 5.52/5.81 thf(fact_4273_nat__mult__dvd__cancel1,axiom,
% 5.52/5.81 ! [K: nat,M: nat,N: nat] :
% 5.52/5.81 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.81 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.52/5.81 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % nat_mult_dvd_cancel1
% 5.52/5.81 thf(fact_4274_dvd__mult__cancel,axiom,
% 5.52/5.81 ! [K: nat,M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.52/5.81 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.81 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_mult_cancel
% 5.52/5.81 thf(fact_4275_bezout__add__strong__nat,axiom,
% 5.52/5.81 ! [A: nat,B: nat] :
% 5.52/5.81 ( ( A != zero_zero_nat )
% 5.52/5.81 => ? [D3: nat,X4: nat,Y3: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ D3 @ A )
% 5.52/5.81 & ( dvd_dvd_nat @ D3 @ B )
% 5.52/5.81 & ( ( times_times_nat @ A @ X4 )
% 5.52/5.81 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % bezout_add_strong_nat
% 5.52/5.81 thf(fact_4276_zdvd__imp__le,axiom,
% 5.52/5.81 ! [Z: int,N: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ Z @ N )
% 5.52/5.81 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.52/5.81 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zdvd_imp_le
% 5.52/5.81 thf(fact_4277_mod__greater__zero__iff__not__dvd,axiom,
% 5.52/5.81 ! [M: nat,N: nat] :
% 5.52/5.81 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.52/5.81 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_greater_zero_iff_not_dvd
% 5.52/5.81 thf(fact_4278_mod__eq__dvd__iff__nat,axiom,
% 5.52/5.81 ! [N: nat,M: nat,Q2: nat] :
% 5.52/5.81 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.81 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.52/5.81 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.52/5.81 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_eq_dvd_iff_nat
% 5.52/5.81 thf(fact_4279_finite__divisors__nat,axiom,
% 5.52/5.81 ! [M: nat] :
% 5.52/5.81 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.81 => ( finite_finite_nat
% 5.52/5.81 @ ( collect_nat
% 5.52/5.81 @ ^ [D: nat] : ( dvd_dvd_nat @ D @ M ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % finite_divisors_nat
% 5.52/5.81 thf(fact_4280_even__zero,axiom,
% 5.52/5.81 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.52/5.81
% 5.52/5.81 % even_zero
% 5.52/5.81 thf(fact_4281_even__zero,axiom,
% 5.52/5.81 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.52/5.81
% 5.52/5.81 % even_zero
% 5.52/5.81 thf(fact_4282_even__zero,axiom,
% 5.52/5.81 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.52/5.81
% 5.52/5.81 % even_zero
% 5.52/5.81 thf(fact_4283_is__unit__div__mult__cancel__right,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( A != zero_z3403309356797280102nteger )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.81 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.52/5.81 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unit_div_mult_cancel_right
% 5.52/5.81 thf(fact_4284_is__unit__div__mult__cancel__right,axiom,
% 5.52/5.81 ! [A: nat,B: nat] :
% 5.52/5.81 ( ( A != zero_zero_nat )
% 5.52/5.81 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.81 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.52/5.81 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unit_div_mult_cancel_right
% 5.52/5.81 thf(fact_4285_is__unit__div__mult__cancel__right,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( A != zero_zero_int )
% 5.52/5.81 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.81 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.52/5.81 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unit_div_mult_cancel_right
% 5.52/5.81 thf(fact_4286_is__unit__div__mult__cancel__left,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( A != zero_z3403309356797280102nteger )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.52/5.81 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.52/5.81 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unit_div_mult_cancel_left
% 5.52/5.81 thf(fact_4287_is__unit__div__mult__cancel__left,axiom,
% 5.52/5.81 ! [A: nat,B: nat] :
% 5.52/5.81 ( ( A != zero_zero_nat )
% 5.52/5.81 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.52/5.81 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.52/5.81 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unit_div_mult_cancel_left
% 5.52/5.81 thf(fact_4288_is__unit__div__mult__cancel__left,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( A != zero_zero_int )
% 5.52/5.81 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.52/5.81 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.52/5.81 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unit_div_mult_cancel_left
% 5.52/5.81 thf(fact_4289_is__unitE,axiom,
% 5.52/5.81 ! [A: code_integer,C: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.52/5.81 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.52/5.81 => ! [B2: code_integer] :
% 5.52/5.81 ( ( B2 != zero_z3403309356797280102nteger )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.52/5.81 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.52/5.81 = B2 )
% 5.52/5.81 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B2 )
% 5.52/5.81 = A )
% 5.52/5.81 => ( ( ( times_3573771949741848930nteger @ A @ B2 )
% 5.52/5.81 = one_one_Code_integer )
% 5.52/5.81 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.52/5.81 != ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unitE
% 5.52/5.81 thf(fact_4290_is__unitE,axiom,
% 5.52/5.81 ! [A: nat,C: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.52/5.81 => ~ ( ( A != zero_zero_nat )
% 5.52/5.81 => ! [B2: nat] :
% 5.52/5.81 ( ( B2 != zero_zero_nat )
% 5.52/5.81 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.52/5.81 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.52/5.81 = B2 )
% 5.52/5.81 => ( ( ( divide_divide_nat @ one_one_nat @ B2 )
% 5.52/5.81 = A )
% 5.52/5.81 => ( ( ( times_times_nat @ A @ B2 )
% 5.52/5.81 = one_one_nat )
% 5.52/5.81 => ( ( divide_divide_nat @ C @ A )
% 5.52/5.81 != ( times_times_nat @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unitE
% 5.52/5.81 thf(fact_4291_is__unitE,axiom,
% 5.52/5.81 ! [A: int,C: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.52/5.81 => ~ ( ( A != zero_zero_int )
% 5.52/5.81 => ! [B2: int] :
% 5.52/5.81 ( ( B2 != zero_zero_int )
% 5.52/5.81 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.52/5.81 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.52/5.81 = B2 )
% 5.52/5.81 => ( ( ( divide_divide_int @ one_one_int @ B2 )
% 5.52/5.81 = A )
% 5.52/5.81 => ( ( ( times_times_int @ A @ B2 )
% 5.52/5.81 = one_one_int )
% 5.52/5.81 => ( ( divide_divide_int @ C @ A )
% 5.52/5.81 != ( times_times_int @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % is_unitE
% 5.52/5.81 thf(fact_4292_evenE,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ~ ! [B2: code_integer] :
% 5.52/5.81 ( A
% 5.52/5.81 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % evenE
% 5.52/5.81 thf(fact_4293_evenE,axiom,
% 5.52/5.81 ! [A: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ~ ! [B2: nat] :
% 5.52/5.81 ( A
% 5.52/5.81 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % evenE
% 5.52/5.81 thf(fact_4294_evenE,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ~ ! [B2: int] :
% 5.52/5.81 ( A
% 5.52/5.81 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % evenE
% 5.52/5.81 thf(fact_4295_odd__one,axiom,
% 5.52/5.81 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.52/5.81
% 5.52/5.81 % odd_one
% 5.52/5.81 thf(fact_4296_odd__one,axiom,
% 5.52/5.81 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.52/5.81
% 5.52/5.81 % odd_one
% 5.52/5.81 thf(fact_4297_odd__one,axiom,
% 5.52/5.81 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.52/5.81
% 5.52/5.81 % odd_one
% 5.52/5.81 thf(fact_4298_odd__even__add,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.52/5.81 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_even_add
% 5.52/5.81 thf(fact_4299_odd__even__add,axiom,
% 5.52/5.81 ! [A: nat,B: nat] :
% 5.52/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.52/5.81 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_even_add
% 5.52/5.81 thf(fact_4300_odd__even__add,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.52/5.81 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_even_add
% 5.52/5.81 thf(fact_4301_bit__eq__rec,axiom,
% 5.52/5.81 ( ( ^ [Y5: code_integer,Z4: code_integer] : ( Y5 = Z4 ) )
% 5.52/5.81 = ( ^ [A4: code_integer,B3: code_integer] :
% 5.52/5.81 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 )
% 5.52/5.81 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) )
% 5.52/5.81 & ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.81 = ( divide6298287555418463151nteger @ B3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % bit_eq_rec
% 5.52/5.81 thf(fact_4302_bit__eq__rec,axiom,
% 5.52/5.81 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.52/5.81 = ( ^ [A4: nat,B3: nat] :
% 5.52/5.81 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 )
% 5.52/5.81 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) )
% 5.52/5.81 & ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.81 = ( divide_divide_nat @ B3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % bit_eq_rec
% 5.52/5.81 thf(fact_4303_bit__eq__rec,axiom,
% 5.52/5.81 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.52/5.81 = ( ^ [A4: int,B3: int] :
% 5.52/5.81 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 )
% 5.52/5.81 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) )
% 5.52/5.81 & ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.81 = ( divide_divide_int @ B3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % bit_eq_rec
% 5.52/5.81 thf(fact_4304_dvd__power__iff,axiom,
% 5.52/5.81 ! [X2: code_integer,M: nat,N: nat] :
% 5.52/5.81 ( ( X2 != zero_z3403309356797280102nteger )
% 5.52/5.81 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ M ) @ ( power_8256067586552552935nteger @ X2 @ N ) )
% 5.52/5.81 = ( ( dvd_dvd_Code_integer @ X2 @ one_one_Code_integer )
% 5.52/5.81 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power_iff
% 5.52/5.81 thf(fact_4305_dvd__power__iff,axiom,
% 5.52/5.81 ! [X2: nat,M: nat,N: nat] :
% 5.52/5.81 ( ( X2 != zero_zero_nat )
% 5.52/5.81 => ( ( dvd_dvd_nat @ ( power_power_nat @ X2 @ M ) @ ( power_power_nat @ X2 @ N ) )
% 5.52/5.81 = ( ( dvd_dvd_nat @ X2 @ one_one_nat )
% 5.52/5.81 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power_iff
% 5.52/5.81 thf(fact_4306_dvd__power__iff,axiom,
% 5.52/5.81 ! [X2: int,M: nat,N: nat] :
% 5.52/5.81 ( ( X2 != zero_zero_int )
% 5.52/5.81 => ( ( dvd_dvd_int @ ( power_power_int @ X2 @ M ) @ ( power_power_int @ X2 @ N ) )
% 5.52/5.81 = ( ( dvd_dvd_int @ X2 @ one_one_int )
% 5.52/5.81 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power_iff
% 5.52/5.81 thf(fact_4307_odd__numeral,axiom,
% 5.52/5.81 ! [N: num] :
% 5.52/5.81 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_numeral
% 5.52/5.81 thf(fact_4308_odd__numeral,axiom,
% 5.52/5.81 ! [N: num] :
% 5.52/5.81 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_numeral
% 5.52/5.81 thf(fact_4309_odd__numeral,axiom,
% 5.52/5.81 ! [N: num] :
% 5.52/5.81 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_numeral
% 5.52/5.81 thf(fact_4310_dvd__power,axiom,
% 5.52/5.81 ! [N: nat,X2: code_integer] :
% 5.52/5.81 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.81 | ( X2 = one_one_Code_integer ) )
% 5.52/5.81 => ( dvd_dvd_Code_integer @ X2 @ ( power_8256067586552552935nteger @ X2 @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power
% 5.52/5.81 thf(fact_4311_dvd__power,axiom,
% 5.52/5.81 ! [N: nat,X2: rat] :
% 5.52/5.81 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.81 | ( X2 = one_one_rat ) )
% 5.52/5.81 => ( dvd_dvd_rat @ X2 @ ( power_power_rat @ X2 @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power
% 5.52/5.81 thf(fact_4312_dvd__power,axiom,
% 5.52/5.81 ! [N: nat,X2: nat] :
% 5.52/5.81 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.81 | ( X2 = one_one_nat ) )
% 5.52/5.81 => ( dvd_dvd_nat @ X2 @ ( power_power_nat @ X2 @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power
% 5.52/5.81 thf(fact_4313_dvd__power,axiom,
% 5.52/5.81 ! [N: nat,X2: real] :
% 5.52/5.81 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.81 | ( X2 = one_one_real ) )
% 5.52/5.81 => ( dvd_dvd_real @ X2 @ ( power_power_real @ X2 @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power
% 5.52/5.81 thf(fact_4314_dvd__power,axiom,
% 5.52/5.81 ! [N: nat,X2: int] :
% 5.52/5.81 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.81 | ( X2 = one_one_int ) )
% 5.52/5.81 => ( dvd_dvd_int @ X2 @ ( power_power_int @ X2 @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power
% 5.52/5.81 thf(fact_4315_dvd__power,axiom,
% 5.52/5.81 ! [N: nat,X2: complex] :
% 5.52/5.81 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.81 | ( X2 = one_one_complex ) )
% 5.52/5.81 => ( dvd_dvd_complex @ X2 @ ( power_power_complex @ X2 @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power
% 5.52/5.81 thf(fact_4316_div2__even__ext__nat,axiom,
% 5.52/5.81 ! [X2: nat,Y2: nat] :
% 5.52/5.81 ( ( ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.81 = ( divide_divide_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.81 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 )
% 5.52/5.81 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y2 ) )
% 5.52/5.81 => ( X2 = Y2 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % div2_even_ext_nat
% 5.52/5.81 thf(fact_4317_even__even__mod__4__iff,axiom,
% 5.52/5.81 ! [N: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_even_mod_4_iff
% 5.52/5.81 thf(fact_4318_dvd__mult__cancel2,axiom,
% 5.52/5.81 ! [M: nat,N: nat] :
% 5.52/5.81 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.81 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 5.52/5.81 = ( N = one_one_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_mult_cancel2
% 5.52/5.81 thf(fact_4319_dvd__mult__cancel1,axiom,
% 5.52/5.81 ! [M: nat,N: nat] :
% 5.52/5.81 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.81 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 5.52/5.81 = ( N = one_one_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_mult_cancel1
% 5.52/5.81 thf(fact_4320_odd__numeral__BitM,axiom,
% 5.52/5.81 ! [W: num] :
% 5.52/5.81 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_numeral_BitM
% 5.52/5.81 thf(fact_4321_odd__numeral__BitM,axiom,
% 5.52/5.81 ! [W: num] :
% 5.52/5.81 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_numeral_BitM
% 5.52/5.81 thf(fact_4322_odd__numeral__BitM,axiom,
% 5.52/5.81 ! [W: num] :
% 5.52/5.81 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_numeral_BitM
% 5.52/5.81 thf(fact_4323_dvd__minus__add,axiom,
% 5.52/5.81 ! [Q2: nat,N: nat,R: nat,M: nat] :
% 5.52/5.81 ( ( ord_less_eq_nat @ Q2 @ N )
% 5.52/5.81 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R @ M ) )
% 5.52/5.81 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 5.52/5.81 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q2 ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_minus_add
% 5.52/5.81 thf(fact_4324_power__dvd__imp__le,axiom,
% 5.52/5.81 ! [I: nat,M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.52/5.81 => ( ( ord_less_nat @ one_one_nat @ I )
% 5.52/5.81 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % power_dvd_imp_le
% 5.52/5.81 thf(fact_4325_mod__nat__eqI,axiom,
% 5.52/5.81 ! [R: nat,N: nat,M: nat] :
% 5.52/5.81 ( ( ord_less_nat @ R @ N )
% 5.52/5.81 => ( ( ord_less_eq_nat @ R @ M )
% 5.52/5.81 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R ) )
% 5.52/5.81 => ( ( modulo_modulo_nat @ M @ N )
% 5.52/5.81 = R ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_nat_eqI
% 5.52/5.81 thf(fact_4326_mod__int__pos__iff,axiom,
% 5.52/5.81 ! [K: int,L: int] :
% 5.52/5.81 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 5.52/5.81 = ( ( dvd_dvd_int @ L @ K )
% 5.52/5.81 | ( ( L = zero_zero_int )
% 5.52/5.81 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.52/5.81 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_int_pos_iff
% 5.52/5.81 thf(fact_4327_even__two__times__div__two,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.52/5.81 = A ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_two_times_div_two
% 5.52/5.81 thf(fact_4328_even__two__times__div__two,axiom,
% 5.52/5.81 ! [A: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.81 = A ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_two_times_div_two
% 5.52/5.81 thf(fact_4329_even__two__times__div__two,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.52/5.81 = A ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_two_times_div_two
% 5.52/5.81 thf(fact_4330_even__iff__mod__2__eq__zero,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.81 = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_iff_mod_2_eq_zero
% 5.52/5.81 thf(fact_4331_even__iff__mod__2__eq__zero,axiom,
% 5.52/5.81 ! [A: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.81 = zero_zero_nat ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_iff_mod_2_eq_zero
% 5.52/5.81 thf(fact_4332_even__iff__mod__2__eq__zero,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.81 = zero_zero_int ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_iff_mod_2_eq_zero
% 5.52/5.81 thf(fact_4333_odd__iff__mod__2__eq__one,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.81 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.81 = one_one_Code_integer ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_iff_mod_2_eq_one
% 5.52/5.81 thf(fact_4334_odd__iff__mod__2__eq__one,axiom,
% 5.52/5.81 ! [A: nat] :
% 5.52/5.81 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.81 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.81 = one_one_nat ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_iff_mod_2_eq_one
% 5.52/5.81 thf(fact_4335_odd__iff__mod__2__eq__one,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.81 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.81 = one_one_int ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_iff_mod_2_eq_one
% 5.52/5.81 thf(fact_4336_power__mono__odd,axiom,
% 5.52/5.81 ! [N: nat,A: real,B: real] :
% 5.52/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 => ( ( ord_less_eq_real @ A @ B )
% 5.52/5.81 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % power_mono_odd
% 5.52/5.81 thf(fact_4337_power__mono__odd,axiom,
% 5.52/5.81 ! [N: nat,A: rat,B: rat] :
% 5.52/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 => ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.81 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % power_mono_odd
% 5.52/5.81 thf(fact_4338_power__mono__odd,axiom,
% 5.52/5.81 ! [N: nat,A: int,B: int] :
% 5.52/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 => ( ( ord_less_eq_int @ A @ B )
% 5.52/5.81 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % power_mono_odd
% 5.52/5.81 thf(fact_4339_odd__pos,axiom,
% 5.52/5.81 ! [N: nat] :
% 5.52/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_pos
% 5.52/5.81 thf(fact_4340_dvd__power__iff__le,axiom,
% 5.52/5.81 ! [K: nat,M: nat,N: nat] :
% 5.52/5.81 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.52/5.81 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 5.52/5.81 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_power_iff_le
% 5.52/5.81 thf(fact_4341_signed__take__bit__int__less__exp,axiom,
% 5.52/5.81 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.81
% 5.52/5.81 % signed_take_bit_int_less_exp
% 5.52/5.81 thf(fact_4342_even__unset__bit__iff,axiom,
% 5.52/5.81 ! [M: nat,A: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.52/5.81 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 | ( M = zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_unset_bit_iff
% 5.52/5.81 thf(fact_4343_even__unset__bit__iff,axiom,
% 5.52/5.81 ! [M: nat,A: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.52/5.81 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 | ( M = zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_unset_bit_iff
% 5.52/5.81 thf(fact_4344_even__unset__bit__iff,axiom,
% 5.52/5.81 ! [M: nat,A: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.52/5.81 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 | ( M = zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_unset_bit_iff
% 5.52/5.81 thf(fact_4345_even__set__bit__iff,axiom,
% 5.52/5.81 ! [M: nat,A: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.52/5.81 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 & ( M != zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_set_bit_iff
% 5.52/5.81 thf(fact_4346_even__set__bit__iff,axiom,
% 5.52/5.81 ! [M: nat,A: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.52/5.81 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 & ( M != zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_set_bit_iff
% 5.52/5.81 thf(fact_4347_even__set__bit__iff,axiom,
% 5.52/5.81 ! [M: nat,A: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.52/5.81 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 & ( M != zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_set_bit_iff
% 5.52/5.81 thf(fact_4348_even__flip__bit__iff,axiom,
% 5.52/5.81 ! [M: nat,A: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.52/5.81 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 != ( M = zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_flip_bit_iff
% 5.52/5.81 thf(fact_4349_even__flip__bit__iff,axiom,
% 5.52/5.81 ! [M: nat,A: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.52/5.81 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 != ( M = zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_flip_bit_iff
% 5.52/5.81 thf(fact_4350_even__flip__bit__iff,axiom,
% 5.52/5.81 ! [M: nat,A: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.52/5.81 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 != ( M = zero_zero_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_flip_bit_iff
% 5.52/5.81 thf(fact_4351_even__diff__iff,axiom,
% 5.52/5.81 ! [K: int,L: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 5.52/5.81 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_diff_iff
% 5.52/5.81 thf(fact_4352_oddE,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ~ ! [B2: code_integer] :
% 5.52/5.81 ( A
% 5.52/5.81 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) @ one_one_Code_integer ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % oddE
% 5.52/5.81 thf(fact_4353_oddE,axiom,
% 5.52/5.81 ! [A: nat] :
% 5.52/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ~ ! [B2: nat] :
% 5.52/5.81 ( A
% 5.52/5.81 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) @ one_one_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % oddE
% 5.52/5.81 thf(fact_4354_oddE,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ~ ! [B2: int] :
% 5.52/5.81 ( A
% 5.52/5.81 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ one_one_int ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % oddE
% 5.52/5.81 thf(fact_4355_parity__cases,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.81 != zero_z3403309356797280102nteger ) )
% 5.52/5.81 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.81 != one_one_Code_integer ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % parity_cases
% 5.52/5.81 thf(fact_4356_parity__cases,axiom,
% 5.52/5.81 ! [A: nat] :
% 5.52/5.81 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.81 != zero_zero_nat ) )
% 5.52/5.81 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.81 != one_one_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % parity_cases
% 5.52/5.81 thf(fact_4357_parity__cases,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.81 != zero_zero_int ) )
% 5.52/5.81 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.81 != one_one_int ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % parity_cases
% 5.52/5.81 thf(fact_4358_mod2__eq__if,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.81 = zero_z3403309356797280102nteger ) )
% 5.52/5.81 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.81 = one_one_Code_integer ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod2_eq_if
% 5.52/5.81 thf(fact_4359_mod2__eq__if,axiom,
% 5.52/5.81 ! [A: nat] :
% 5.52/5.81 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.81 = zero_zero_nat ) )
% 5.52/5.81 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.81 = one_one_nat ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod2_eq_if
% 5.52/5.81 thf(fact_4360_mod2__eq__if,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.81 = zero_zero_int ) )
% 5.52/5.81 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.81 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.81 = one_one_int ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod2_eq_if
% 5.52/5.81 thf(fact_4361_zero__le__even__power,axiom,
% 5.52/5.81 ! [N: nat,A: real] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zero_le_even_power
% 5.52/5.81 thf(fact_4362_zero__le__even__power,axiom,
% 5.52/5.81 ! [N: nat,A: rat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zero_le_even_power
% 5.52/5.81 thf(fact_4363_zero__le__even__power,axiom,
% 5.52/5.81 ! [N: nat,A: int] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zero_le_even_power
% 5.52/5.81 thf(fact_4364_zero__le__odd__power,axiom,
% 5.52/5.81 ! [N: nat,A: real] :
% 5.52/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.52/5.81 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zero_le_odd_power
% 5.52/5.81 thf(fact_4365_zero__le__odd__power,axiom,
% 5.52/5.81 ! [N: nat,A: rat] :
% 5.52/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.52/5.81 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zero_le_odd_power
% 5.52/5.81 thf(fact_4366_zero__le__odd__power,axiom,
% 5.52/5.81 ! [N: nat,A: int] :
% 5.52/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.52/5.81 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zero_le_odd_power
% 5.52/5.81 thf(fact_4367_zero__le__power__eq,axiom,
% 5.52/5.81 ! [A: real,N: nat] :
% 5.52/5.81 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.52/5.81 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zero_le_power_eq
% 5.52/5.81 thf(fact_4368_zero__le__power__eq,axiom,
% 5.52/5.81 ! [A: rat,N: nat] :
% 5.52/5.81 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.52/5.81 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zero_le_power_eq
% 5.52/5.81 thf(fact_4369_zero__le__power__eq,axiom,
% 5.52/5.81 ! [A: int,N: nat] :
% 5.52/5.81 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.52/5.81 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zero_le_power_eq
% 5.52/5.81 thf(fact_4370_signed__take__bit__int__less__self__iff,axiom,
% 5.52/5.81 ! [N: nat,K: int] :
% 5.52/5.81 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.52/5.81 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.52/5.81
% 5.52/5.81 % signed_take_bit_int_less_self_iff
% 5.52/5.81 thf(fact_4371_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.52/5.81 ! [K: int,N: nat] :
% 5.52/5.81 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.52/5.81 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % signed_take_bit_int_greater_eq_self_iff
% 5.52/5.81 thf(fact_4372_zero__less__power__eq,axiom,
% 5.52/5.81 ! [A: real,N: nat] :
% 5.52/5.81 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.52/5.81 = ( ( N = zero_zero_nat )
% 5.52/5.81 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( A != zero_zero_real ) )
% 5.52/5.81 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zero_less_power_eq
% 5.52/5.81 thf(fact_4373_zero__less__power__eq,axiom,
% 5.52/5.81 ! [A: rat,N: nat] :
% 5.52/5.81 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.52/5.81 = ( ( N = zero_zero_nat )
% 5.52/5.81 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( A != zero_zero_rat ) )
% 5.52/5.81 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zero_less_power_eq
% 5.52/5.81 thf(fact_4374_zero__less__power__eq,axiom,
% 5.52/5.81 ! [A: int,N: nat] :
% 5.52/5.81 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.52/5.81 = ( ( N = zero_zero_nat )
% 5.52/5.81 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( A != zero_zero_int ) )
% 5.52/5.81 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % zero_less_power_eq
% 5.52/5.81 thf(fact_4375_signed__take__bit__int__less__eq,axiom,
% 5.52/5.81 ! [N: nat,K: int] :
% 5.52/5.81 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.52/5.81 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % signed_take_bit_int_less_eq
% 5.52/5.81 thf(fact_4376_even__mask__div__iff_H,axiom,
% 5.52/5.81 ! [M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.81 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_mask_div_iff'
% 5.52/5.81 thf(fact_4377_even__mask__div__iff_H,axiom,
% 5.52/5.81 ! [M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.81 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_mask_div_iff'
% 5.52/5.81 thf(fact_4378_even__mask__div__iff_H,axiom,
% 5.52/5.81 ! [M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.81 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_mask_div_iff'
% 5.52/5.81 thf(fact_4379_power__le__zero__eq,axiom,
% 5.52/5.81 ! [A: real,N: nat] :
% 5.52/5.81 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.52/5.81 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.81 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.52/5.81 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % power_le_zero_eq
% 5.52/5.81 thf(fact_4380_power__le__zero__eq,axiom,
% 5.52/5.81 ! [A: rat,N: nat] :
% 5.52/5.81 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.52/5.81 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.81 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.52/5.81 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % power_le_zero_eq
% 5.52/5.81 thf(fact_4381_power__le__zero__eq,axiom,
% 5.52/5.81 ! [A: int,N: nat] :
% 5.52/5.81 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.52/5.81 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.81 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.52/5.81 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % power_le_zero_eq
% 5.52/5.81 thf(fact_4382_option_Osize__gen_I1_J,axiom,
% 5.52/5.81 ! [X2: nat > nat] :
% 5.52/5.81 ( ( size_option_nat @ X2 @ none_nat )
% 5.52/5.81 = ( suc @ zero_zero_nat ) ) ).
% 5.52/5.81
% 5.52/5.81 % option.size_gen(1)
% 5.52/5.81 thf(fact_4383_option_Osize__gen_I1_J,axiom,
% 5.52/5.81 ! [X2: product_prod_nat_nat > nat] :
% 5.52/5.81 ( ( size_o8335143837870341156at_nat @ X2 @ none_P5556105721700978146at_nat )
% 5.52/5.81 = ( suc @ zero_zero_nat ) ) ).
% 5.52/5.81
% 5.52/5.81 % option.size_gen(1)
% 5.52/5.81 thf(fact_4384_option_Osize__gen_I1_J,axiom,
% 5.52/5.81 ! [X2: num > nat] :
% 5.52/5.81 ( ( size_option_num @ X2 @ none_num )
% 5.52/5.81 = ( suc @ zero_zero_nat ) ) ).
% 5.52/5.81
% 5.52/5.81 % option.size_gen(1)
% 5.52/5.81 thf(fact_4385_even__mod__4__div__2,axiom,
% 5.52/5.81 ! [N: nat] :
% 5.52/5.81 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.52/5.81 = ( suc @ zero_zero_nat ) )
% 5.52/5.81 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_mod_4_div_2
% 5.52/5.81 thf(fact_4386_divmod__step__nat__def,axiom,
% 5.52/5.81 ( unique5026877609467782581ep_nat
% 5.52/5.81 = ( ^ [L2: num] :
% 5.52/5.81 ( produc2626176000494625587at_nat
% 5.52/5.81 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ 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 @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % divmod_step_nat_def
% 5.52/5.81 thf(fact_4387_even__mask__div__iff,axiom,
% 5.52/5.81 ! [M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.81 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 = zero_z3403309356797280102nteger )
% 5.52/5.81 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_mask_div_iff
% 5.52/5.81 thf(fact_4388_even__mask__div__iff,axiom,
% 5.52/5.81 ! [M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.81 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 = zero_zero_nat )
% 5.52/5.81 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_mask_div_iff
% 5.52/5.81 thf(fact_4389_even__mask__div__iff,axiom,
% 5.52/5.81 ! [M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.81 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 = zero_zero_int )
% 5.52/5.81 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_mask_div_iff
% 5.52/5.81 thf(fact_4390_divmod__step__int__def,axiom,
% 5.52/5.81 ( unique5024387138958732305ep_int
% 5.52/5.81 = ( ^ [L2: num] :
% 5.52/5.81 ( produc4245557441103728435nt_int
% 5.52/5.81 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ 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 @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % divmod_step_int_def
% 5.52/5.81 thf(fact_4391_odd__mod__4__div__2,axiom,
% 5.52/5.81 ! [N: nat] :
% 5.52/5.81 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.52/5.81 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.52/5.81 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % odd_mod_4_div_2
% 5.52/5.81 thf(fact_4392_even__mult__exp__div__exp__iff,axiom,
% 5.52/5.81 ! [A: code_integer,M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.81 = ( ( ord_less_nat @ N @ M )
% 5.52/5.81 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 = zero_z3403309356797280102nteger )
% 5.52/5.81 | ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_mult_exp_div_exp_iff
% 5.52/5.81 thf(fact_4393_even__mult__exp__div__exp__iff,axiom,
% 5.52/5.81 ! [A: nat,M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.81 = ( ( ord_less_nat @ N @ M )
% 5.52/5.81 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 = zero_zero_nat )
% 5.52/5.81 | ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_mult_exp_div_exp_iff
% 5.52/5.81 thf(fact_4394_even__mult__exp__div__exp__iff,axiom,
% 5.52/5.81 ! [A: int,M: nat,N: nat] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.81 = ( ( ord_less_nat @ N @ M )
% 5.52/5.81 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.52/5.81 = zero_zero_int )
% 5.52/5.81 | ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.81 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % even_mult_exp_div_exp_iff
% 5.52/5.81 thf(fact_4395_divmod__step__def,axiom,
% 5.52/5.81 ( unique5026877609467782581ep_nat
% 5.52/5.81 = ( ^ [L2: num] :
% 5.52/5.81 ( produc2626176000494625587at_nat
% 5.52/5.81 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ 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 @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % divmod_step_def
% 5.52/5.81 thf(fact_4396_divmod__step__def,axiom,
% 5.52/5.81 ( unique5024387138958732305ep_int
% 5.52/5.81 = ( ^ [L2: num] :
% 5.52/5.81 ( produc4245557441103728435nt_int
% 5.52/5.81 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ 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 @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % divmod_step_def
% 5.52/5.81 thf(fact_4397_divmod__step__def,axiom,
% 5.52/5.81 ( unique4921790084139445826nteger
% 5.52/5.81 = ( ^ [L2: num] :
% 5.52/5.81 ( produc6916734918728496179nteger
% 5.52/5.81 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % divmod_step_def
% 5.52/5.81 thf(fact_4398_infinite__growing,axiom,
% 5.52/5.81 ! [X8: set_Extended_enat] :
% 5.52/5.81 ( ( X8 != bot_bo7653980558646680370d_enat )
% 5.52/5.81 => ( ! [X4: extended_enat] :
% 5.52/5.81 ( ( member_Extended_enat @ X4 @ X8 )
% 5.52/5.81 => ? [Xa: extended_enat] :
% 5.52/5.81 ( ( member_Extended_enat @ Xa @ X8 )
% 5.52/5.81 & ( ord_le72135733267957522d_enat @ X4 @ Xa ) ) )
% 5.52/5.81 => ~ ( finite4001608067531595151d_enat @ X8 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % infinite_growing
% 5.52/5.81 thf(fact_4399_infinite__growing,axiom,
% 5.52/5.81 ! [X8: set_real] :
% 5.52/5.81 ( ( X8 != bot_bot_set_real )
% 5.52/5.81 => ( ! [X4: real] :
% 5.52/5.81 ( ( member_real @ X4 @ X8 )
% 5.52/5.81 => ? [Xa: real] :
% 5.52/5.81 ( ( member_real @ Xa @ X8 )
% 5.52/5.81 & ( ord_less_real @ X4 @ Xa ) ) )
% 5.52/5.81 => ~ ( finite_finite_real @ X8 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % infinite_growing
% 5.52/5.81 thf(fact_4400_infinite__growing,axiom,
% 5.52/5.81 ! [X8: set_rat] :
% 5.52/5.81 ( ( X8 != bot_bot_set_rat )
% 5.52/5.81 => ( ! [X4: rat] :
% 5.52/5.81 ( ( member_rat @ X4 @ X8 )
% 5.52/5.81 => ? [Xa: rat] :
% 5.52/5.81 ( ( member_rat @ Xa @ X8 )
% 5.52/5.81 & ( ord_less_rat @ X4 @ Xa ) ) )
% 5.52/5.81 => ~ ( finite_finite_rat @ X8 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % infinite_growing
% 5.52/5.81 thf(fact_4401_infinite__growing,axiom,
% 5.52/5.81 ! [X8: set_num] :
% 5.52/5.81 ( ( X8 != bot_bot_set_num )
% 5.52/5.81 => ( ! [X4: num] :
% 5.52/5.81 ( ( member_num @ X4 @ X8 )
% 5.52/5.81 => ? [Xa: num] :
% 5.52/5.81 ( ( member_num @ Xa @ X8 )
% 5.52/5.81 & ( ord_less_num @ X4 @ Xa ) ) )
% 5.52/5.81 => ~ ( finite_finite_num @ X8 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % infinite_growing
% 5.52/5.81 thf(fact_4402_infinite__growing,axiom,
% 5.52/5.81 ! [X8: set_nat] :
% 5.52/5.81 ( ( X8 != bot_bot_set_nat )
% 5.52/5.81 => ( ! [X4: nat] :
% 5.52/5.81 ( ( member_nat @ X4 @ X8 )
% 5.52/5.81 => ? [Xa: nat] :
% 5.52/5.81 ( ( member_nat @ Xa @ X8 )
% 5.52/5.81 & ( ord_less_nat @ X4 @ Xa ) ) )
% 5.52/5.81 => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % infinite_growing
% 5.52/5.81 thf(fact_4403_infinite__growing,axiom,
% 5.52/5.81 ! [X8: set_int] :
% 5.52/5.81 ( ( X8 != bot_bot_set_int )
% 5.52/5.81 => ( ! [X4: int] :
% 5.52/5.81 ( ( member_int @ X4 @ X8 )
% 5.52/5.81 => ? [Xa: int] :
% 5.52/5.81 ( ( member_int @ Xa @ X8 )
% 5.52/5.81 & ( ord_less_int @ X4 @ Xa ) ) )
% 5.52/5.81 => ~ ( finite_finite_int @ X8 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % infinite_growing
% 5.52/5.81 thf(fact_4404_ex__min__if__finite,axiom,
% 5.52/5.81 ! [S3: set_Extended_enat] :
% 5.52/5.81 ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.81 => ( ( S3 != bot_bo7653980558646680370d_enat )
% 5.52/5.81 => ? [X4: extended_enat] :
% 5.52/5.81 ( ( member_Extended_enat @ X4 @ S3 )
% 5.52/5.81 & ~ ? [Xa: extended_enat] :
% 5.52/5.81 ( ( member_Extended_enat @ Xa @ S3 )
% 5.52/5.81 & ( ord_le72135733267957522d_enat @ Xa @ X4 ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % ex_min_if_finite
% 5.52/5.81 thf(fact_4405_ex__min__if__finite,axiom,
% 5.52/5.81 ! [S3: set_real] :
% 5.52/5.81 ( ( finite_finite_real @ S3 )
% 5.52/5.81 => ( ( S3 != bot_bot_set_real )
% 5.52/5.81 => ? [X4: real] :
% 5.52/5.81 ( ( member_real @ X4 @ S3 )
% 5.52/5.81 & ~ ? [Xa: real] :
% 5.52/5.81 ( ( member_real @ Xa @ S3 )
% 5.52/5.81 & ( ord_less_real @ Xa @ X4 ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % ex_min_if_finite
% 5.52/5.81 thf(fact_4406_ex__min__if__finite,axiom,
% 5.52/5.81 ! [S3: set_rat] :
% 5.52/5.81 ( ( finite_finite_rat @ S3 )
% 5.52/5.81 => ( ( S3 != bot_bot_set_rat )
% 5.52/5.81 => ? [X4: rat] :
% 5.52/5.81 ( ( member_rat @ X4 @ S3 )
% 5.52/5.81 & ~ ? [Xa: rat] :
% 5.52/5.81 ( ( member_rat @ Xa @ S3 )
% 5.52/5.81 & ( ord_less_rat @ Xa @ X4 ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % ex_min_if_finite
% 5.52/5.81 thf(fact_4407_ex__min__if__finite,axiom,
% 5.52/5.81 ! [S3: set_num] :
% 5.52/5.81 ( ( finite_finite_num @ S3 )
% 5.52/5.81 => ( ( S3 != bot_bot_set_num )
% 5.52/5.81 => ? [X4: num] :
% 5.52/5.81 ( ( member_num @ X4 @ S3 )
% 5.52/5.81 & ~ ? [Xa: num] :
% 5.52/5.81 ( ( member_num @ Xa @ S3 )
% 5.52/5.81 & ( ord_less_num @ Xa @ X4 ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % ex_min_if_finite
% 5.52/5.81 thf(fact_4408_ex__min__if__finite,axiom,
% 5.52/5.81 ! [S3: set_nat] :
% 5.52/5.81 ( ( finite_finite_nat @ S3 )
% 5.52/5.81 => ( ( S3 != bot_bot_set_nat )
% 5.52/5.81 => ? [X4: nat] :
% 5.52/5.81 ( ( member_nat @ X4 @ S3 )
% 5.52/5.81 & ~ ? [Xa: nat] :
% 5.52/5.81 ( ( member_nat @ Xa @ S3 )
% 5.52/5.81 & ( ord_less_nat @ Xa @ X4 ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % ex_min_if_finite
% 5.52/5.81 thf(fact_4409_ex__min__if__finite,axiom,
% 5.52/5.81 ! [S3: set_int] :
% 5.52/5.81 ( ( finite_finite_int @ S3 )
% 5.52/5.81 => ( ( S3 != bot_bot_set_int )
% 5.52/5.81 => ? [X4: int] :
% 5.52/5.81 ( ( member_int @ X4 @ S3 )
% 5.52/5.81 & ~ ? [Xa: int] :
% 5.52/5.81 ( ( member_int @ Xa @ S3 )
% 5.52/5.81 & ( ord_less_int @ Xa @ X4 ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % ex_min_if_finite
% 5.52/5.81 thf(fact_4410_vebt__buildup_Oelims,axiom,
% 5.52/5.81 ! [X2: nat,Y2: vEBT_VEBT] :
% 5.52/5.81 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.52/5.81 = Y2 )
% 5.52/5.81 => ( ( ( X2 = zero_zero_nat )
% 5.52/5.81 => ( Y2
% 5.52/5.81 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.52/5.81 => ( ( ( X2
% 5.52/5.81 = ( suc @ zero_zero_nat ) )
% 5.52/5.81 => ( Y2
% 5.52/5.81 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.52/5.81 => ~ ! [Va3: nat] :
% 5.52/5.81 ( ( X2
% 5.52/5.81 = ( suc @ ( suc @ Va3 ) ) )
% 5.52/5.81 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.52/5.81 => ( Y2
% 5.52/5.81 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.52/5.81 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.52/5.81 => ( Y2
% 5.52/5.81 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % vebt_buildup.elims
% 5.52/5.81 thf(fact_4411_divmod__nat__if,axiom,
% 5.52/5.81 ( divmod_nat
% 5.52/5.81 = ( ^ [M3: nat,N3: nat] :
% 5.52/5.81 ( if_Pro6206227464963214023at_nat
% 5.52/5.81 @ ( ( N3 = zero_zero_nat )
% 5.52/5.81 | ( ord_less_nat @ M3 @ N3 ) )
% 5.52/5.81 @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 5.52/5.81 @ ( produc2626176000494625587at_nat
% 5.52/5.81 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.52/5.81 @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N3 ) @ N3 ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % divmod_nat_if
% 5.52/5.81 thf(fact_4412_signed__take__bit__Suc__minus__bit1,axiom,
% 5.52/5.81 ! [N: nat,K: num] :
% 5.52/5.81 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.52/5.81 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.52/5.81
% 5.52/5.81 % signed_take_bit_Suc_minus_bit1
% 5.52/5.81 thf(fact_4413_signed__take__bit__rec,axiom,
% 5.52/5.81 ( bit_ri6519982836138164636nteger
% 5.52/5.81 = ( ^ [N3: nat,A4: code_integer] : ( if_Code_integer @ ( N3 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % signed_take_bit_rec
% 5.52/5.81 thf(fact_4414_signed__take__bit__rec,axiom,
% 5.52/5.81 ( bit_ri631733984087533419it_int
% 5.52/5.81 = ( ^ [N3: nat,A4: int] : ( if_int @ ( N3 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % signed_take_bit_rec
% 5.52/5.81 thf(fact_4415_signed__take__bit__numeral__bit1,axiom,
% 5.52/5.81 ! [L: num,K: num] :
% 5.52/5.81 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.52/5.81 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.52/5.81
% 5.52/5.81 % signed_take_bit_numeral_bit1
% 5.52/5.81 thf(fact_4416_flip__bit__0,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.52/5.81 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % flip_bit_0
% 5.52/5.81 thf(fact_4417_flip__bit__0,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.52/5.81 = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % flip_bit_0
% 5.52/5.81 thf(fact_4418_flip__bit__0,axiom,
% 5.52/5.81 ! [A: nat] :
% 5.52/5.81 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.52/5.81 = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % flip_bit_0
% 5.52/5.81 thf(fact_4419_set__decode__Suc,axiom,
% 5.52/5.81 ! [N: nat,X2: nat] :
% 5.52/5.81 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X2 ) )
% 5.52/5.81 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % set_decode_Suc
% 5.52/5.81 thf(fact_4420_intind,axiom,
% 5.52/5.81 ! [I: nat,N: nat,P: nat > $o,X2: nat] :
% 5.52/5.81 ( ( ord_less_nat @ I @ N )
% 5.52/5.81 => ( ( P @ X2 )
% 5.52/5.81 => ( P @ ( nth_nat @ ( replicate_nat @ N @ X2 ) @ I ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % intind
% 5.52/5.81 thf(fact_4421_intind,axiom,
% 5.52/5.81 ! [I: nat,N: nat,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 5.52/5.81 ( ( ord_less_nat @ I @ N )
% 5.52/5.81 => ( ( P @ X2 )
% 5.52/5.81 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) @ I ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % intind
% 5.52/5.81 thf(fact_4422_add_Oinverse__inverse,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.52/5.81 = A ) ).
% 5.52/5.81
% 5.52/5.81 % add.inverse_inverse
% 5.52/5.81 thf(fact_4423_add_Oinverse__inverse,axiom,
% 5.52/5.81 ! [A: real] :
% 5.52/5.81 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.52/5.81 = A ) ).
% 5.52/5.81
% 5.52/5.81 % add.inverse_inverse
% 5.52/5.81 thf(fact_4424_add_Oinverse__inverse,axiom,
% 5.52/5.81 ! [A: complex] :
% 5.52/5.81 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.52/5.81 = A ) ).
% 5.52/5.81
% 5.52/5.81 % add.inverse_inverse
% 5.52/5.81 thf(fact_4425_add_Oinverse__inverse,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.81 = A ) ).
% 5.52/5.81
% 5.52/5.81 % add.inverse_inverse
% 5.52/5.81 thf(fact_4426_add_Oinverse__inverse,axiom,
% 5.52/5.81 ! [A: rat] :
% 5.52/5.81 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.52/5.81 = A ) ).
% 5.52/5.81
% 5.52/5.81 % add.inverse_inverse
% 5.52/5.81 thf(fact_4427_neg__equal__iff__equal,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( ( uminus_uminus_int @ A )
% 5.52/5.81 = ( uminus_uminus_int @ B ) )
% 5.52/5.81 = ( A = B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_iff_equal
% 5.52/5.81 thf(fact_4428_neg__equal__iff__equal,axiom,
% 5.52/5.81 ! [A: real,B: real] :
% 5.52/5.81 ( ( ( uminus_uminus_real @ A )
% 5.52/5.81 = ( uminus_uminus_real @ B ) )
% 5.52/5.81 = ( A = B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_iff_equal
% 5.52/5.81 thf(fact_4429_neg__equal__iff__equal,axiom,
% 5.52/5.81 ! [A: complex,B: complex] :
% 5.52/5.81 ( ( ( uminus1482373934393186551omplex @ A )
% 5.52/5.81 = ( uminus1482373934393186551omplex @ B ) )
% 5.52/5.81 = ( A = B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_iff_equal
% 5.52/5.81 thf(fact_4430_neg__equal__iff__equal,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( ( uminus1351360451143612070nteger @ A )
% 5.52/5.81 = ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.81 = ( A = B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_iff_equal
% 5.52/5.81 thf(fact_4431_neg__equal__iff__equal,axiom,
% 5.52/5.81 ! [A: rat,B: rat] :
% 5.52/5.81 ( ( ( uminus_uminus_rat @ A )
% 5.52/5.81 = ( uminus_uminus_rat @ B ) )
% 5.52/5.81 = ( A = B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_iff_equal
% 5.52/5.81 thf(fact_4432_case__prodI,axiom,
% 5.52/5.81 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.52/5.81 ( ( F @ A @ B )
% 5.52/5.81 => ( produc6590410687421337004_nat_o @ F @ ( produc6161850002892822231at_nat @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % case_prodI
% 5.52/5.81 thf(fact_4433_case__prodI,axiom,
% 5.52/5.81 ! [F: num > num > $o,A: num,B: num] :
% 5.52/5.81 ( ( F @ A @ B )
% 5.52/5.81 => ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % case_prodI
% 5.52/5.81 thf(fact_4434_case__prodI,axiom,
% 5.52/5.81 ! [F: nat > num > $o,A: nat,B: num] :
% 5.52/5.81 ( ( F @ A @ B )
% 5.52/5.81 => ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % case_prodI
% 5.52/5.81 thf(fact_4435_case__prodI,axiom,
% 5.52/5.81 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.52/5.81 ( ( F @ A @ B )
% 5.52/5.81 => ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % case_prodI
% 5.52/5.81 thf(fact_4436_case__prodI,axiom,
% 5.52/5.81 ! [F: int > int > $o,A: int,B: int] :
% 5.52/5.81 ( ( F @ A @ B )
% 5.52/5.81 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % case_prodI
% 5.52/5.81 thf(fact_4437_case__prodI2,axiom,
% 5.52/5.81 ! [P6: produc859450856879609959at_nat,C: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.52/5.81 ( ! [A3: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( produc6161850002892822231at_nat @ A3 @ B2 ) )
% 5.52/5.81 => ( C @ A3 @ B2 ) )
% 5.52/5.81 => ( produc6590410687421337004_nat_o @ C @ P6 ) ) ).
% 5.52/5.81
% 5.52/5.81 % case_prodI2
% 5.52/5.81 thf(fact_4438_case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_num_num,C: num > num > $o] :
% 5.52/5.81 ( ! [A3: num,B2: num] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_num_num @ A3 @ B2 ) )
% 5.52/5.81 => ( C @ A3 @ B2 ) )
% 5.52/5.81 => ( produc5703948589228662326_num_o @ C @ P6 ) ) ).
% 5.52/5.81
% 5.52/5.81 % case_prodI2
% 5.52/5.81 thf(fact_4439_case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_nat_num,C: nat > num > $o] :
% 5.52/5.81 ( ! [A3: nat,B2: num] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_nat_num @ A3 @ B2 ) )
% 5.52/5.81 => ( C @ A3 @ B2 ) )
% 5.52/5.81 => ( produc4927758841916487424_num_o @ C @ P6 ) ) ).
% 5.52/5.81
% 5.52/5.81 % case_prodI2
% 5.52/5.81 thf(fact_4440_case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_nat_nat,C: nat > nat > $o] :
% 5.52/5.81 ( ! [A3: nat,B2: nat] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_nat_nat @ A3 @ B2 ) )
% 5.52/5.81 => ( C @ A3 @ B2 ) )
% 5.52/5.81 => ( produc6081775807080527818_nat_o @ C @ P6 ) ) ).
% 5.52/5.81
% 5.52/5.81 % case_prodI2
% 5.52/5.81 thf(fact_4441_case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_int_int,C: int > int > $o] :
% 5.52/5.81 ( ! [A3: int,B2: int] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.52/5.81 => ( C @ A3 @ B2 ) )
% 5.52/5.81 => ( produc4947309494688390418_int_o @ C @ P6 ) ) ).
% 5.52/5.81
% 5.52/5.81 % case_prodI2
% 5.52/5.81 thf(fact_4442_mem__case__prodI,axiom,
% 5.52/5.81 ! [Z: real,C: num > num > set_real,A: num,B: num] :
% 5.52/5.81 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.52/5.81 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI
% 5.52/5.81 thf(fact_4443_mem__case__prodI,axiom,
% 5.52/5.81 ! [Z: nat,C: num > num > set_nat,A: num,B: num] :
% 5.52/5.81 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.52/5.81 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI
% 5.52/5.81 thf(fact_4444_mem__case__prodI,axiom,
% 5.52/5.81 ! [Z: int,C: num > num > set_int,A: num,B: num] :
% 5.52/5.81 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.52/5.81 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI
% 5.52/5.81 thf(fact_4445_mem__case__prodI,axiom,
% 5.52/5.81 ! [Z: real,C: nat > num > set_real,A: nat,B: num] :
% 5.52/5.81 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.52/5.81 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI
% 5.52/5.81 thf(fact_4446_mem__case__prodI,axiom,
% 5.52/5.81 ! [Z: nat,C: nat > num > set_nat,A: nat,B: num] :
% 5.52/5.81 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.52/5.81 => ( member_nat @ Z @ ( produc4130284055270567454et_nat @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI
% 5.52/5.81 thf(fact_4447_mem__case__prodI,axiom,
% 5.52/5.81 ! [Z: int,C: nat > num > set_int,A: nat,B: num] :
% 5.52/5.81 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.52/5.81 => ( member_int @ Z @ ( produc9175805072616146554et_int @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI
% 5.52/5.81 thf(fact_4448_mem__case__prodI,axiom,
% 5.52/5.81 ! [Z: real,C: nat > nat > set_real,A: nat,B: nat] :
% 5.52/5.81 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.52/5.81 => ( member_real @ Z @ ( produc3668448655016342576t_real @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI
% 5.52/5.81 thf(fact_4449_mem__case__prodI,axiom,
% 5.52/5.81 ! [Z: nat,C: nat > nat > set_nat,A: nat,B: nat] :
% 5.52/5.81 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.52/5.81 => ( member_nat @ Z @ ( produc6189476227299908564et_nat @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI
% 5.52/5.81 thf(fact_4450_mem__case__prodI,axiom,
% 5.52/5.81 ! [Z: int,C: nat > nat > set_int,A: nat,B: nat] :
% 5.52/5.81 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.52/5.81 => ( member_int @ Z @ ( produc2011625207790711856et_int @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI
% 5.52/5.81 thf(fact_4451_mem__case__prodI,axiom,
% 5.52/5.81 ! [Z: real,C: int > int > set_real,A: int,B: int] :
% 5.52/5.81 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.52/5.81 => ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI
% 5.52/5.81 thf(fact_4452_mem__case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_num_num,Z: real,C: num > num > set_real] :
% 5.52/5.81 ( ! [A3: num,B2: num] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_num_num @ A3 @ B2 ) )
% 5.52/5.81 => ( member_real @ Z @ ( C @ A3 @ B2 ) ) )
% 5.52/5.81 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P6 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI2
% 5.52/5.81 thf(fact_4453_mem__case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_num_num,Z: nat,C: num > num > set_nat] :
% 5.52/5.81 ( ! [A3: num,B2: num] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_num_num @ A3 @ B2 ) )
% 5.52/5.81 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 5.52/5.81 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P6 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI2
% 5.52/5.81 thf(fact_4454_mem__case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_num_num,Z: int,C: num > num > set_int] :
% 5.52/5.81 ( ! [A3: num,B2: num] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_num_num @ A3 @ B2 ) )
% 5.52/5.81 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 5.52/5.81 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P6 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI2
% 5.52/5.81 thf(fact_4455_mem__case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_nat_num,Z: real,C: nat > num > set_real] :
% 5.52/5.81 ( ! [A3: nat,B2: num] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_nat_num @ A3 @ B2 ) )
% 5.52/5.81 => ( member_real @ Z @ ( C @ A3 @ B2 ) ) )
% 5.52/5.81 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P6 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI2
% 5.52/5.81 thf(fact_4456_mem__case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_nat_num,Z: nat,C: nat > num > set_nat] :
% 5.52/5.81 ( ! [A3: nat,B2: num] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_nat_num @ A3 @ B2 ) )
% 5.52/5.81 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 5.52/5.81 => ( member_nat @ Z @ ( produc4130284055270567454et_nat @ C @ P6 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI2
% 5.52/5.81 thf(fact_4457_mem__case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_nat_num,Z: int,C: nat > num > set_int] :
% 5.52/5.81 ( ! [A3: nat,B2: num] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_nat_num @ A3 @ B2 ) )
% 5.52/5.81 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 5.52/5.81 => ( member_int @ Z @ ( produc9175805072616146554et_int @ C @ P6 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI2
% 5.52/5.81 thf(fact_4458_mem__case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_nat_nat,Z: real,C: nat > nat > set_real] :
% 5.52/5.81 ( ! [A3: nat,B2: nat] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_nat_nat @ A3 @ B2 ) )
% 5.52/5.81 => ( member_real @ Z @ ( C @ A3 @ B2 ) ) )
% 5.52/5.81 => ( member_real @ Z @ ( produc3668448655016342576t_real @ C @ P6 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI2
% 5.52/5.81 thf(fact_4459_mem__case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_nat_nat,Z: nat,C: nat > nat > set_nat] :
% 5.52/5.81 ( ! [A3: nat,B2: nat] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_nat_nat @ A3 @ B2 ) )
% 5.52/5.81 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 5.52/5.81 => ( member_nat @ Z @ ( produc6189476227299908564et_nat @ C @ P6 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI2
% 5.52/5.81 thf(fact_4460_mem__case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_nat_nat,Z: int,C: nat > nat > set_int] :
% 5.52/5.81 ( ! [A3: nat,B2: nat] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_nat_nat @ A3 @ B2 ) )
% 5.52/5.81 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 5.52/5.81 => ( member_int @ Z @ ( produc2011625207790711856et_int @ C @ P6 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI2
% 5.52/5.81 thf(fact_4461_mem__case__prodI2,axiom,
% 5.52/5.81 ! [P6: product_prod_int_int,Z: real,C: int > int > set_real] :
% 5.52/5.81 ( ! [A3: int,B2: int] :
% 5.52/5.81 ( ( P6
% 5.52/5.81 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.52/5.81 => ( member_real @ Z @ ( C @ A3 @ B2 ) ) )
% 5.52/5.81 => ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ P6 ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mem_case_prodI2
% 5.52/5.81 thf(fact_4462_case__prodI2_H,axiom,
% 5.52/5.81 ! [P6: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X2: product_prod_nat_nat] :
% 5.52/5.81 ( ! [A3: nat,B2: nat] :
% 5.52/5.81 ( ( ( product_Pair_nat_nat @ A3 @ B2 )
% 5.52/5.81 = P6 )
% 5.52/5.81 => ( C @ A3 @ B2 @ X2 ) )
% 5.52/5.81 => ( produc8739625826339149834_nat_o @ C @ P6 @ X2 ) ) ).
% 5.52/5.81
% 5.52/5.81 % case_prodI2'
% 5.52/5.81 thf(fact_4463_neg__le__iff__le,axiom,
% 5.52/5.81 ! [B: real,A: real] :
% 5.52/5.81 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.52/5.81 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_le_iff_le
% 5.52/5.81 thf(fact_4464_neg__le__iff__le,axiom,
% 5.52/5.81 ! [B: code_integer,A: code_integer] :
% 5.52/5.81 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.81 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_le_iff_le
% 5.52/5.81 thf(fact_4465_neg__le__iff__le,axiom,
% 5.52/5.81 ! [B: rat,A: rat] :
% 5.52/5.81 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.52/5.81 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_le_iff_le
% 5.52/5.81 thf(fact_4466_neg__le__iff__le,axiom,
% 5.52/5.81 ! [B: int,A: int] :
% 5.52/5.81 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.52/5.81 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_le_iff_le
% 5.52/5.81 thf(fact_4467_add_Oinverse__neutral,axiom,
% 5.52/5.81 ( ( uminus_uminus_int @ zero_zero_int )
% 5.52/5.81 = zero_zero_int ) ).
% 5.52/5.81
% 5.52/5.81 % add.inverse_neutral
% 5.52/5.81 thf(fact_4468_add_Oinverse__neutral,axiom,
% 5.52/5.81 ( ( uminus_uminus_real @ zero_zero_real )
% 5.52/5.81 = zero_zero_real ) ).
% 5.52/5.81
% 5.52/5.81 % add.inverse_neutral
% 5.52/5.81 thf(fact_4469_add_Oinverse__neutral,axiom,
% 5.52/5.81 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.52/5.81 = zero_zero_complex ) ).
% 5.52/5.81
% 5.52/5.81 % add.inverse_neutral
% 5.52/5.81 thf(fact_4470_add_Oinverse__neutral,axiom,
% 5.52/5.81 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.52/5.81 = zero_z3403309356797280102nteger ) ).
% 5.52/5.81
% 5.52/5.81 % add.inverse_neutral
% 5.52/5.81 thf(fact_4471_add_Oinverse__neutral,axiom,
% 5.52/5.81 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.52/5.81 = zero_zero_rat ) ).
% 5.52/5.81
% 5.52/5.81 % add.inverse_neutral
% 5.52/5.81 thf(fact_4472_neg__0__equal__iff__equal,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ( zero_zero_int
% 5.52/5.81 = ( uminus_uminus_int @ A ) )
% 5.52/5.81 = ( zero_zero_int = A ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_0_equal_iff_equal
% 5.52/5.81 thf(fact_4473_neg__0__equal__iff__equal,axiom,
% 5.52/5.81 ! [A: real] :
% 5.52/5.81 ( ( zero_zero_real
% 5.52/5.81 = ( uminus_uminus_real @ A ) )
% 5.52/5.81 = ( zero_zero_real = A ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_0_equal_iff_equal
% 5.52/5.81 thf(fact_4474_neg__0__equal__iff__equal,axiom,
% 5.52/5.81 ! [A: complex] :
% 5.52/5.81 ( ( zero_zero_complex
% 5.52/5.81 = ( uminus1482373934393186551omplex @ A ) )
% 5.52/5.81 = ( zero_zero_complex = A ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_0_equal_iff_equal
% 5.52/5.81 thf(fact_4475_neg__0__equal__iff__equal,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ( zero_z3403309356797280102nteger
% 5.52/5.81 = ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.81 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_0_equal_iff_equal
% 5.52/5.81 thf(fact_4476_neg__0__equal__iff__equal,axiom,
% 5.52/5.81 ! [A: rat] :
% 5.52/5.81 ( ( zero_zero_rat
% 5.52/5.81 = ( uminus_uminus_rat @ A ) )
% 5.52/5.81 = ( zero_zero_rat = A ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_0_equal_iff_equal
% 5.52/5.81 thf(fact_4477_neg__equal__0__iff__equal,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ( ( uminus_uminus_int @ A )
% 5.52/5.81 = zero_zero_int )
% 5.52/5.81 = ( A = zero_zero_int ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_0_iff_equal
% 5.52/5.81 thf(fact_4478_neg__equal__0__iff__equal,axiom,
% 5.52/5.81 ! [A: real] :
% 5.52/5.81 ( ( ( uminus_uminus_real @ A )
% 5.52/5.81 = zero_zero_real )
% 5.52/5.81 = ( A = zero_zero_real ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_0_iff_equal
% 5.52/5.81 thf(fact_4479_neg__equal__0__iff__equal,axiom,
% 5.52/5.81 ! [A: complex] :
% 5.52/5.81 ( ( ( uminus1482373934393186551omplex @ A )
% 5.52/5.81 = zero_zero_complex )
% 5.52/5.81 = ( A = zero_zero_complex ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_0_iff_equal
% 5.52/5.81 thf(fact_4480_neg__equal__0__iff__equal,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ( ( uminus1351360451143612070nteger @ A )
% 5.52/5.81 = zero_z3403309356797280102nteger )
% 5.52/5.81 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_0_iff_equal
% 5.52/5.81 thf(fact_4481_neg__equal__0__iff__equal,axiom,
% 5.52/5.81 ! [A: rat] :
% 5.52/5.81 ( ( ( uminus_uminus_rat @ A )
% 5.52/5.81 = zero_zero_rat )
% 5.52/5.81 = ( A = zero_zero_rat ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_0_iff_equal
% 5.52/5.81 thf(fact_4482_equal__neg__zero,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ( A
% 5.52/5.81 = ( uminus_uminus_int @ A ) )
% 5.52/5.81 = ( A = zero_zero_int ) ) ).
% 5.52/5.81
% 5.52/5.81 % equal_neg_zero
% 5.52/5.81 thf(fact_4483_equal__neg__zero,axiom,
% 5.52/5.81 ! [A: real] :
% 5.52/5.81 ( ( A
% 5.52/5.81 = ( uminus_uminus_real @ A ) )
% 5.52/5.81 = ( A = zero_zero_real ) ) ).
% 5.52/5.81
% 5.52/5.81 % equal_neg_zero
% 5.52/5.81 thf(fact_4484_equal__neg__zero,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ( A
% 5.52/5.81 = ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.81 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.81
% 5.52/5.81 % equal_neg_zero
% 5.52/5.81 thf(fact_4485_equal__neg__zero,axiom,
% 5.52/5.81 ! [A: rat] :
% 5.52/5.81 ( ( A
% 5.52/5.81 = ( uminus_uminus_rat @ A ) )
% 5.52/5.81 = ( A = zero_zero_rat ) ) ).
% 5.52/5.81
% 5.52/5.81 % equal_neg_zero
% 5.52/5.81 thf(fact_4486_neg__equal__zero,axiom,
% 5.52/5.81 ! [A: int] :
% 5.52/5.81 ( ( ( uminus_uminus_int @ A )
% 5.52/5.81 = A )
% 5.52/5.81 = ( A = zero_zero_int ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_zero
% 5.52/5.81 thf(fact_4487_neg__equal__zero,axiom,
% 5.52/5.81 ! [A: real] :
% 5.52/5.81 ( ( ( uminus_uminus_real @ A )
% 5.52/5.81 = A )
% 5.52/5.81 = ( A = zero_zero_real ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_zero
% 5.52/5.81 thf(fact_4488_neg__equal__zero,axiom,
% 5.52/5.81 ! [A: code_integer] :
% 5.52/5.81 ( ( ( uminus1351360451143612070nteger @ A )
% 5.52/5.81 = A )
% 5.52/5.81 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_zero
% 5.52/5.81 thf(fact_4489_neg__equal__zero,axiom,
% 5.52/5.81 ! [A: rat] :
% 5.52/5.81 ( ( ( uminus_uminus_rat @ A )
% 5.52/5.81 = A )
% 5.52/5.81 = ( A = zero_zero_rat ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_equal_zero
% 5.52/5.81 thf(fact_4490_neg__less__iff__less,axiom,
% 5.52/5.81 ! [B: int,A: int] :
% 5.52/5.81 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.52/5.81 = ( ord_less_int @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_less_iff_less
% 5.52/5.81 thf(fact_4491_neg__less__iff__less,axiom,
% 5.52/5.81 ! [B: real,A: real] :
% 5.52/5.81 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.52/5.81 = ( ord_less_real @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_less_iff_less
% 5.52/5.81 thf(fact_4492_neg__less__iff__less,axiom,
% 5.52/5.81 ! [B: code_integer,A: code_integer] :
% 5.52/5.81 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.81 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_less_iff_less
% 5.52/5.81 thf(fact_4493_neg__less__iff__less,axiom,
% 5.52/5.81 ! [B: rat,A: rat] :
% 5.52/5.81 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.52/5.81 = ( ord_less_rat @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_less_iff_less
% 5.52/5.81 thf(fact_4494_neg__numeral__eq__iff,axiom,
% 5.52/5.81 ! [M: num,N: num] :
% 5.52/5.81 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.52/5.81 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.81 = ( M = N ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_numeral_eq_iff
% 5.52/5.81 thf(fact_4495_neg__numeral__eq__iff,axiom,
% 5.52/5.81 ! [M: num,N: num] :
% 5.52/5.81 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.52/5.81 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.81 = ( M = N ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_numeral_eq_iff
% 5.52/5.81 thf(fact_4496_neg__numeral__eq__iff,axiom,
% 5.52/5.81 ! [M: num,N: num] :
% 5.52/5.81 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.52/5.81 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.52/5.81 = ( M = N ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_numeral_eq_iff
% 5.52/5.81 thf(fact_4497_neg__numeral__eq__iff,axiom,
% 5.52/5.81 ! [M: num,N: num] :
% 5.52/5.81 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.52/5.81 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.52/5.81 = ( M = N ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_numeral_eq_iff
% 5.52/5.81 thf(fact_4498_neg__numeral__eq__iff,axiom,
% 5.52/5.81 ! [M: num,N: num] :
% 5.52/5.81 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.52/5.81 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.52/5.81 = ( M = N ) ) ).
% 5.52/5.81
% 5.52/5.81 % neg_numeral_eq_iff
% 5.52/5.81 thf(fact_4499_mult__minus__left,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.52/5.81 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mult_minus_left
% 5.52/5.81 thf(fact_4500_mult__minus__left,axiom,
% 5.52/5.81 ! [A: real,B: real] :
% 5.52/5.81 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.52/5.81 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mult_minus_left
% 5.52/5.81 thf(fact_4501_mult__minus__left,axiom,
% 5.52/5.81 ! [A: complex,B: complex] :
% 5.52/5.81 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.52/5.81 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mult_minus_left
% 5.52/5.81 thf(fact_4502_mult__minus__left,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.52/5.81 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mult_minus_left
% 5.52/5.81 thf(fact_4503_mult__minus__left,axiom,
% 5.52/5.81 ! [A: rat,B: rat] :
% 5.52/5.81 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.52/5.81 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mult_minus_left
% 5.52/5.81 thf(fact_4504_minus__mult__minus,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.52/5.81 = ( times_times_int @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_mult_minus
% 5.52/5.81 thf(fact_4505_minus__mult__minus,axiom,
% 5.52/5.81 ! [A: real,B: real] :
% 5.52/5.81 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.52/5.81 = ( times_times_real @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_mult_minus
% 5.52/5.81 thf(fact_4506_minus__mult__minus,axiom,
% 5.52/5.81 ! [A: complex,B: complex] :
% 5.52/5.81 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.52/5.81 = ( times_times_complex @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_mult_minus
% 5.52/5.81 thf(fact_4507_minus__mult__minus,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.81 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_mult_minus
% 5.52/5.81 thf(fact_4508_minus__mult__minus,axiom,
% 5.52/5.81 ! [A: rat,B: rat] :
% 5.52/5.81 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.52/5.81 = ( times_times_rat @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_mult_minus
% 5.52/5.81 thf(fact_4509_mult__minus__right,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.52/5.81 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mult_minus_right
% 5.52/5.81 thf(fact_4510_mult__minus__right,axiom,
% 5.52/5.81 ! [A: real,B: real] :
% 5.52/5.81 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.52/5.81 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mult_minus_right
% 5.52/5.81 thf(fact_4511_mult__minus__right,axiom,
% 5.52/5.81 ! [A: complex,B: complex] :
% 5.52/5.81 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.52/5.81 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mult_minus_right
% 5.52/5.81 thf(fact_4512_mult__minus__right,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.81 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mult_minus_right
% 5.52/5.81 thf(fact_4513_mult__minus__right,axiom,
% 5.52/5.81 ! [A: rat,B: rat] :
% 5.52/5.81 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.52/5.81 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mult_minus_right
% 5.52/5.81 thf(fact_4514_add__minus__cancel,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.52/5.81 = B ) ).
% 5.52/5.81
% 5.52/5.81 % add_minus_cancel
% 5.52/5.81 thf(fact_4515_add__minus__cancel,axiom,
% 5.52/5.81 ! [A: real,B: real] :
% 5.52/5.81 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.52/5.81 = B ) ).
% 5.52/5.81
% 5.52/5.81 % add_minus_cancel
% 5.52/5.81 thf(fact_4516_add__minus__cancel,axiom,
% 5.52/5.81 ! [A: complex,B: complex] :
% 5.52/5.81 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.52/5.81 = B ) ).
% 5.52/5.81
% 5.52/5.81 % add_minus_cancel
% 5.52/5.81 thf(fact_4517_add__minus__cancel,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.52/5.81 = B ) ).
% 5.52/5.81
% 5.52/5.81 % add_minus_cancel
% 5.52/5.81 thf(fact_4518_add__minus__cancel,axiom,
% 5.52/5.81 ! [A: rat,B: rat] :
% 5.52/5.81 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.52/5.81 = B ) ).
% 5.52/5.81
% 5.52/5.81 % add_minus_cancel
% 5.52/5.81 thf(fact_4519_minus__add__cancel,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.52/5.81 = B ) ).
% 5.52/5.81
% 5.52/5.81 % minus_add_cancel
% 5.52/5.81 thf(fact_4520_minus__add__cancel,axiom,
% 5.52/5.81 ! [A: real,B: real] :
% 5.52/5.81 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.52/5.81 = B ) ).
% 5.52/5.81
% 5.52/5.81 % minus_add_cancel
% 5.52/5.81 thf(fact_4521_minus__add__cancel,axiom,
% 5.52/5.81 ! [A: complex,B: complex] :
% 5.52/5.81 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.52/5.81 = B ) ).
% 5.52/5.81
% 5.52/5.81 % minus_add_cancel
% 5.52/5.81 thf(fact_4522_minus__add__cancel,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.52/5.81 = B ) ).
% 5.52/5.81
% 5.52/5.81 % minus_add_cancel
% 5.52/5.81 thf(fact_4523_minus__add__cancel,axiom,
% 5.52/5.81 ! [A: rat,B: rat] :
% 5.52/5.81 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.52/5.81 = B ) ).
% 5.52/5.81
% 5.52/5.81 % minus_add_cancel
% 5.52/5.81 thf(fact_4524_minus__add__distrib,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.52/5.81 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_add_distrib
% 5.52/5.81 thf(fact_4525_minus__add__distrib,axiom,
% 5.52/5.81 ! [A: real,B: real] :
% 5.52/5.81 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.52/5.81 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_add_distrib
% 5.52/5.81 thf(fact_4526_minus__add__distrib,axiom,
% 5.52/5.81 ! [A: complex,B: complex] :
% 5.52/5.81 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.52/5.81 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_add_distrib
% 5.52/5.81 thf(fact_4527_minus__add__distrib,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.52/5.81 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_add_distrib
% 5.52/5.81 thf(fact_4528_minus__add__distrib,axiom,
% 5.52/5.81 ! [A: rat,B: rat] :
% 5.52/5.81 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.52/5.81 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_add_distrib
% 5.52/5.81 thf(fact_4529_minus__diff__eq,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.52/5.81 = ( minus_minus_int @ B @ A ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_diff_eq
% 5.52/5.81 thf(fact_4530_minus__diff__eq,axiom,
% 5.52/5.81 ! [A: real,B: real] :
% 5.52/5.81 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.52/5.81 = ( minus_minus_real @ B @ A ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_diff_eq
% 5.52/5.81 thf(fact_4531_minus__diff__eq,axiom,
% 5.52/5.81 ! [A: complex,B: complex] :
% 5.52/5.81 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.52/5.81 = ( minus_minus_complex @ B @ A ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_diff_eq
% 5.52/5.81 thf(fact_4532_minus__diff__eq,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.52/5.81 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_diff_eq
% 5.52/5.81 thf(fact_4533_minus__diff__eq,axiom,
% 5.52/5.81 ! [A: rat,B: rat] :
% 5.52/5.81 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.52/5.81 = ( minus_minus_rat @ B @ A ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_diff_eq
% 5.52/5.81 thf(fact_4534_div__minus__minus,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.52/5.81 = ( divide_divide_int @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_minus_minus
% 5.52/5.81 thf(fact_4535_div__minus__minus,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.81 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.52/5.81
% 5.52/5.81 % div_minus_minus
% 5.52/5.81 thf(fact_4536_dvd__minus__iff,axiom,
% 5.52/5.81 ! [X2: int,Y2: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ X2 @ ( uminus_uminus_int @ Y2 ) )
% 5.52/5.81 = ( dvd_dvd_int @ X2 @ Y2 ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_minus_iff
% 5.52/5.81 thf(fact_4537_dvd__minus__iff,axiom,
% 5.52/5.81 ! [X2: real,Y2: real] :
% 5.52/5.81 ( ( dvd_dvd_real @ X2 @ ( uminus_uminus_real @ Y2 ) )
% 5.52/5.81 = ( dvd_dvd_real @ X2 @ Y2 ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_minus_iff
% 5.52/5.81 thf(fact_4538_dvd__minus__iff,axiom,
% 5.52/5.81 ! [X2: complex,Y2: complex] :
% 5.52/5.81 ( ( dvd_dvd_complex @ X2 @ ( uminus1482373934393186551omplex @ Y2 ) )
% 5.52/5.81 = ( dvd_dvd_complex @ X2 @ Y2 ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_minus_iff
% 5.52/5.81 thf(fact_4539_dvd__minus__iff,axiom,
% 5.52/5.81 ! [X2: code_integer,Y2: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ X2 @ ( uminus1351360451143612070nteger @ Y2 ) )
% 5.52/5.81 = ( dvd_dvd_Code_integer @ X2 @ Y2 ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_minus_iff
% 5.52/5.81 thf(fact_4540_dvd__minus__iff,axiom,
% 5.52/5.81 ! [X2: rat,Y2: rat] :
% 5.52/5.81 ( ( dvd_dvd_rat @ X2 @ ( uminus_uminus_rat @ Y2 ) )
% 5.52/5.81 = ( dvd_dvd_rat @ X2 @ Y2 ) ) ).
% 5.52/5.81
% 5.52/5.81 % dvd_minus_iff
% 5.52/5.81 thf(fact_4541_minus__dvd__iff,axiom,
% 5.52/5.81 ! [X2: int,Y2: int] :
% 5.52/5.81 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X2 ) @ Y2 )
% 5.52/5.81 = ( dvd_dvd_int @ X2 @ Y2 ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_dvd_iff
% 5.52/5.81 thf(fact_4542_minus__dvd__iff,axiom,
% 5.52/5.81 ! [X2: real,Y2: real] :
% 5.52/5.81 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X2 ) @ Y2 )
% 5.52/5.81 = ( dvd_dvd_real @ X2 @ Y2 ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_dvd_iff
% 5.52/5.81 thf(fact_4543_minus__dvd__iff,axiom,
% 5.52/5.81 ! [X2: complex,Y2: complex] :
% 5.52/5.81 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X2 ) @ Y2 )
% 5.52/5.81 = ( dvd_dvd_complex @ X2 @ Y2 ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_dvd_iff
% 5.52/5.81 thf(fact_4544_minus__dvd__iff,axiom,
% 5.52/5.81 ! [X2: code_integer,Y2: code_integer] :
% 5.52/5.81 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X2 ) @ Y2 )
% 5.52/5.81 = ( dvd_dvd_Code_integer @ X2 @ Y2 ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_dvd_iff
% 5.52/5.81 thf(fact_4545_minus__dvd__iff,axiom,
% 5.52/5.81 ! [X2: rat,Y2: rat] :
% 5.52/5.81 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X2 ) @ Y2 )
% 5.52/5.81 = ( dvd_dvd_rat @ X2 @ Y2 ) ) ).
% 5.52/5.81
% 5.52/5.81 % minus_dvd_iff
% 5.52/5.81 thf(fact_4546_mod__minus__minus,axiom,
% 5.52/5.81 ! [A: int,B: int] :
% 5.52/5.81 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.52/5.81 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_minus_minus
% 5.52/5.81 thf(fact_4547_mod__minus__minus,axiom,
% 5.52/5.81 ! [A: code_integer,B: code_integer] :
% 5.52/5.81 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.81 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.52/5.81
% 5.52/5.81 % mod_minus_minus
% 5.52/5.81 thf(fact_4548_of__bool__less__eq__iff,axiom,
% 5.52/5.81 ! [P: $o,Q: $o] :
% 5.52/5.81 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.52/5.81 = ( P
% 5.52/5.81 => Q ) ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_less_eq_iff
% 5.52/5.81 thf(fact_4549_of__bool__less__eq__iff,axiom,
% 5.52/5.81 ! [P: $o,Q: $o] :
% 5.52/5.81 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.52/5.81 = ( P
% 5.52/5.81 => Q ) ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_less_eq_iff
% 5.52/5.81 thf(fact_4550_of__bool__less__eq__iff,axiom,
% 5.52/5.81 ! [P: $o,Q: $o] :
% 5.52/5.81 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.52/5.81 = ( P
% 5.52/5.81 => Q ) ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_less_eq_iff
% 5.52/5.81 thf(fact_4551_of__bool__less__eq__iff,axiom,
% 5.52/5.81 ! [P: $o,Q: $o] :
% 5.52/5.81 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.52/5.81 = ( P
% 5.52/5.81 => Q ) ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_less_eq_iff
% 5.52/5.81 thf(fact_4552_of__bool__eq_I1_J,axiom,
% 5.52/5.81 ( ( zero_n3304061248610475627l_real @ $false )
% 5.52/5.81 = zero_zero_real ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq(1)
% 5.52/5.81 thf(fact_4553_of__bool__eq_I1_J,axiom,
% 5.52/5.81 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.52/5.81 = zero_zero_rat ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq(1)
% 5.52/5.81 thf(fact_4554_of__bool__eq_I1_J,axiom,
% 5.52/5.81 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.52/5.81 = zero_zero_nat ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq(1)
% 5.52/5.81 thf(fact_4555_of__bool__eq_I1_J,axiom,
% 5.52/5.81 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.52/5.81 = zero_zero_int ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq(1)
% 5.52/5.81 thf(fact_4556_of__bool__eq_I1_J,axiom,
% 5.52/5.81 ( ( zero_n356916108424825756nteger @ $false )
% 5.52/5.81 = zero_z3403309356797280102nteger ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq(1)
% 5.52/5.81 thf(fact_4557_of__bool__eq__0__iff,axiom,
% 5.52/5.81 ! [P: $o] :
% 5.52/5.81 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.52/5.81 = zero_zero_real )
% 5.52/5.81 = ~ P ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq_0_iff
% 5.52/5.81 thf(fact_4558_of__bool__eq__0__iff,axiom,
% 5.52/5.81 ! [P: $o] :
% 5.52/5.81 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.52/5.81 = zero_zero_rat )
% 5.52/5.81 = ~ P ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq_0_iff
% 5.52/5.81 thf(fact_4559_of__bool__eq__0__iff,axiom,
% 5.52/5.81 ! [P: $o] :
% 5.52/5.81 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.52/5.81 = zero_zero_nat )
% 5.52/5.81 = ~ P ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq_0_iff
% 5.52/5.81 thf(fact_4560_of__bool__eq__0__iff,axiom,
% 5.52/5.81 ! [P: $o] :
% 5.52/5.81 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.52/5.81 = zero_zero_int )
% 5.52/5.81 = ~ P ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq_0_iff
% 5.52/5.81 thf(fact_4561_of__bool__eq__0__iff,axiom,
% 5.52/5.81 ! [P: $o] :
% 5.52/5.81 ( ( ( zero_n356916108424825756nteger @ P )
% 5.52/5.81 = zero_z3403309356797280102nteger )
% 5.52/5.81 = ~ P ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq_0_iff
% 5.52/5.81 thf(fact_4562_real__add__minus__iff,axiom,
% 5.52/5.81 ! [X2: real,A: real] :
% 5.52/5.81 ( ( ( plus_plus_real @ X2 @ ( uminus_uminus_real @ A ) )
% 5.52/5.81 = zero_zero_real )
% 5.52/5.81 = ( X2 = A ) ) ).
% 5.52/5.81
% 5.52/5.81 % real_add_minus_iff
% 5.52/5.81 thf(fact_4563_of__bool__less__iff,axiom,
% 5.52/5.81 ! [P: $o,Q: $o] :
% 5.52/5.81 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.52/5.81 = ( ~ P
% 5.52/5.81 & Q ) ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_less_iff
% 5.52/5.81 thf(fact_4564_of__bool__less__iff,axiom,
% 5.52/5.81 ! [P: $o,Q: $o] :
% 5.52/5.81 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.52/5.81 = ( ~ P
% 5.52/5.81 & Q ) ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_less_iff
% 5.52/5.81 thf(fact_4565_of__bool__less__iff,axiom,
% 5.52/5.81 ! [P: $o,Q: $o] :
% 5.52/5.81 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.52/5.81 = ( ~ P
% 5.52/5.81 & Q ) ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_less_iff
% 5.52/5.81 thf(fact_4566_of__bool__less__iff,axiom,
% 5.52/5.81 ! [P: $o,Q: $o] :
% 5.52/5.81 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.52/5.81 = ( ~ P
% 5.52/5.81 & Q ) ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_less_iff
% 5.52/5.81 thf(fact_4567_of__bool__less__iff,axiom,
% 5.52/5.81 ! [P: $o,Q: $o] :
% 5.52/5.81 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.52/5.81 = ( ~ P
% 5.52/5.81 & Q ) ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_less_iff
% 5.52/5.81 thf(fact_4568_of__bool__eq_I2_J,axiom,
% 5.52/5.81 ( ( zero_n1201886186963655149omplex @ $true )
% 5.52/5.81 = one_one_complex ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq(2)
% 5.52/5.81 thf(fact_4569_of__bool__eq_I2_J,axiom,
% 5.52/5.81 ( ( zero_n3304061248610475627l_real @ $true )
% 5.52/5.81 = one_one_real ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq(2)
% 5.52/5.81 thf(fact_4570_of__bool__eq_I2_J,axiom,
% 5.52/5.81 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.52/5.81 = one_one_rat ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq(2)
% 5.52/5.81 thf(fact_4571_of__bool__eq_I2_J,axiom,
% 5.52/5.81 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.52/5.81 = one_one_nat ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq(2)
% 5.52/5.81 thf(fact_4572_of__bool__eq_I2_J,axiom,
% 5.52/5.81 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.52/5.81 = one_one_int ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq(2)
% 5.52/5.81 thf(fact_4573_of__bool__eq_I2_J,axiom,
% 5.52/5.81 ( ( zero_n356916108424825756nteger @ $true )
% 5.52/5.81 = one_one_Code_integer ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq(2)
% 5.52/5.81 thf(fact_4574_of__bool__eq__1__iff,axiom,
% 5.52/5.81 ! [P: $o] :
% 5.52/5.81 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.52/5.81 = one_one_complex )
% 5.52/5.81 = P ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq_1_iff
% 5.52/5.81 thf(fact_4575_of__bool__eq__1__iff,axiom,
% 5.52/5.81 ! [P: $o] :
% 5.52/5.81 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.52/5.81 = one_one_real )
% 5.52/5.81 = P ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq_1_iff
% 5.52/5.81 thf(fact_4576_of__bool__eq__1__iff,axiom,
% 5.52/5.81 ! [P: $o] :
% 5.52/5.81 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.52/5.81 = one_one_rat )
% 5.52/5.81 = P ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq_1_iff
% 5.52/5.81 thf(fact_4577_of__bool__eq__1__iff,axiom,
% 5.52/5.81 ! [P: $o] :
% 5.52/5.81 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.52/5.81 = one_one_nat )
% 5.52/5.81 = P ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq_1_iff
% 5.52/5.81 thf(fact_4578_of__bool__eq__1__iff,axiom,
% 5.52/5.81 ! [P: $o] :
% 5.52/5.81 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.52/5.81 = one_one_int )
% 5.52/5.81 = P ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq_1_iff
% 5.52/5.81 thf(fact_4579_of__bool__eq__1__iff,axiom,
% 5.52/5.81 ! [P: $o] :
% 5.52/5.81 ( ( ( zero_n356916108424825756nteger @ P )
% 5.52/5.81 = one_one_Code_integer )
% 5.52/5.81 = P ) ).
% 5.52/5.81
% 5.52/5.81 % of_bool_eq_1_iff
% 5.52/5.81 thf(fact_4580_length__replicate,axiom,
% 5.52/5.81 ! [N: nat,X2: vEBT_VEBT] :
% 5.52/5.81 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.52/5.82 = N ) ).
% 5.52/5.82
% 5.52/5.82 % length_replicate
% 5.52/5.82 thf(fact_4581_length__replicate,axiom,
% 5.52/5.82 ! [N: nat,X2: $o] :
% 5.52/5.82 ( ( size_size_list_o @ ( replicate_o @ N @ X2 ) )
% 5.52/5.82 = N ) ).
% 5.52/5.82
% 5.52/5.82 % length_replicate
% 5.52/5.82 thf(fact_4582_length__replicate,axiom,
% 5.52/5.82 ! [N: nat,X2: nat] :
% 5.52/5.82 ( ( size_size_list_nat @ ( replicate_nat @ N @ X2 ) )
% 5.52/5.82 = N ) ).
% 5.52/5.82
% 5.52/5.82 % length_replicate
% 5.52/5.82 thf(fact_4583_of__bool__or__iff,axiom,
% 5.52/5.82 ! [P: $o,Q: $o] :
% 5.52/5.82 ( ( zero_n2687167440665602831ol_nat
% 5.52/5.82 @ ( P
% 5.52/5.82 | Q ) )
% 5.52/5.82 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_or_iff
% 5.52/5.82 thf(fact_4584_of__bool__or__iff,axiom,
% 5.52/5.82 ! [P: $o,Q: $o] :
% 5.52/5.82 ( ( zero_n2684676970156552555ol_int
% 5.52/5.82 @ ( P
% 5.52/5.82 | Q ) )
% 5.52/5.82 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_or_iff
% 5.52/5.82 thf(fact_4585_of__bool__or__iff,axiom,
% 5.52/5.82 ! [P: $o,Q: $o] :
% 5.52/5.82 ( ( zero_n356916108424825756nteger
% 5.52/5.82 @ ( P
% 5.52/5.82 | Q ) )
% 5.52/5.82 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_or_iff
% 5.52/5.82 thf(fact_4586_neg__less__eq__nonneg,axiom,
% 5.52/5.82 ! [A: real] :
% 5.52/5.82 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.52/5.82 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_less_eq_nonneg
% 5.52/5.82 thf(fact_4587_neg__less__eq__nonneg,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.52/5.82 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_less_eq_nonneg
% 5.52/5.82 thf(fact_4588_neg__less__eq__nonneg,axiom,
% 5.52/5.82 ! [A: rat] :
% 5.52/5.82 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.52/5.82 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_less_eq_nonneg
% 5.52/5.82 thf(fact_4589_neg__less__eq__nonneg,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.52/5.82 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_less_eq_nonneg
% 5.52/5.82 thf(fact_4590_less__eq__neg__nonpos,axiom,
% 5.52/5.82 ! [A: real] :
% 5.52/5.82 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.52/5.82 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_eq_neg_nonpos
% 5.52/5.82 thf(fact_4591_less__eq__neg__nonpos,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.82 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_eq_neg_nonpos
% 5.52/5.82 thf(fact_4592_less__eq__neg__nonpos,axiom,
% 5.52/5.82 ! [A: rat] :
% 5.52/5.82 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.52/5.82 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_eq_neg_nonpos
% 5.52/5.82 thf(fact_4593_less__eq__neg__nonpos,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.52/5.82 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_eq_neg_nonpos
% 5.52/5.82 thf(fact_4594_neg__le__0__iff__le,axiom,
% 5.52/5.82 ! [A: real] :
% 5.52/5.82 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.52/5.82 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_le_0_iff_le
% 5.52/5.82 thf(fact_4595_neg__le__0__iff__le,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.52/5.82 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_le_0_iff_le
% 5.52/5.82 thf(fact_4596_neg__le__0__iff__le,axiom,
% 5.52/5.82 ! [A: rat] :
% 5.52/5.82 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.52/5.82 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_le_0_iff_le
% 5.52/5.82 thf(fact_4597_neg__le__0__iff__le,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.52/5.82 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_le_0_iff_le
% 5.52/5.82 thf(fact_4598_neg__0__le__iff__le,axiom,
% 5.52/5.82 ! [A: real] :
% 5.52/5.82 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.52/5.82 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_0_le_iff_le
% 5.52/5.82 thf(fact_4599_neg__0__le__iff__le,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.82 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_0_le_iff_le
% 5.52/5.82 thf(fact_4600_neg__0__le__iff__le,axiom,
% 5.52/5.82 ! [A: rat] :
% 5.52/5.82 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.52/5.82 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_0_le_iff_le
% 5.52/5.82 thf(fact_4601_neg__0__le__iff__le,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.52/5.82 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_0_le_iff_le
% 5.52/5.82 thf(fact_4602_less__neg__neg,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.52/5.82 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_neg_neg
% 5.52/5.82 thf(fact_4603_less__neg__neg,axiom,
% 5.52/5.82 ! [A: real] :
% 5.52/5.82 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.52/5.82 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_neg_neg
% 5.52/5.82 thf(fact_4604_less__neg__neg,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.82 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_neg_neg
% 5.52/5.82 thf(fact_4605_less__neg__neg,axiom,
% 5.52/5.82 ! [A: rat] :
% 5.52/5.82 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.52/5.82 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_neg_neg
% 5.52/5.82 thf(fact_4606_neg__less__pos,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.52/5.82 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_less_pos
% 5.52/5.82 thf(fact_4607_neg__less__pos,axiom,
% 5.52/5.82 ! [A: real] :
% 5.52/5.82 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.52/5.82 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_less_pos
% 5.52/5.82 thf(fact_4608_neg__less__pos,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.52/5.82 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_less_pos
% 5.52/5.82 thf(fact_4609_neg__less__pos,axiom,
% 5.52/5.82 ! [A: rat] :
% 5.52/5.82 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.52/5.82 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_less_pos
% 5.52/5.82 thf(fact_4610_neg__0__less__iff__less,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.52/5.82 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_0_less_iff_less
% 5.52/5.82 thf(fact_4611_neg__0__less__iff__less,axiom,
% 5.52/5.82 ! [A: real] :
% 5.52/5.82 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.52/5.82 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_0_less_iff_less
% 5.52/5.82 thf(fact_4612_neg__0__less__iff__less,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.82 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_0_less_iff_less
% 5.52/5.82 thf(fact_4613_neg__0__less__iff__less,axiom,
% 5.52/5.82 ! [A: rat] :
% 5.52/5.82 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.52/5.82 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_0_less_iff_less
% 5.52/5.82 thf(fact_4614_neg__less__0__iff__less,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.52/5.82 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_less_0_iff_less
% 5.52/5.82 thf(fact_4615_neg__less__0__iff__less,axiom,
% 5.52/5.82 ! [A: real] :
% 5.52/5.82 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.52/5.82 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_less_0_iff_less
% 5.52/5.82 thf(fact_4616_neg__less__0__iff__less,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.52/5.82 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_less_0_iff_less
% 5.52/5.82 thf(fact_4617_neg__less__0__iff__less,axiom,
% 5.52/5.82 ! [A: rat] :
% 5.52/5.82 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.52/5.82 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_less_0_iff_less
% 5.52/5.82 thf(fact_4618_add_Oright__inverse,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.52/5.82 = zero_zero_int ) ).
% 5.52/5.82
% 5.52/5.82 % add.right_inverse
% 5.52/5.82 thf(fact_4619_add_Oright__inverse,axiom,
% 5.52/5.82 ! [A: real] :
% 5.52/5.82 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.52/5.82 = zero_zero_real ) ).
% 5.52/5.82
% 5.52/5.82 % add.right_inverse
% 5.52/5.82 thf(fact_4620_add_Oright__inverse,axiom,
% 5.52/5.82 ! [A: complex] :
% 5.52/5.82 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.52/5.82 = zero_zero_complex ) ).
% 5.52/5.82
% 5.52/5.82 % add.right_inverse
% 5.52/5.82 thf(fact_4621_add_Oright__inverse,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.82 = zero_z3403309356797280102nteger ) ).
% 5.52/5.82
% 5.52/5.82 % add.right_inverse
% 5.52/5.82 thf(fact_4622_add_Oright__inverse,axiom,
% 5.52/5.82 ! [A: rat] :
% 5.52/5.82 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.52/5.82 = zero_zero_rat ) ).
% 5.52/5.82
% 5.52/5.82 % add.right_inverse
% 5.52/5.82 thf(fact_4623_ab__left__minus,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.52/5.82 = zero_zero_int ) ).
% 5.52/5.82
% 5.52/5.82 % ab_left_minus
% 5.52/5.82 thf(fact_4624_ab__left__minus,axiom,
% 5.52/5.82 ! [A: real] :
% 5.52/5.82 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.52/5.82 = zero_zero_real ) ).
% 5.52/5.82
% 5.52/5.82 % ab_left_minus
% 5.52/5.82 thf(fact_4625_ab__left__minus,axiom,
% 5.52/5.82 ! [A: complex] :
% 5.52/5.82 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.52/5.82 = zero_zero_complex ) ).
% 5.52/5.82
% 5.52/5.82 % ab_left_minus
% 5.52/5.82 thf(fact_4626_ab__left__minus,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.52/5.82 = zero_z3403309356797280102nteger ) ).
% 5.52/5.82
% 5.52/5.82 % ab_left_minus
% 5.52/5.82 thf(fact_4627_ab__left__minus,axiom,
% 5.52/5.82 ! [A: rat] :
% 5.52/5.82 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.52/5.82 = zero_zero_rat ) ).
% 5.52/5.82
% 5.52/5.82 % ab_left_minus
% 5.52/5.82 thf(fact_4628_diff__0,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.52/5.82 = ( uminus_uminus_int @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_0
% 5.52/5.82 thf(fact_4629_diff__0,axiom,
% 5.52/5.82 ! [A: real] :
% 5.52/5.82 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.52/5.82 = ( uminus_uminus_real @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_0
% 5.52/5.82 thf(fact_4630_diff__0,axiom,
% 5.52/5.82 ! [A: complex] :
% 5.52/5.82 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_0
% 5.52/5.82 thf(fact_4631_diff__0,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_0
% 5.52/5.82 thf(fact_4632_diff__0,axiom,
% 5.52/5.82 ! [A: rat] :
% 5.52/5.82 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.52/5.82 = ( uminus_uminus_rat @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_0
% 5.52/5.82 thf(fact_4633_add__neg__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_simps(3)
% 5.52/5.82 thf(fact_4634_add__neg__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.82 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_simps(3)
% 5.52/5.82 thf(fact_4635_add__neg__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_simps(3)
% 5.52/5.82 thf(fact_4636_add__neg__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_simps(3)
% 5.52/5.82 thf(fact_4637_add__neg__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.52/5.82 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_simps(3)
% 5.52/5.82 thf(fact_4638_mult__minus1,axiom,
% 5.52/5.82 ! [Z: int] :
% 5.52/5.82 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.52/5.82 = ( uminus_uminus_int @ Z ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_minus1
% 5.52/5.82 thf(fact_4639_mult__minus1,axiom,
% 5.52/5.82 ! [Z: real] :
% 5.52/5.82 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.52/5.82 = ( uminus_uminus_real @ Z ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_minus1
% 5.52/5.82 thf(fact_4640_mult__minus1,axiom,
% 5.52/5.82 ! [Z: complex] :
% 5.52/5.82 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_minus1
% 5.52/5.82 thf(fact_4641_mult__minus1,axiom,
% 5.52/5.82 ! [Z: code_integer] :
% 5.52/5.82 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_minus1
% 5.52/5.82 thf(fact_4642_mult__minus1,axiom,
% 5.52/5.82 ! [Z: rat] :
% 5.52/5.82 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.52/5.82 = ( uminus_uminus_rat @ Z ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_minus1
% 5.52/5.82 thf(fact_4643_mult__minus1__right,axiom,
% 5.52/5.82 ! [Z: int] :
% 5.52/5.82 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.82 = ( uminus_uminus_int @ Z ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_minus1_right
% 5.52/5.82 thf(fact_4644_mult__minus1__right,axiom,
% 5.52/5.82 ! [Z: real] :
% 5.52/5.82 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.82 = ( uminus_uminus_real @ Z ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_minus1_right
% 5.52/5.82 thf(fact_4645_mult__minus1__right,axiom,
% 5.52/5.82 ! [Z: complex] :
% 5.52/5.82 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_minus1_right
% 5.52/5.82 thf(fact_4646_mult__minus1__right,axiom,
% 5.52/5.82 ! [Z: code_integer] :
% 5.52/5.82 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_minus1_right
% 5.52/5.82 thf(fact_4647_mult__minus1__right,axiom,
% 5.52/5.82 ! [Z: rat] :
% 5.52/5.82 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.82 = ( uminus_uminus_rat @ Z ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_minus1_right
% 5.52/5.82 thf(fact_4648_diff__minus__eq__add,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.52/5.82 = ( plus_plus_int @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_minus_eq_add
% 5.52/5.82 thf(fact_4649_diff__minus__eq__add,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.52/5.82 = ( plus_plus_real @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_minus_eq_add
% 5.52/5.82 thf(fact_4650_diff__minus__eq__add,axiom,
% 5.52/5.82 ! [A: complex,B: complex] :
% 5.52/5.82 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.52/5.82 = ( plus_plus_complex @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_minus_eq_add
% 5.52/5.82 thf(fact_4651_diff__minus__eq__add,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.82 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_minus_eq_add
% 5.52/5.82 thf(fact_4652_diff__minus__eq__add,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.52/5.82 = ( plus_plus_rat @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_minus_eq_add
% 5.52/5.82 thf(fact_4653_uminus__add__conv__diff,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.52/5.82 = ( minus_minus_int @ B @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % uminus_add_conv_diff
% 5.52/5.82 thf(fact_4654_uminus__add__conv__diff,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.52/5.82 = ( minus_minus_real @ B @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % uminus_add_conv_diff
% 5.52/5.82 thf(fact_4655_uminus__add__conv__diff,axiom,
% 5.52/5.82 ! [A: complex,B: complex] :
% 5.52/5.82 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.52/5.82 = ( minus_minus_complex @ B @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % uminus_add_conv_diff
% 5.52/5.82 thf(fact_4656_uminus__add__conv__diff,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.52/5.82 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % uminus_add_conv_diff
% 5.52/5.82 thf(fact_4657_uminus__add__conv__diff,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.52/5.82 = ( minus_minus_rat @ B @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % uminus_add_conv_diff
% 5.52/5.82 thf(fact_4658_div__minus1__right,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.82 = ( uminus_uminus_int @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % div_minus1_right
% 5.52/5.82 thf(fact_4659_div__minus1__right,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % div_minus1_right
% 5.52/5.82 thf(fact_4660_divide__minus1,axiom,
% 5.52/5.82 ! [X2: real] :
% 5.52/5.82 ( ( divide_divide_real @ X2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.82 = ( uminus_uminus_real @ X2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % divide_minus1
% 5.52/5.82 thf(fact_4661_divide__minus1,axiom,
% 5.52/5.82 ! [X2: complex] :
% 5.52/5.82 ( ( divide1717551699836669952omplex @ X2 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ X2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % divide_minus1
% 5.52/5.82 thf(fact_4662_divide__minus1,axiom,
% 5.52/5.82 ! [X2: rat] :
% 5.52/5.82 ( ( divide_divide_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.82 = ( uminus_uminus_rat @ X2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % divide_minus1
% 5.52/5.82 thf(fact_4663_minus__mod__self1,axiom,
% 5.52/5.82 ! [B: int,A: int] :
% 5.52/5.82 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.52/5.82 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_mod_self1
% 5.52/5.82 thf(fact_4664_minus__mod__self1,axiom,
% 5.52/5.82 ! [B: code_integer,A: code_integer] :
% 5.52/5.82 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.52/5.82 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_mod_self1
% 5.52/5.82 thf(fact_4665_zero__less__of__bool__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.52/5.82 = P ) ).
% 5.52/5.82
% 5.52/5.82 % zero_less_of_bool_iff
% 5.52/5.82 thf(fact_4666_zero__less__of__bool__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.52/5.82 = P ) ).
% 5.52/5.82
% 5.52/5.82 % zero_less_of_bool_iff
% 5.52/5.82 thf(fact_4667_zero__less__of__bool__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.52/5.82 = P ) ).
% 5.52/5.82
% 5.52/5.82 % zero_less_of_bool_iff
% 5.52/5.82 thf(fact_4668_zero__less__of__bool__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.52/5.82 = P ) ).
% 5.52/5.82
% 5.52/5.82 % zero_less_of_bool_iff
% 5.52/5.82 thf(fact_4669_zero__less__of__bool__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.52/5.82 = P ) ).
% 5.52/5.82
% 5.52/5.82 % zero_less_of_bool_iff
% 5.52/5.82 thf(fact_4670_of__bool__less__one__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.52/5.82 = ~ P ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_less_one_iff
% 5.52/5.82 thf(fact_4671_of__bool__less__one__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.52/5.82 = ~ P ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_less_one_iff
% 5.52/5.82 thf(fact_4672_of__bool__less__one__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.52/5.82 = ~ P ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_less_one_iff
% 5.52/5.82 thf(fact_4673_of__bool__less__one__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.52/5.82 = ~ P ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_less_one_iff
% 5.52/5.82 thf(fact_4674_of__bool__less__one__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.52/5.82 = ~ P ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_less_one_iff
% 5.52/5.82 thf(fact_4675_of__bool__not__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.52/5.82 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_not_iff
% 5.52/5.82 thf(fact_4676_of__bool__not__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.52/5.82 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_not_iff
% 5.52/5.82 thf(fact_4677_of__bool__not__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.52/5.82 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_not_iff
% 5.52/5.82 thf(fact_4678_of__bool__not__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.52/5.82 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_not_iff
% 5.52/5.82 thf(fact_4679_of__bool__not__iff,axiom,
% 5.52/5.82 ! [P: $o] :
% 5.52/5.82 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.52/5.82 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_not_iff
% 5.52/5.82 thf(fact_4680_Suc__0__mod__eq,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.52/5.82 = ( zero_n2687167440665602831ol_nat
% 5.52/5.82 @ ( N
% 5.52/5.82 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % Suc_0_mod_eq
% 5.52/5.82 thf(fact_4681_signed__take__bit__of__minus__1,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.82
% 5.52/5.82 % signed_take_bit_of_minus_1
% 5.52/5.82 thf(fact_4682_signed__take__bit__of__minus__1,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.82 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.82
% 5.52/5.82 % signed_take_bit_of_minus_1
% 5.52/5.82 thf(fact_4683_pred__numeral__simps_I1_J,axiom,
% 5.52/5.82 ( ( pred_numeral @ one )
% 5.52/5.82 = zero_zero_nat ) ).
% 5.52/5.82
% 5.52/5.82 % pred_numeral_simps(1)
% 5.52/5.82 thf(fact_4684_eq__numeral__Suc,axiom,
% 5.52/5.82 ! [K: num,N: nat] :
% 5.52/5.82 ( ( ( numeral_numeral_nat @ K )
% 5.52/5.82 = ( suc @ N ) )
% 5.52/5.82 = ( ( pred_numeral @ K )
% 5.52/5.82 = N ) ) ).
% 5.52/5.82
% 5.52/5.82 % eq_numeral_Suc
% 5.52/5.82 thf(fact_4685_Suc__eq__numeral,axiom,
% 5.52/5.82 ! [N: nat,K: num] :
% 5.52/5.82 ( ( ( suc @ N )
% 5.52/5.82 = ( numeral_numeral_nat @ K ) )
% 5.52/5.82 = ( N
% 5.52/5.82 = ( pred_numeral @ K ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % Suc_eq_numeral
% 5.52/5.82 thf(fact_4686_nth__replicate,axiom,
% 5.52/5.82 ! [I: nat,N: nat,X2: nat] :
% 5.52/5.82 ( ( ord_less_nat @ I @ N )
% 5.52/5.82 => ( ( nth_nat @ ( replicate_nat @ N @ X2 ) @ I )
% 5.52/5.82 = X2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % nth_replicate
% 5.52/5.82 thf(fact_4687_nth__replicate,axiom,
% 5.52/5.82 ! [I: nat,N: nat,X2: vEBT_VEBT] :
% 5.52/5.82 ( ( ord_less_nat @ I @ N )
% 5.52/5.82 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) @ I )
% 5.52/5.82 = X2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % nth_replicate
% 5.52/5.82 thf(fact_4688_dbl__simps_I1_J,axiom,
% 5.52/5.82 ! [K: num] :
% 5.52/5.82 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_simps(1)
% 5.52/5.82 thf(fact_4689_dbl__simps_I1_J,axiom,
% 5.52/5.82 ! [K: num] :
% 5.52/5.82 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.52/5.82 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_simps(1)
% 5.52/5.82 thf(fact_4690_dbl__simps_I1_J,axiom,
% 5.52/5.82 ! [K: num] :
% 5.52/5.82 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_simps(1)
% 5.52/5.82 thf(fact_4691_dbl__simps_I1_J,axiom,
% 5.52/5.82 ! [K: num] :
% 5.52/5.82 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_simps(1)
% 5.52/5.82 thf(fact_4692_dbl__simps_I1_J,axiom,
% 5.52/5.82 ! [K: num] :
% 5.52/5.82 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.52/5.82 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_simps(1)
% 5.52/5.82 thf(fact_4693_dbl__inc__simps_I4_J,axiom,
% 5.52/5.82 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.82 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_inc_simps(4)
% 5.52/5.82 thf(fact_4694_dbl__inc__simps_I4_J,axiom,
% 5.52/5.82 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.82 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_inc_simps(4)
% 5.52/5.82 thf(fact_4695_dbl__inc__simps_I4_J,axiom,
% 5.52/5.82 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_inc_simps(4)
% 5.52/5.82 thf(fact_4696_dbl__inc__simps_I4_J,axiom,
% 5.52/5.82 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_inc_simps(4)
% 5.52/5.82 thf(fact_4697_dbl__inc__simps_I4_J,axiom,
% 5.52/5.82 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.82 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_inc_simps(4)
% 5.52/5.82 thf(fact_4698_add__neg__numeral__special_I8_J,axiom,
% 5.52/5.82 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.52/5.82 = zero_zero_int ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(8)
% 5.52/5.82 thf(fact_4699_add__neg__numeral__special_I8_J,axiom,
% 5.52/5.82 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.52/5.82 = zero_zero_real ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(8)
% 5.52/5.82 thf(fact_4700_add__neg__numeral__special_I8_J,axiom,
% 5.52/5.82 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.52/5.82 = zero_zero_complex ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(8)
% 5.52/5.82 thf(fact_4701_add__neg__numeral__special_I8_J,axiom,
% 5.52/5.82 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.52/5.82 = zero_z3403309356797280102nteger ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(8)
% 5.52/5.82 thf(fact_4702_add__neg__numeral__special_I8_J,axiom,
% 5.52/5.82 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.52/5.82 = zero_zero_rat ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(8)
% 5.52/5.82 thf(fact_4703_add__neg__numeral__special_I7_J,axiom,
% 5.52/5.82 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.82 = zero_zero_int ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(7)
% 5.52/5.82 thf(fact_4704_add__neg__numeral__special_I7_J,axiom,
% 5.52/5.82 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.82 = zero_zero_real ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(7)
% 5.52/5.82 thf(fact_4705_add__neg__numeral__special_I7_J,axiom,
% 5.52/5.82 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.82 = zero_zero_complex ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(7)
% 5.52/5.82 thf(fact_4706_add__neg__numeral__special_I7_J,axiom,
% 5.52/5.82 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.82 = zero_z3403309356797280102nteger ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(7)
% 5.52/5.82 thf(fact_4707_add__neg__numeral__special_I7_J,axiom,
% 5.52/5.82 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.82 = zero_zero_rat ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(7)
% 5.52/5.82 thf(fact_4708_diff__numeral__special_I12_J,axiom,
% 5.52/5.82 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.82 = zero_zero_int ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(12)
% 5.52/5.82 thf(fact_4709_diff__numeral__special_I12_J,axiom,
% 5.52/5.82 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.82 = zero_zero_real ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(12)
% 5.52/5.82 thf(fact_4710_diff__numeral__special_I12_J,axiom,
% 5.52/5.82 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.82 = zero_zero_complex ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(12)
% 5.52/5.82 thf(fact_4711_diff__numeral__special_I12_J,axiom,
% 5.52/5.82 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.82 = zero_z3403309356797280102nteger ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(12)
% 5.52/5.82 thf(fact_4712_diff__numeral__special_I12_J,axiom,
% 5.52/5.82 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.82 = zero_zero_rat ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(12)
% 5.52/5.82 thf(fact_4713_neg__one__eq__numeral__iff,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( ( uminus_uminus_int @ one_one_int )
% 5.52/5.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.82 = ( N = one ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_eq_numeral_iff
% 5.52/5.82 thf(fact_4714_neg__one__eq__numeral__iff,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( ( uminus_uminus_real @ one_one_real )
% 5.52/5.82 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.82 = ( N = one ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_eq_numeral_iff
% 5.52/5.82 thf(fact_4715_neg__one__eq__numeral__iff,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.52/5.82 = ( N = one ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_eq_numeral_iff
% 5.52/5.82 thf(fact_4716_neg__one__eq__numeral__iff,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.52/5.82 = ( N = one ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_eq_numeral_iff
% 5.52/5.82 thf(fact_4717_neg__one__eq__numeral__iff,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.52/5.82 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.52/5.82 = ( N = one ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_eq_numeral_iff
% 5.52/5.82 thf(fact_4718_numeral__eq__neg__one__iff,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 5.52/5.82 = ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.82 = ( N = one ) ) ).
% 5.52/5.82
% 5.52/5.82 % numeral_eq_neg_one_iff
% 5.52/5.82 thf(fact_4719_numeral__eq__neg__one__iff,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 5.52/5.82 = ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.82 = ( N = one ) ) ).
% 5.52/5.82
% 5.52/5.82 % numeral_eq_neg_one_iff
% 5.52/5.82 thf(fact_4720_numeral__eq__neg__one__iff,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.82 = ( N = one ) ) ).
% 5.52/5.82
% 5.52/5.82 % numeral_eq_neg_one_iff
% 5.52/5.82 thf(fact_4721_numeral__eq__neg__one__iff,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.82 = ( N = one ) ) ).
% 5.52/5.82
% 5.52/5.82 % numeral_eq_neg_one_iff
% 5.52/5.82 thf(fact_4722_numeral__eq__neg__one__iff,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 5.52/5.82 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.82 = ( N = one ) ) ).
% 5.52/5.82
% 5.52/5.82 % numeral_eq_neg_one_iff
% 5.52/5.82 thf(fact_4723_minus__one__mult__self,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 5.52/5.82 = one_one_int ) ).
% 5.52/5.82
% 5.52/5.82 % minus_one_mult_self
% 5.52/5.82 thf(fact_4724_minus__one__mult__self,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 5.52/5.82 = one_one_real ) ).
% 5.52/5.82
% 5.52/5.82 % minus_one_mult_self
% 5.52/5.82 thf(fact_4725_minus__one__mult__self,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 5.52/5.82 = one_one_complex ) ).
% 5.52/5.82
% 5.52/5.82 % minus_one_mult_self
% 5.52/5.82 thf(fact_4726_minus__one__mult__self,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 5.52/5.82 = one_one_Code_integer ) ).
% 5.52/5.82
% 5.52/5.82 % minus_one_mult_self
% 5.52/5.82 thf(fact_4727_minus__one__mult__self,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 5.52/5.82 = one_one_rat ) ).
% 5.52/5.82
% 5.52/5.82 % minus_one_mult_self
% 5.52/5.82 thf(fact_4728_left__minus__one__mult__self,axiom,
% 5.52/5.82 ! [N: nat,A: int] :
% 5.52/5.82 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 5.52/5.82 = A ) ).
% 5.52/5.82
% 5.52/5.82 % left_minus_one_mult_self
% 5.52/5.82 thf(fact_4729_left__minus__one__mult__self,axiom,
% 5.52/5.82 ! [N: nat,A: real] :
% 5.52/5.82 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 5.52/5.82 = A ) ).
% 5.52/5.82
% 5.52/5.82 % left_minus_one_mult_self
% 5.52/5.82 thf(fact_4730_left__minus__one__mult__self,axiom,
% 5.52/5.82 ! [N: nat,A: complex] :
% 5.52/5.82 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 5.52/5.82 = A ) ).
% 5.52/5.82
% 5.52/5.82 % left_minus_one_mult_self
% 5.52/5.82 thf(fact_4731_left__minus__one__mult__self,axiom,
% 5.52/5.82 ! [N: nat,A: code_integer] :
% 5.52/5.82 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 5.52/5.82 = A ) ).
% 5.52/5.82
% 5.52/5.82 % left_minus_one_mult_self
% 5.52/5.82 thf(fact_4732_left__minus__one__mult__self,axiom,
% 5.52/5.82 ! [N: nat,A: rat] :
% 5.52/5.82 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 5.52/5.82 = A ) ).
% 5.52/5.82
% 5.52/5.82 % left_minus_one_mult_self
% 5.52/5.82 thf(fact_4733_mod__minus1__right,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.82 = zero_zero_int ) ).
% 5.52/5.82
% 5.52/5.82 % mod_minus1_right
% 5.52/5.82 thf(fact_4734_mod__minus1__right,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.82 = zero_z3403309356797280102nteger ) ).
% 5.52/5.82
% 5.52/5.82 % mod_minus1_right
% 5.52/5.82 thf(fact_4735_max__number__of_I4_J,axiom,
% 5.52/5.82 ! [U: num,V: num] :
% 5.52/5.82 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.82 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.82 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.52/5.82 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.82 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.82 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_number_of(4)
% 5.52/5.82 thf(fact_4736_max__number__of_I4_J,axiom,
% 5.52/5.82 ! [U: num,V: num] :
% 5.52/5.82 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.52/5.82 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.52/5.82 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.52/5.82 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_number_of(4)
% 5.52/5.82 thf(fact_4737_max__number__of_I4_J,axiom,
% 5.52/5.82 ! [U: num,V: num] :
% 5.52/5.82 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.82 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.82 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.52/5.82 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.82 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.82 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_number_of(4)
% 5.52/5.82 thf(fact_4738_max__number__of_I4_J,axiom,
% 5.52/5.82 ! [U: num,V: num] :
% 5.52/5.82 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.82 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.52/5.82 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.82 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_number_of(4)
% 5.52/5.82 thf(fact_4739_max__number__of_I3_J,axiom,
% 5.52/5.82 ! [U: num,V: num] :
% 5.52/5.82 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.52/5.82 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.52/5.82 = ( numeral_numeral_real @ V ) ) )
% 5.52/5.82 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.52/5.82 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.52/5.82 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_number_of(3)
% 5.52/5.82 thf(fact_4740_max__number__of_I3_J,axiom,
% 5.52/5.82 ! [U: num,V: num] :
% 5.52/5.82 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.52/5.82 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.52/5.82 = ( numera6620942414471956472nteger @ V ) ) )
% 5.52/5.82 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.52/5.82 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_number_of(3)
% 5.52/5.82 thf(fact_4741_max__number__of_I3_J,axiom,
% 5.52/5.82 ! [U: num,V: num] :
% 5.52/5.82 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.52/5.82 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.52/5.82 = ( numeral_numeral_rat @ V ) ) )
% 5.52/5.82 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.52/5.82 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.52/5.82 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_number_of(3)
% 5.52/5.82 thf(fact_4742_max__number__of_I3_J,axiom,
% 5.52/5.82 ! [U: num,V: num] :
% 5.52/5.82 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.82 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.82 = ( numeral_numeral_int @ V ) ) )
% 5.52/5.82 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.82 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_number_of(3)
% 5.52/5.82 thf(fact_4743_max__number__of_I2_J,axiom,
% 5.52/5.82 ! [U: num,V: num] :
% 5.52/5.82 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.82 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.82 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.52/5.82 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.82 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.82 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_number_of(2)
% 5.52/5.82 thf(fact_4744_max__number__of_I2_J,axiom,
% 5.52/5.82 ! [U: num,V: num] :
% 5.52/5.82 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.52/5.82 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.52/5.82 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.52/5.82 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.52/5.82 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_number_of(2)
% 5.52/5.82 thf(fact_4745_max__number__of_I2_J,axiom,
% 5.52/5.82 ! [U: num,V: num] :
% 5.52/5.82 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.82 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.82 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.52/5.82 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.82 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.82 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_number_of(2)
% 5.52/5.82 thf(fact_4746_max__number__of_I2_J,axiom,
% 5.52/5.82 ! [U: num,V: num] :
% 5.52/5.82 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.82 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.52/5.82 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.82 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.82 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_number_of(2)
% 5.52/5.82 thf(fact_4747_semiring__norm_I168_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: int] :
% 5.52/5.82 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(168)
% 5.52/5.82 thf(fact_4748_semiring__norm_I168_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: real] :
% 5.52/5.82 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(168)
% 5.52/5.82 thf(fact_4749_semiring__norm_I168_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: complex] :
% 5.52/5.82 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(168)
% 5.52/5.82 thf(fact_4750_semiring__norm_I168_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: code_integer] :
% 5.52/5.82 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(168)
% 5.52/5.82 thf(fact_4751_semiring__norm_I168_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: rat] :
% 5.52/5.82 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(168)
% 5.52/5.82 thf(fact_4752_diff__numeral__simps_I2_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.82 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_simps(2)
% 5.52/5.82 thf(fact_4753_diff__numeral__simps_I2_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.82 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_simps(2)
% 5.52/5.82 thf(fact_4754_diff__numeral__simps_I2_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.52/5.82 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_simps(2)
% 5.52/5.82 thf(fact_4755_diff__numeral__simps_I2_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.52/5.82 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_simps(2)
% 5.52/5.82 thf(fact_4756_diff__numeral__simps_I2_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.52/5.82 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_simps(2)
% 5.52/5.82 thf(fact_4757_diff__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_simps(3)
% 5.52/5.82 thf(fact_4758_diff__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.52/5.82 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_simps(3)
% 5.52/5.82 thf(fact_4759_diff__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_simps(3)
% 5.52/5.82 thf(fact_4760_diff__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_simps(3)
% 5.52/5.82 thf(fact_4761_diff__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.52/5.82 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_simps(3)
% 5.52/5.82 thf(fact_4762_semiring__norm_I172_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: int] :
% 5.52/5.82 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(172)
% 5.52/5.82 thf(fact_4763_semiring__norm_I172_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: real] :
% 5.52/5.82 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(172)
% 5.52/5.82 thf(fact_4764_semiring__norm_I172_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: complex] :
% 5.52/5.82 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(172)
% 5.52/5.82 thf(fact_4765_semiring__norm_I172_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: code_integer] :
% 5.52/5.82 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(172)
% 5.52/5.82 thf(fact_4766_semiring__norm_I172_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: rat] :
% 5.52/5.82 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(172)
% 5.52/5.82 thf(fact_4767_semiring__norm_I171_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: int] :
% 5.52/5.82 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(171)
% 5.52/5.82 thf(fact_4768_semiring__norm_I171_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: real] :
% 5.52/5.82 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(171)
% 5.52/5.82 thf(fact_4769_semiring__norm_I171_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: complex] :
% 5.52/5.82 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(171)
% 5.52/5.82 thf(fact_4770_semiring__norm_I171_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: code_integer] :
% 5.52/5.82 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(171)
% 5.52/5.82 thf(fact_4771_semiring__norm_I171_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: rat] :
% 5.52/5.82 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 5.52/5.82 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(171)
% 5.52/5.82 thf(fact_4772_semiring__norm_I170_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: int] :
% 5.52/5.82 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y2 ) )
% 5.52/5.82 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(170)
% 5.52/5.82 thf(fact_4773_semiring__norm_I170_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: real] :
% 5.52/5.82 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y2 ) )
% 5.52/5.82 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(170)
% 5.52/5.82 thf(fact_4774_semiring__norm_I170_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: complex] :
% 5.52/5.82 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y2 ) )
% 5.52/5.82 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(170)
% 5.52/5.82 thf(fact_4775_semiring__norm_I170_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: code_integer] :
% 5.52/5.82 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y2 ) )
% 5.52/5.82 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(170)
% 5.52/5.82 thf(fact_4776_semiring__norm_I170_J,axiom,
% 5.52/5.82 ! [V: num,W: num,Y2: rat] :
% 5.52/5.82 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y2 ) )
% 5.52/5.82 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % semiring_norm(170)
% 5.52/5.82 thf(fact_4777_mult__neg__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(3)
% 5.52/5.82 thf(fact_4778_mult__neg__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.82 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(3)
% 5.52/5.82 thf(fact_4779_mult__neg__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(3)
% 5.52/5.82 thf(fact_4780_mult__neg__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(3)
% 5.52/5.82 thf(fact_4781_mult__neg__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.52/5.82 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(3)
% 5.52/5.82 thf(fact_4782_mult__neg__numeral__simps_I2_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(2)
% 5.52/5.82 thf(fact_4783_mult__neg__numeral__simps_I2_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.52/5.82 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(2)
% 5.52/5.82 thf(fact_4784_mult__neg__numeral__simps_I2_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(2)
% 5.52/5.82 thf(fact_4785_mult__neg__numeral__simps_I2_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(2)
% 5.52/5.82 thf(fact_4786_mult__neg__numeral__simps_I2_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.52/5.82 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(2)
% 5.52/5.82 thf(fact_4787_mult__neg__numeral__simps_I1_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.82 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(1)
% 5.52/5.82 thf(fact_4788_mult__neg__numeral__simps_I1_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.82 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(1)
% 5.52/5.82 thf(fact_4789_mult__neg__numeral__simps_I1_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.52/5.82 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(1)
% 5.52/5.82 thf(fact_4790_mult__neg__numeral__simps_I1_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.52/5.82 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(1)
% 5.52/5.82 thf(fact_4791_mult__neg__numeral__simps_I1_J,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.52/5.82 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mult_neg_numeral_simps(1)
% 5.52/5.82 thf(fact_4792_less__Suc__numeral,axiom,
% 5.52/5.82 ! [N: nat,K: num] :
% 5.52/5.82 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.52/5.82 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_Suc_numeral
% 5.52/5.82 thf(fact_4793_less__numeral__Suc,axiom,
% 5.52/5.82 ! [K: num,N: nat] :
% 5.52/5.82 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.52/5.82 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_numeral_Suc
% 5.52/5.82 thf(fact_4794_pred__numeral__simps_I3_J,axiom,
% 5.52/5.82 ! [K: num] :
% 5.52/5.82 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.52/5.82 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % pred_numeral_simps(3)
% 5.52/5.82 thf(fact_4795_le__Suc__numeral,axiom,
% 5.52/5.82 ! [N: nat,K: num] :
% 5.52/5.82 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.52/5.82 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_Suc_numeral
% 5.52/5.82 thf(fact_4796_le__numeral__Suc,axiom,
% 5.52/5.82 ! [K: num,N: nat] :
% 5.52/5.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.52/5.82 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_numeral_Suc
% 5.52/5.82 thf(fact_4797_neg__numeral__le__iff,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.82 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_le_iff
% 5.52/5.82 thf(fact_4798_neg__numeral__le__iff,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.52/5.82 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_le_iff
% 5.52/5.82 thf(fact_4799_neg__numeral__le__iff,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.52/5.82 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_le_iff
% 5.52/5.82 thf(fact_4800_neg__numeral__le__iff,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.82 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_le_iff
% 5.52/5.82 thf(fact_4801_diff__numeral__Suc,axiom,
% 5.52/5.82 ! [K: num,N: nat] :
% 5.52/5.82 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.52/5.82 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_Suc
% 5.52/5.82 thf(fact_4802_diff__Suc__numeral,axiom,
% 5.52/5.82 ! [N: nat,K: num] :
% 5.52/5.82 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.52/5.82 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_Suc_numeral
% 5.52/5.82 thf(fact_4803_neg__numeral__less__iff,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.82 = ( ord_less_num @ N @ M ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_less_iff
% 5.52/5.82 thf(fact_4804_neg__numeral__less__iff,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.82 = ( ord_less_num @ N @ M ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_less_iff
% 5.52/5.82 thf(fact_4805_neg__numeral__less__iff,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.52/5.82 = ( ord_less_num @ N @ M ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_less_iff
% 5.52/5.82 thf(fact_4806_neg__numeral__less__iff,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.52/5.82 = ( ord_less_num @ N @ M ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_less_iff
% 5.52/5.82 thf(fact_4807_max__Suc__numeral,axiom,
% 5.52/5.82 ! [N: nat,K: num] :
% 5.52/5.82 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.52/5.82 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_Suc_numeral
% 5.52/5.82 thf(fact_4808_max__numeral__Suc,axiom,
% 5.52/5.82 ! [K: num,N: nat] :
% 5.52/5.82 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.52/5.82 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % max_numeral_Suc
% 5.52/5.82 thf(fact_4809_pred__numeral__simps_I2_J,axiom,
% 5.52/5.82 ! [K: num] :
% 5.52/5.82 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.52/5.82 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % pred_numeral_simps(2)
% 5.52/5.82 thf(fact_4810_not__neg__one__le__neg__numeral__iff,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.52/5.82 = ( M != one ) ) ).
% 5.52/5.82
% 5.52/5.82 % not_neg_one_le_neg_numeral_iff
% 5.52/5.82 thf(fact_4811_not__neg__one__le__neg__numeral__iff,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.52/5.82 = ( M != one ) ) ).
% 5.52/5.82
% 5.52/5.82 % not_neg_one_le_neg_numeral_iff
% 5.52/5.82 thf(fact_4812_not__neg__one__le__neg__numeral__iff,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.52/5.82 = ( M != one ) ) ).
% 5.52/5.82
% 5.52/5.82 % not_neg_one_le_neg_numeral_iff
% 5.52/5.82 thf(fact_4813_not__neg__one__le__neg__numeral__iff,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.52/5.82 = ( M != one ) ) ).
% 5.52/5.82
% 5.52/5.82 % not_neg_one_le_neg_numeral_iff
% 5.52/5.82 thf(fact_4814_neg__numeral__less__neg__one__iff,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.82 = ( M != one ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_less_neg_one_iff
% 5.52/5.82 thf(fact_4815_neg__numeral__less__neg__one__iff,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.82 = ( M != one ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_less_neg_one_iff
% 5.52/5.82 thf(fact_4816_neg__numeral__less__neg__one__iff,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.82 = ( M != one ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_less_neg_one_iff
% 5.52/5.82 thf(fact_4817_neg__numeral__less__neg__one__iff,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.82 = ( M != one ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_less_neg_one_iff
% 5.52/5.82 thf(fact_4818_divide__le__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [B: real,W: num,A: real] :
% 5.52/5.82 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.52/5.82 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % divide_le_eq_numeral1(2)
% 5.52/5.82 thf(fact_4819_divide__le__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [B: rat,W: num,A: rat] :
% 5.52/5.82 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.52/5.82 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % divide_le_eq_numeral1(2)
% 5.52/5.82 thf(fact_4820_le__divide__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [A: real,B: real,W: num] :
% 5.52/5.82 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.52/5.82 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_divide_eq_numeral1(2)
% 5.52/5.82 thf(fact_4821_le__divide__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [A: rat,B: rat,W: num] :
% 5.52/5.82 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.52/5.82 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_divide_eq_numeral1(2)
% 5.52/5.82 thf(fact_4822_divide__eq__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [B: real,W: num,A: real] :
% 5.52/5.82 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.52/5.82 = A )
% 5.52/5.82 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.52/5.82 != zero_zero_real )
% 5.52/5.82 => ( B
% 5.52/5.82 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.52/5.82 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.52/5.82 = zero_zero_real )
% 5.52/5.82 => ( A = zero_zero_real ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % divide_eq_eq_numeral1(2)
% 5.52/5.82 thf(fact_4823_divide__eq__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [B: complex,W: num,A: complex] :
% 5.52/5.82 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.52/5.82 = A )
% 5.52/5.82 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.52/5.82 != zero_zero_complex )
% 5.52/5.82 => ( B
% 5.52/5.82 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.52/5.82 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.52/5.82 = zero_zero_complex )
% 5.52/5.82 => ( A = zero_zero_complex ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % divide_eq_eq_numeral1(2)
% 5.52/5.82 thf(fact_4824_divide__eq__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [B: rat,W: num,A: rat] :
% 5.52/5.82 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.52/5.82 = A )
% 5.52/5.82 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.52/5.82 != zero_zero_rat )
% 5.52/5.82 => ( B
% 5.52/5.82 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.52/5.82 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.52/5.82 = zero_zero_rat )
% 5.52/5.82 => ( A = zero_zero_rat ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % divide_eq_eq_numeral1(2)
% 5.52/5.82 thf(fact_4825_eq__divide__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [A: real,B: real,W: num] :
% 5.52/5.82 ( ( A
% 5.52/5.82 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.52/5.82 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.52/5.82 != zero_zero_real )
% 5.52/5.82 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.52/5.82 = B ) )
% 5.52/5.82 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.52/5.82 = zero_zero_real )
% 5.52/5.82 => ( A = zero_zero_real ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % eq_divide_eq_numeral1(2)
% 5.52/5.82 thf(fact_4826_eq__divide__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [A: complex,B: complex,W: num] :
% 5.52/5.82 ( ( A
% 5.52/5.82 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.52/5.82 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.52/5.82 != zero_zero_complex )
% 5.52/5.82 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.52/5.82 = B ) )
% 5.52/5.82 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.52/5.82 = zero_zero_complex )
% 5.52/5.82 => ( A = zero_zero_complex ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % eq_divide_eq_numeral1(2)
% 5.52/5.82 thf(fact_4827_eq__divide__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [A: rat,B: rat,W: num] :
% 5.52/5.82 ( ( A
% 5.52/5.82 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.52/5.82 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.52/5.82 != zero_zero_rat )
% 5.52/5.82 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.52/5.82 = B ) )
% 5.52/5.82 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.52/5.82 = zero_zero_rat )
% 5.52/5.82 => ( A = zero_zero_rat ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % eq_divide_eq_numeral1(2)
% 5.52/5.82 thf(fact_4828_divide__less__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [B: real,W: num,A: real] :
% 5.52/5.82 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.52/5.82 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % divide_less_eq_numeral1(2)
% 5.52/5.82 thf(fact_4829_divide__less__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [B: rat,W: num,A: rat] :
% 5.52/5.82 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.52/5.82 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % divide_less_eq_numeral1(2)
% 5.52/5.82 thf(fact_4830_less__divide__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [A: real,B: real,W: num] :
% 5.52/5.82 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.52/5.82 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_divide_eq_numeral1(2)
% 5.52/5.82 thf(fact_4831_less__divide__eq__numeral1_I2_J,axiom,
% 5.52/5.82 ! [A: rat,B: rat,W: num] :
% 5.52/5.82 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.52/5.82 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_divide_eq_numeral1(2)
% 5.52/5.82 thf(fact_4832_power2__minus,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.82 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % power2_minus
% 5.52/5.82 thf(fact_4833_power2__minus,axiom,
% 5.52/5.82 ! [A: real] :
% 5.52/5.82 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.82 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % power2_minus
% 5.52/5.82 thf(fact_4834_power2__minus,axiom,
% 5.52/5.82 ! [A: complex] :
% 5.52/5.82 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.82 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % power2_minus
% 5.52/5.82 thf(fact_4835_power2__minus,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.82 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % power2_minus
% 5.52/5.82 thf(fact_4836_power2__minus,axiom,
% 5.52/5.82 ! [A: rat] :
% 5.52/5.82 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.82 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % power2_minus
% 5.52/5.82 thf(fact_4837_odd__of__bool__self,axiom,
% 5.52/5.82 ! [P6: $o] :
% 5.52/5.82 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P6 ) ) )
% 5.52/5.82 = P6 ) ).
% 5.52/5.82
% 5.52/5.82 % odd_of_bool_self
% 5.52/5.82 thf(fact_4838_odd__of__bool__self,axiom,
% 5.52/5.82 ! [P6: $o] :
% 5.52/5.82 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P6 ) ) )
% 5.52/5.82 = P6 ) ).
% 5.52/5.82
% 5.52/5.82 % odd_of_bool_self
% 5.52/5.82 thf(fact_4839_odd__of__bool__self,axiom,
% 5.52/5.82 ! [P6: $o] :
% 5.52/5.82 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P6 ) ) )
% 5.52/5.82 = P6 ) ).
% 5.52/5.82
% 5.52/5.82 % odd_of_bool_self
% 5.52/5.82 thf(fact_4840_add__neg__numeral__special_I9_J,axiom,
% 5.52/5.82 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(9)
% 5.52/5.82 thf(fact_4841_add__neg__numeral__special_I9_J,axiom,
% 5.52/5.82 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.82 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(9)
% 5.52/5.82 thf(fact_4842_add__neg__numeral__special_I9_J,axiom,
% 5.52/5.82 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(9)
% 5.52/5.82 thf(fact_4843_add__neg__numeral__special_I9_J,axiom,
% 5.52/5.82 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(9)
% 5.52/5.82 thf(fact_4844_add__neg__numeral__special_I9_J,axiom,
% 5.52/5.82 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.82 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add_neg_numeral_special(9)
% 5.52/5.82 thf(fact_4845_diff__numeral__special_I11_J,axiom,
% 5.52/5.82 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.82 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(11)
% 5.52/5.82 thf(fact_4846_diff__numeral__special_I11_J,axiom,
% 5.52/5.82 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.82 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(11)
% 5.52/5.82 thf(fact_4847_diff__numeral__special_I11_J,axiom,
% 5.52/5.82 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.82 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(11)
% 5.52/5.82 thf(fact_4848_diff__numeral__special_I11_J,axiom,
% 5.52/5.82 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.82 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(11)
% 5.52/5.82 thf(fact_4849_diff__numeral__special_I11_J,axiom,
% 5.52/5.82 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.82 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(11)
% 5.52/5.82 thf(fact_4850_diff__numeral__special_I10_J,axiom,
% 5.52/5.82 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.52/5.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(10)
% 5.52/5.82 thf(fact_4851_diff__numeral__special_I10_J,axiom,
% 5.52/5.82 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.52/5.82 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(10)
% 5.52/5.82 thf(fact_4852_diff__numeral__special_I10_J,axiom,
% 5.52/5.82 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(10)
% 5.52/5.82 thf(fact_4853_diff__numeral__special_I10_J,axiom,
% 5.52/5.82 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(10)
% 5.52/5.82 thf(fact_4854_diff__numeral__special_I10_J,axiom,
% 5.52/5.82 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.52/5.82 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(10)
% 5.52/5.82 thf(fact_4855_minus__1__div__2__eq,axiom,
% 5.52/5.82 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.82 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_1_div_2_eq
% 5.52/5.82 thf(fact_4856_minus__1__div__2__eq,axiom,
% 5.52/5.82 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_1_div_2_eq
% 5.52/5.82 thf(fact_4857_minus__1__mod__2__eq,axiom,
% 5.52/5.82 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.82 = one_one_int ) ).
% 5.52/5.82
% 5.52/5.82 % minus_1_mod_2_eq
% 5.52/5.82 thf(fact_4858_minus__1__mod__2__eq,axiom,
% 5.52/5.82 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.82 = one_one_Code_integer ) ).
% 5.52/5.82
% 5.52/5.82 % minus_1_mod_2_eq
% 5.52/5.82 thf(fact_4859_bits__minus__1__mod__2__eq,axiom,
% 5.52/5.82 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.82 = one_one_int ) ).
% 5.52/5.82
% 5.52/5.82 % bits_minus_1_mod_2_eq
% 5.52/5.82 thf(fact_4860_bits__minus__1__mod__2__eq,axiom,
% 5.52/5.82 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.82 = one_one_Code_integer ) ).
% 5.52/5.82
% 5.52/5.82 % bits_minus_1_mod_2_eq
% 5.52/5.82 thf(fact_4861_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.52/5.82 ! [A: int,N: nat] :
% 5.52/5.82 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % Power.ring_1_class.power_minus_even
% 5.52/5.82 thf(fact_4862_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.52/5.82 ! [A: real,N: nat] :
% 5.52/5.82 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % Power.ring_1_class.power_minus_even
% 5.52/5.82 thf(fact_4863_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.52/5.82 ! [A: complex,N: nat] :
% 5.52/5.82 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % Power.ring_1_class.power_minus_even
% 5.52/5.82 thf(fact_4864_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.52/5.82 ! [A: code_integer,N: nat] :
% 5.52/5.82 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % Power.ring_1_class.power_minus_even
% 5.52/5.82 thf(fact_4865_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.52/5.82 ! [A: rat,N: nat] :
% 5.52/5.82 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % Power.ring_1_class.power_minus_even
% 5.52/5.82 thf(fact_4866_of__bool__half__eq__0,axiom,
% 5.52/5.82 ! [B: $o] :
% 5.52/5.82 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.82 = zero_zero_nat ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_half_eq_0
% 5.52/5.82 thf(fact_4867_of__bool__half__eq__0,axiom,
% 5.52/5.82 ! [B: $o] :
% 5.52/5.82 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.82 = zero_zero_int ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_half_eq_0
% 5.52/5.82 thf(fact_4868_of__bool__half__eq__0,axiom,
% 5.52/5.82 ! [B: $o] :
% 5.52/5.82 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.82 = zero_z3403309356797280102nteger ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_half_eq_0
% 5.52/5.82 thf(fact_4869_power__minus__odd,axiom,
% 5.52/5.82 ! [N: nat,A: int] :
% 5.52/5.82 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.52/5.82 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % power_minus_odd
% 5.52/5.82 thf(fact_4870_power__minus__odd,axiom,
% 5.52/5.82 ! [N: nat,A: real] :
% 5.52/5.82 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.52/5.82 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % power_minus_odd
% 5.52/5.82 thf(fact_4871_power__minus__odd,axiom,
% 5.52/5.82 ! [N: nat,A: complex] :
% 5.52/5.82 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % power_minus_odd
% 5.52/5.82 thf(fact_4872_power__minus__odd,axiom,
% 5.52/5.82 ! [N: nat,A: code_integer] :
% 5.52/5.82 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % power_minus_odd
% 5.52/5.82 thf(fact_4873_power__minus__odd,axiom,
% 5.52/5.82 ! [N: nat,A: rat] :
% 5.52/5.82 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.52/5.82 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % power_minus_odd
% 5.52/5.82 thf(fact_4874_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.52/5.82 ! [N: nat,A: int] :
% 5.52/5.82 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.52/5.82 = ( power_power_int @ A @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % Parity.ring_1_class.power_minus_even
% 5.52/5.82 thf(fact_4875_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.52/5.82 ! [N: nat,A: real] :
% 5.52/5.82 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.52/5.82 = ( power_power_real @ A @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % Parity.ring_1_class.power_minus_even
% 5.52/5.82 thf(fact_4876_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.52/5.82 ! [N: nat,A: complex] :
% 5.52/5.82 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.52/5.82 = ( power_power_complex @ A @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % Parity.ring_1_class.power_minus_even
% 5.52/5.82 thf(fact_4877_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.52/5.82 ! [N: nat,A: code_integer] :
% 5.52/5.82 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.52/5.82 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % Parity.ring_1_class.power_minus_even
% 5.52/5.82 thf(fact_4878_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.52/5.82 ! [N: nat,A: rat] :
% 5.52/5.82 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.52/5.82 = ( power_power_rat @ A @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % Parity.ring_1_class.power_minus_even
% 5.52/5.82 thf(fact_4879_diff__numeral__special_I4_J,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.52/5.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(4)
% 5.52/5.82 thf(fact_4880_diff__numeral__special_I4_J,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.52/5.82 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(4)
% 5.52/5.82 thf(fact_4881_diff__numeral__special_I4_J,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(4)
% 5.52/5.82 thf(fact_4882_diff__numeral__special_I4_J,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(4)
% 5.52/5.82 thf(fact_4883_diff__numeral__special_I4_J,axiom,
% 5.52/5.82 ! [M: num] :
% 5.52/5.82 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.52/5.82 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(4)
% 5.52/5.82 thf(fact_4884_diff__numeral__special_I3_J,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.82 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(3)
% 5.52/5.82 thf(fact_4885_diff__numeral__special_I3_J,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.82 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(3)
% 5.52/5.82 thf(fact_4886_diff__numeral__special_I3_J,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.52/5.82 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(3)
% 5.52/5.82 thf(fact_4887_diff__numeral__special_I3_J,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.52/5.82 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(3)
% 5.52/5.82 thf(fact_4888_diff__numeral__special_I3_J,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.52/5.82 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % diff_numeral_special(3)
% 5.52/5.82 thf(fact_4889_set__decode__0,axiom,
% 5.52/5.82 ! [X2: nat] :
% 5.52/5.82 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X2 ) )
% 5.52/5.82 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % set_decode_0
% 5.52/5.82 thf(fact_4890_dbl__simps_I4_J,axiom,
% 5.52/5.82 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_simps(4)
% 5.52/5.82 thf(fact_4891_dbl__simps_I4_J,axiom,
% 5.52/5.82 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.82 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_simps(4)
% 5.52/5.82 thf(fact_4892_dbl__simps_I4_J,axiom,
% 5.52/5.82 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_simps(4)
% 5.52/5.82 thf(fact_4893_dbl__simps_I4_J,axiom,
% 5.52/5.82 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_simps(4)
% 5.52/5.82 thf(fact_4894_dbl__simps_I4_J,axiom,
% 5.52/5.82 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.82 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % dbl_simps(4)
% 5.52/5.82 thf(fact_4895_power__minus1__even,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = one_one_int ) ).
% 5.52/5.82
% 5.52/5.82 % power_minus1_even
% 5.52/5.82 thf(fact_4896_power__minus1__even,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = one_one_real ) ).
% 5.52/5.82
% 5.52/5.82 % power_minus1_even
% 5.52/5.82 thf(fact_4897_power__minus1__even,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = one_one_complex ) ).
% 5.52/5.82
% 5.52/5.82 % power_minus1_even
% 5.52/5.82 thf(fact_4898_power__minus1__even,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = one_one_Code_integer ) ).
% 5.52/5.82
% 5.52/5.82 % power_minus1_even
% 5.52/5.82 thf(fact_4899_power__minus1__even,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = one_one_rat ) ).
% 5.52/5.82
% 5.52/5.82 % power_minus1_even
% 5.52/5.82 thf(fact_4900_neg__one__odd__power,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.52/5.82 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_odd_power
% 5.52/5.82 thf(fact_4901_neg__one__odd__power,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.52/5.82 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_odd_power
% 5.52/5.82 thf(fact_4902_neg__one__odd__power,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_odd_power
% 5.52/5.82 thf(fact_4903_neg__one__odd__power,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_odd_power
% 5.52/5.82 thf(fact_4904_neg__one__odd__power,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.52/5.82 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_odd_power
% 5.52/5.82 thf(fact_4905_neg__one__even__power,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.52/5.82 = one_one_int ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_even_power
% 5.52/5.82 thf(fact_4906_neg__one__even__power,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.52/5.82 = one_one_real ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_even_power
% 5.52/5.82 thf(fact_4907_neg__one__even__power,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.52/5.82 = one_one_complex ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_even_power
% 5.52/5.82 thf(fact_4908_neg__one__even__power,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.52/5.82 = one_one_Code_integer ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_even_power
% 5.52/5.82 thf(fact_4909_neg__one__even__power,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.82 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.52/5.82 = one_one_rat ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_one_even_power
% 5.52/5.82 thf(fact_4910_signed__take__bit__0,axiom,
% 5.52/5.82 ! [A: code_integer] :
% 5.52/5.82 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % signed_take_bit_0
% 5.52/5.82 thf(fact_4911_signed__take__bit__0,axiom,
% 5.52/5.82 ! [A: int] :
% 5.52/5.82 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.52/5.82 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % signed_take_bit_0
% 5.52/5.82 thf(fact_4912_signed__take__bit__Suc__minus__bit0,axiom,
% 5.52/5.82 ! [N: nat,K: num] :
% 5.52/5.82 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.52/5.82 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % signed_take_bit_Suc_minus_bit0
% 5.52/5.82 thf(fact_4913_signed__take__bit__numeral__bit0,axiom,
% 5.52/5.82 ! [L: num,K: num] :
% 5.52/5.82 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.52/5.82 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % signed_take_bit_numeral_bit0
% 5.52/5.82 thf(fact_4914_one__div__2__pow__eq,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % one_div_2_pow_eq
% 5.52/5.82 thf(fact_4915_one__div__2__pow__eq,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % one_div_2_pow_eq
% 5.52/5.82 thf(fact_4916_one__div__2__pow__eq,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % one_div_2_pow_eq
% 5.52/5.82 thf(fact_4917_bits__1__div__exp,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % bits_1_div_exp
% 5.52/5.82 thf(fact_4918_bits__1__div__exp,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % bits_1_div_exp
% 5.52/5.82 thf(fact_4919_bits__1__div__exp,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % bits_1_div_exp
% 5.52/5.82 thf(fact_4920_signed__take__bit__numeral__minus__bit0,axiom,
% 5.52/5.82 ! [L: num,K: num] :
% 5.52/5.82 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.52/5.82 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % signed_take_bit_numeral_minus_bit0
% 5.52/5.82 thf(fact_4921_one__mod__2__pow__eq,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % one_mod_2_pow_eq
% 5.52/5.82 thf(fact_4922_one__mod__2__pow__eq,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % one_mod_2_pow_eq
% 5.52/5.82 thf(fact_4923_one__mod__2__pow__eq,axiom,
% 5.52/5.82 ! [N: nat] :
% 5.52/5.82 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.82 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % one_mod_2_pow_eq
% 5.52/5.82 thf(fact_4924_signed__take__bit__numeral__minus__bit1,axiom,
% 5.52/5.82 ! [L: num,K: num] :
% 5.52/5.82 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.52/5.82 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.52/5.82
% 5.52/5.82 % signed_take_bit_numeral_minus_bit1
% 5.52/5.82 thf(fact_4925_signed__take__bit__minus,axiom,
% 5.52/5.82 ! [N: nat,K: int] :
% 5.52/5.82 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 5.52/5.82 = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % signed_take_bit_minus
% 5.52/5.82 thf(fact_4926_dvd__antisym,axiom,
% 5.52/5.82 ! [M: nat,N: nat] :
% 5.52/5.82 ( ( dvd_dvd_nat @ M @ N )
% 5.52/5.82 => ( ( dvd_dvd_nat @ N @ M )
% 5.52/5.82 => ( M = N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % dvd_antisym
% 5.52/5.82 thf(fact_4927_of__bool__eq__iff,axiom,
% 5.52/5.82 ! [P6: $o,Q2: $o] :
% 5.52/5.82 ( ( ( zero_n2687167440665602831ol_nat @ P6 )
% 5.52/5.82 = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 5.52/5.82 = ( P6 = Q2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_eq_iff
% 5.52/5.82 thf(fact_4928_of__bool__eq__iff,axiom,
% 5.52/5.82 ! [P6: $o,Q2: $o] :
% 5.52/5.82 ( ( ( zero_n2684676970156552555ol_int @ P6 )
% 5.52/5.82 = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 5.52/5.82 = ( P6 = Q2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_eq_iff
% 5.52/5.82 thf(fact_4929_of__bool__eq__iff,axiom,
% 5.52/5.82 ! [P6: $o,Q2: $o] :
% 5.52/5.82 ( ( ( zero_n356916108424825756nteger @ P6 )
% 5.52/5.82 = ( zero_n356916108424825756nteger @ Q2 ) )
% 5.52/5.82 = ( P6 = Q2 ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_eq_iff
% 5.52/5.82 thf(fact_4930_equation__minus__iff,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( A
% 5.52/5.82 = ( uminus_uminus_int @ B ) )
% 5.52/5.82 = ( B
% 5.52/5.82 = ( uminus_uminus_int @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % equation_minus_iff
% 5.52/5.82 thf(fact_4931_equation__minus__iff,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( A
% 5.52/5.82 = ( uminus_uminus_real @ B ) )
% 5.52/5.82 = ( B
% 5.52/5.82 = ( uminus_uminus_real @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % equation_minus_iff
% 5.52/5.82 thf(fact_4932_equation__minus__iff,axiom,
% 5.52/5.82 ! [A: complex,B: complex] :
% 5.52/5.82 ( ( A
% 5.52/5.82 = ( uminus1482373934393186551omplex @ B ) )
% 5.52/5.82 = ( B
% 5.52/5.82 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % equation_minus_iff
% 5.52/5.82 thf(fact_4933_equation__minus__iff,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( A
% 5.52/5.82 = ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.82 = ( B
% 5.52/5.82 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % equation_minus_iff
% 5.52/5.82 thf(fact_4934_equation__minus__iff,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( A
% 5.52/5.82 = ( uminus_uminus_rat @ B ) )
% 5.52/5.82 = ( B
% 5.52/5.82 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % equation_minus_iff
% 5.52/5.82 thf(fact_4935_minus__equation__iff,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( ( uminus_uminus_int @ A )
% 5.52/5.82 = B )
% 5.52/5.82 = ( ( uminus_uminus_int @ B )
% 5.52/5.82 = A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_equation_iff
% 5.52/5.82 thf(fact_4936_minus__equation__iff,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( ( uminus_uminus_real @ A )
% 5.52/5.82 = B )
% 5.52/5.82 = ( ( uminus_uminus_real @ B )
% 5.52/5.82 = A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_equation_iff
% 5.52/5.82 thf(fact_4937_minus__equation__iff,axiom,
% 5.52/5.82 ! [A: complex,B: complex] :
% 5.52/5.82 ( ( ( uminus1482373934393186551omplex @ A )
% 5.52/5.82 = B )
% 5.52/5.82 = ( ( uminus1482373934393186551omplex @ B )
% 5.52/5.82 = A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_equation_iff
% 5.52/5.82 thf(fact_4938_minus__equation__iff,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( ( uminus1351360451143612070nteger @ A )
% 5.52/5.82 = B )
% 5.52/5.82 = ( ( uminus1351360451143612070nteger @ B )
% 5.52/5.82 = A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_equation_iff
% 5.52/5.82 thf(fact_4939_minus__equation__iff,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( ( uminus_uminus_rat @ A )
% 5.52/5.82 = B )
% 5.52/5.82 = ( ( uminus_uminus_rat @ B )
% 5.52/5.82 = A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_equation_iff
% 5.52/5.82 thf(fact_4940_of__bool__conj,axiom,
% 5.52/5.82 ! [P: $o,Q: $o] :
% 5.52/5.82 ( ( zero_n3304061248610475627l_real
% 5.52/5.82 @ ( P
% 5.52/5.82 & Q ) )
% 5.52/5.82 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_conj
% 5.52/5.82 thf(fact_4941_of__bool__conj,axiom,
% 5.52/5.82 ! [P: $o,Q: $o] :
% 5.52/5.82 ( ( zero_n2052037380579107095ol_rat
% 5.52/5.82 @ ( P
% 5.52/5.82 & Q ) )
% 5.52/5.82 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_conj
% 5.52/5.82 thf(fact_4942_of__bool__conj,axiom,
% 5.52/5.82 ! [P: $o,Q: $o] :
% 5.52/5.82 ( ( zero_n2687167440665602831ol_nat
% 5.52/5.82 @ ( P
% 5.52/5.82 & Q ) )
% 5.52/5.82 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_conj
% 5.52/5.82 thf(fact_4943_of__bool__conj,axiom,
% 5.52/5.82 ! [P: $o,Q: $o] :
% 5.52/5.82 ( ( zero_n2684676970156552555ol_int
% 5.52/5.82 @ ( P
% 5.52/5.82 & Q ) )
% 5.52/5.82 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_conj
% 5.52/5.82 thf(fact_4944_of__bool__conj,axiom,
% 5.52/5.82 ! [P: $o,Q: $o] :
% 5.52/5.82 ( ( zero_n356916108424825756nteger
% 5.52/5.82 @ ( P
% 5.52/5.82 & Q ) )
% 5.52/5.82 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_conj
% 5.52/5.82 thf(fact_4945_mem__case__prodE,axiom,
% 5.52/5.82 ! [Z: real,C: num > num > set_real,P6: product_prod_num_num] :
% 5.52/5.82 ( ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P6 ) )
% 5.52/5.82 => ~ ! [X4: num,Y3: num] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_num_num @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( member_real @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mem_case_prodE
% 5.52/5.82 thf(fact_4946_mem__case__prodE,axiom,
% 5.52/5.82 ! [Z: nat,C: num > num > set_nat,P6: product_prod_num_num] :
% 5.52/5.82 ( ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P6 ) )
% 5.52/5.82 => ~ ! [X4: num,Y3: num] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_num_num @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( member_nat @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mem_case_prodE
% 5.52/5.82 thf(fact_4947_mem__case__prodE,axiom,
% 5.52/5.82 ! [Z: int,C: num > num > set_int,P6: product_prod_num_num] :
% 5.52/5.82 ( ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P6 ) )
% 5.52/5.82 => ~ ! [X4: num,Y3: num] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_num_num @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( member_int @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mem_case_prodE
% 5.52/5.82 thf(fact_4948_mem__case__prodE,axiom,
% 5.52/5.82 ! [Z: real,C: nat > num > set_real,P6: product_prod_nat_num] :
% 5.52/5.82 ( ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P6 ) )
% 5.52/5.82 => ~ ! [X4: nat,Y3: num] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_nat_num @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( member_real @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mem_case_prodE
% 5.52/5.82 thf(fact_4949_mem__case__prodE,axiom,
% 5.52/5.82 ! [Z: nat,C: nat > num > set_nat,P6: product_prod_nat_num] :
% 5.52/5.82 ( ( member_nat @ Z @ ( produc4130284055270567454et_nat @ C @ P6 ) )
% 5.52/5.82 => ~ ! [X4: nat,Y3: num] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_nat_num @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( member_nat @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mem_case_prodE
% 5.52/5.82 thf(fact_4950_mem__case__prodE,axiom,
% 5.52/5.82 ! [Z: int,C: nat > num > set_int,P6: product_prod_nat_num] :
% 5.52/5.82 ( ( member_int @ Z @ ( produc9175805072616146554et_int @ C @ P6 ) )
% 5.52/5.82 => ~ ! [X4: nat,Y3: num] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_nat_num @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( member_int @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mem_case_prodE
% 5.52/5.82 thf(fact_4951_mem__case__prodE,axiom,
% 5.52/5.82 ! [Z: real,C: nat > nat > set_real,P6: product_prod_nat_nat] :
% 5.52/5.82 ( ( member_real @ Z @ ( produc3668448655016342576t_real @ C @ P6 ) )
% 5.52/5.82 => ~ ! [X4: nat,Y3: nat] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_nat_nat @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( member_real @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mem_case_prodE
% 5.52/5.82 thf(fact_4952_mem__case__prodE,axiom,
% 5.52/5.82 ! [Z: nat,C: nat > nat > set_nat,P6: product_prod_nat_nat] :
% 5.52/5.82 ( ( member_nat @ Z @ ( produc6189476227299908564et_nat @ C @ P6 ) )
% 5.52/5.82 => ~ ! [X4: nat,Y3: nat] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_nat_nat @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( member_nat @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mem_case_prodE
% 5.52/5.82 thf(fact_4953_mem__case__prodE,axiom,
% 5.52/5.82 ! [Z: int,C: nat > nat > set_int,P6: product_prod_nat_nat] :
% 5.52/5.82 ( ( member_int @ Z @ ( produc2011625207790711856et_int @ C @ P6 ) )
% 5.52/5.82 => ~ ! [X4: nat,Y3: nat] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_nat_nat @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( member_int @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mem_case_prodE
% 5.52/5.82 thf(fact_4954_mem__case__prodE,axiom,
% 5.52/5.82 ! [Z: real,C: int > int > set_real,P6: product_prod_int_int] :
% 5.52/5.82 ( ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ P6 ) )
% 5.52/5.82 => ~ ! [X4: int,Y3: int] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_int_int @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( member_real @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mem_case_prodE
% 5.52/5.82 thf(fact_4955_le__minus__iff,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.52/5.82 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_minus_iff
% 5.52/5.82 thf(fact_4956_le__minus__iff,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.82 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_minus_iff
% 5.52/5.82 thf(fact_4957_le__minus__iff,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.52/5.82 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_minus_iff
% 5.52/5.82 thf(fact_4958_le__minus__iff,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.52/5.82 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_minus_iff
% 5.52/5.82 thf(fact_4959_minus__le__iff,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.52/5.82 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_le_iff
% 5.52/5.82 thf(fact_4960_minus__le__iff,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.52/5.82 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_le_iff
% 5.52/5.82 thf(fact_4961_minus__le__iff,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.52/5.82 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_le_iff
% 5.52/5.82 thf(fact_4962_minus__le__iff,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.52/5.82 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_le_iff
% 5.52/5.82 thf(fact_4963_le__imp__neg__le,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.82 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_imp_neg_le
% 5.52/5.82 thf(fact_4964_le__imp__neg__le,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.52/5.82 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_imp_neg_le
% 5.52/5.82 thf(fact_4965_le__imp__neg__le,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.82 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_imp_neg_le
% 5.52/5.82 thf(fact_4966_le__imp__neg__le,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( ord_less_eq_int @ A @ B )
% 5.52/5.82 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_imp_neg_le
% 5.52/5.82 thf(fact_4967_minus__less__iff,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.52/5.82 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_less_iff
% 5.52/5.82 thf(fact_4968_minus__less__iff,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.52/5.82 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_less_iff
% 5.52/5.82 thf(fact_4969_minus__less__iff,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.52/5.82 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_less_iff
% 5.52/5.82 thf(fact_4970_minus__less__iff,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.52/5.82 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_less_iff
% 5.52/5.82 thf(fact_4971_less__minus__iff,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.52/5.82 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_minus_iff
% 5.52/5.82 thf(fact_4972_less__minus__iff,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.52/5.82 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_minus_iff
% 5.52/5.82 thf(fact_4973_less__minus__iff,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.82 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_minus_iff
% 5.52/5.82 thf(fact_4974_less__minus__iff,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.52/5.82 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % less_minus_iff
% 5.52/5.82 thf(fact_4975_verit__negate__coefficient_I2_J,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( ord_less_int @ A @ B )
% 5.52/5.82 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % verit_negate_coefficient(2)
% 5.52/5.82 thf(fact_4976_verit__negate__coefficient_I2_J,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( ord_less_real @ A @ B )
% 5.52/5.82 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % verit_negate_coefficient(2)
% 5.52/5.82 thf(fact_4977_verit__negate__coefficient_I2_J,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.52/5.82 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % verit_negate_coefficient(2)
% 5.52/5.82 thf(fact_4978_verit__negate__coefficient_I2_J,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( ord_less_rat @ A @ B )
% 5.52/5.82 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % verit_negate_coefficient(2)
% 5.52/5.82 thf(fact_4979_neg__numeral__neq__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.52/5.82 != ( numeral_numeral_int @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_neq_numeral
% 5.52/5.82 thf(fact_4980_neg__numeral__neq__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.52/5.82 != ( numeral_numeral_real @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_neq_numeral
% 5.52/5.82 thf(fact_4981_neg__numeral__neq__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.52/5.82 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_neq_numeral
% 5.52/5.82 thf(fact_4982_neg__numeral__neq__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.52/5.82 != ( numera6620942414471956472nteger @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_neq_numeral
% 5.52/5.82 thf(fact_4983_neg__numeral__neq__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.52/5.82 != ( numeral_numeral_rat @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_neq_numeral
% 5.52/5.82 thf(fact_4984_numeral__neq__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( numeral_numeral_int @ M )
% 5.52/5.82 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % numeral_neq_neg_numeral
% 5.52/5.82 thf(fact_4985_numeral__neq__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( numeral_numeral_real @ M )
% 5.52/5.82 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % numeral_neq_neg_numeral
% 5.52/5.82 thf(fact_4986_numeral__neq__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( numera6690914467698888265omplex @ M )
% 5.52/5.82 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % numeral_neq_neg_numeral
% 5.52/5.82 thf(fact_4987_numeral__neq__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( numera6620942414471956472nteger @ M )
% 5.52/5.82 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % numeral_neq_neg_numeral
% 5.52/5.82 thf(fact_4988_numeral__neq__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ( ( numeral_numeral_rat @ M )
% 5.52/5.82 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % numeral_neq_neg_numeral
% 5.52/5.82 thf(fact_4989_square__eq__iff,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( ( times_times_int @ A @ A )
% 5.52/5.82 = ( times_times_int @ B @ B ) )
% 5.52/5.82 = ( ( A = B )
% 5.52/5.82 | ( A
% 5.52/5.82 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % square_eq_iff
% 5.52/5.82 thf(fact_4990_square__eq__iff,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( ( times_times_real @ A @ A )
% 5.52/5.82 = ( times_times_real @ B @ B ) )
% 5.52/5.82 = ( ( A = B )
% 5.52/5.82 | ( A
% 5.52/5.82 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % square_eq_iff
% 5.52/5.82 thf(fact_4991_square__eq__iff,axiom,
% 5.52/5.82 ! [A: complex,B: complex] :
% 5.52/5.82 ( ( ( times_times_complex @ A @ A )
% 5.52/5.82 = ( times_times_complex @ B @ B ) )
% 5.52/5.82 = ( ( A = B )
% 5.52/5.82 | ( A
% 5.52/5.82 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % square_eq_iff
% 5.52/5.82 thf(fact_4992_square__eq__iff,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.52/5.82 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.52/5.82 = ( ( A = B )
% 5.52/5.82 | ( A
% 5.52/5.82 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % square_eq_iff
% 5.52/5.82 thf(fact_4993_square__eq__iff,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( ( times_times_rat @ A @ A )
% 5.52/5.82 = ( times_times_rat @ B @ B ) )
% 5.52/5.82 = ( ( A = B )
% 5.52/5.82 | ( A
% 5.52/5.82 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % square_eq_iff
% 5.52/5.82 thf(fact_4994_minus__mult__commute,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.52/5.82 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_mult_commute
% 5.52/5.82 thf(fact_4995_minus__mult__commute,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.52/5.82 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_mult_commute
% 5.52/5.82 thf(fact_4996_minus__mult__commute,axiom,
% 5.52/5.82 ! [A: complex,B: complex] :
% 5.52/5.82 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.52/5.82 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_mult_commute
% 5.52/5.82 thf(fact_4997_minus__mult__commute,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.52/5.82 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_mult_commute
% 5.52/5.82 thf(fact_4998_minus__mult__commute,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.52/5.82 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_mult_commute
% 5.52/5.82 thf(fact_4999_one__neq__neg__one,axiom,
% 5.52/5.82 ( one_one_int
% 5.52/5.82 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.82
% 5.52/5.82 % one_neq_neg_one
% 5.52/5.82 thf(fact_5000_one__neq__neg__one,axiom,
% 5.52/5.82 ( one_one_real
% 5.52/5.82 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.82
% 5.52/5.82 % one_neq_neg_one
% 5.52/5.82 thf(fact_5001_one__neq__neg__one,axiom,
% 5.52/5.82 ( one_one_complex
% 5.52/5.82 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.52/5.82
% 5.52/5.82 % one_neq_neg_one
% 5.52/5.82 thf(fact_5002_one__neq__neg__one,axiom,
% 5.52/5.82 ( one_one_Code_integer
% 5.52/5.82 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.82
% 5.52/5.82 % one_neq_neg_one
% 5.52/5.82 thf(fact_5003_one__neq__neg__one,axiom,
% 5.52/5.82 ( one_one_rat
% 5.52/5.82 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.82
% 5.52/5.82 % one_neq_neg_one
% 5.52/5.82 thf(fact_5004_group__cancel_Oneg1,axiom,
% 5.52/5.82 ! [A2: int,K: int,A: int] :
% 5.52/5.82 ( ( A2
% 5.52/5.82 = ( plus_plus_int @ K @ A ) )
% 5.52/5.82 => ( ( uminus_uminus_int @ A2 )
% 5.52/5.82 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % group_cancel.neg1
% 5.52/5.82 thf(fact_5005_group__cancel_Oneg1,axiom,
% 5.52/5.82 ! [A2: real,K: real,A: real] :
% 5.52/5.82 ( ( A2
% 5.52/5.82 = ( plus_plus_real @ K @ A ) )
% 5.52/5.82 => ( ( uminus_uminus_real @ A2 )
% 5.52/5.82 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % group_cancel.neg1
% 5.52/5.82 thf(fact_5006_group__cancel_Oneg1,axiom,
% 5.52/5.82 ! [A2: complex,K: complex,A: complex] :
% 5.52/5.82 ( ( A2
% 5.52/5.82 = ( plus_plus_complex @ K @ A ) )
% 5.52/5.82 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.52/5.82 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % group_cancel.neg1
% 5.52/5.82 thf(fact_5007_group__cancel_Oneg1,axiom,
% 5.52/5.82 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 5.52/5.82 ( ( A2
% 5.52/5.82 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.52/5.82 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.52/5.82 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % group_cancel.neg1
% 5.52/5.82 thf(fact_5008_group__cancel_Oneg1,axiom,
% 5.52/5.82 ! [A2: rat,K: rat,A: rat] :
% 5.52/5.82 ( ( A2
% 5.52/5.82 = ( plus_plus_rat @ K @ A ) )
% 5.52/5.82 => ( ( uminus_uminus_rat @ A2 )
% 5.52/5.82 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % group_cancel.neg1
% 5.52/5.82 thf(fact_5009_add_Oinverse__distrib__swap,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.52/5.82 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add.inverse_distrib_swap
% 5.52/5.82 thf(fact_5010_add_Oinverse__distrib__swap,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.52/5.82 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add.inverse_distrib_swap
% 5.52/5.82 thf(fact_5011_add_Oinverse__distrib__swap,axiom,
% 5.52/5.82 ! [A: complex,B: complex] :
% 5.52/5.82 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.52/5.82 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add.inverse_distrib_swap
% 5.52/5.82 thf(fact_5012_add_Oinverse__distrib__swap,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.52/5.82 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add.inverse_distrib_swap
% 5.52/5.82 thf(fact_5013_add_Oinverse__distrib__swap,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.52/5.82 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % add.inverse_distrib_swap
% 5.52/5.82 thf(fact_5014_is__num__normalize_I8_J,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.52/5.82 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % is_num_normalize(8)
% 5.52/5.82 thf(fact_5015_is__num__normalize_I8_J,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.52/5.82 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % is_num_normalize(8)
% 5.52/5.82 thf(fact_5016_is__num__normalize_I8_J,axiom,
% 5.52/5.82 ! [A: complex,B: complex] :
% 5.52/5.82 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.52/5.82 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % is_num_normalize(8)
% 5.52/5.82 thf(fact_5017_is__num__normalize_I8_J,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.52/5.82 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % is_num_normalize(8)
% 5.52/5.82 thf(fact_5018_is__num__normalize_I8_J,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.52/5.82 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % is_num_normalize(8)
% 5.52/5.82 thf(fact_5019_minus__diff__commute,axiom,
% 5.52/5.82 ! [B: int,A: int] :
% 5.52/5.82 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.52/5.82 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_diff_commute
% 5.52/5.82 thf(fact_5020_minus__diff__commute,axiom,
% 5.52/5.82 ! [B: real,A: real] :
% 5.52/5.82 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.52/5.82 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_diff_commute
% 5.52/5.82 thf(fact_5021_minus__diff__commute,axiom,
% 5.52/5.82 ! [B: complex,A: complex] :
% 5.52/5.82 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.52/5.82 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_diff_commute
% 5.52/5.82 thf(fact_5022_minus__diff__commute,axiom,
% 5.52/5.82 ! [B: code_integer,A: code_integer] :
% 5.52/5.82 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.52/5.82 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_diff_commute
% 5.52/5.82 thf(fact_5023_minus__diff__commute,axiom,
% 5.52/5.82 ! [B: rat,A: rat] :
% 5.52/5.82 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.52/5.82 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_diff_commute
% 5.52/5.82 thf(fact_5024_minus__diff__minus,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_diff_minus
% 5.52/5.82 thf(fact_5025_minus__diff__minus,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.52/5.82 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_diff_minus
% 5.52/5.82 thf(fact_5026_minus__diff__minus,axiom,
% 5.52/5.82 ! [A: complex,B: complex] :
% 5.52/5.82 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.52/5.82 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_diff_minus
% 5.52/5.82 thf(fact_5027_minus__diff__minus,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_diff_minus
% 5.52/5.82 thf(fact_5028_minus__diff__minus,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.52/5.82 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_diff_minus
% 5.52/5.82 thf(fact_5029_div__minus__right,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.52/5.82 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % div_minus_right
% 5.52/5.82 thf(fact_5030_div__minus__right,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.82 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % div_minus_right
% 5.52/5.82 thf(fact_5031_minus__divide__left,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.52/5.82 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_divide_left
% 5.52/5.82 thf(fact_5032_minus__divide__left,axiom,
% 5.52/5.82 ! [A: complex,B: complex] :
% 5.52/5.82 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.52/5.82 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_divide_left
% 5.52/5.82 thf(fact_5033_minus__divide__left,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.52/5.82 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_divide_left
% 5.52/5.82 thf(fact_5034_minus__divide__divide,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.52/5.82 = ( divide_divide_real @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_divide_divide
% 5.52/5.82 thf(fact_5035_minus__divide__divide,axiom,
% 5.52/5.82 ! [A: complex,B: complex] :
% 5.52/5.82 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.52/5.82 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_divide_divide
% 5.52/5.82 thf(fact_5036_minus__divide__divide,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.52/5.82 = ( divide_divide_rat @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_divide_divide
% 5.52/5.82 thf(fact_5037_minus__divide__right,axiom,
% 5.52/5.82 ! [A: real,B: real] :
% 5.52/5.82 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.52/5.82 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_divide_right
% 5.52/5.82 thf(fact_5038_minus__divide__right,axiom,
% 5.52/5.82 ! [A: complex,B: complex] :
% 5.52/5.82 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.52/5.82 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_divide_right
% 5.52/5.82 thf(fact_5039_minus__divide__right,axiom,
% 5.52/5.82 ! [A: rat,B: rat] :
% 5.52/5.82 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.52/5.82 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % minus_divide_right
% 5.52/5.82 thf(fact_5040_mod__minus__eq,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.52/5.82 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % mod_minus_eq
% 5.52/5.82 thf(fact_5041_mod__minus__eq,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.52/5.82 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % mod_minus_eq
% 5.52/5.82 thf(fact_5042_mod__minus__cong,axiom,
% 5.52/5.82 ! [A: int,B: int,A5: int] :
% 5.52/5.82 ( ( ( modulo_modulo_int @ A @ B )
% 5.52/5.82 = ( modulo_modulo_int @ A5 @ B ) )
% 5.52/5.82 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.52/5.82 = ( modulo_modulo_int @ ( uminus_uminus_int @ A5 ) @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mod_minus_cong
% 5.52/5.82 thf(fact_5043_mod__minus__cong,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer,A5: code_integer] :
% 5.52/5.82 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.52/5.82 = ( modulo364778990260209775nteger @ A5 @ B ) )
% 5.52/5.82 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.52/5.82 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A5 ) @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mod_minus_cong
% 5.52/5.82 thf(fact_5044_mod__minus__right,axiom,
% 5.52/5.82 ! [A: int,B: int] :
% 5.52/5.82 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.52/5.82 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mod_minus_right
% 5.52/5.82 thf(fact_5045_mod__minus__right,axiom,
% 5.52/5.82 ! [A: code_integer,B: code_integer] :
% 5.52/5.82 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.82 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % mod_minus_right
% 5.52/5.82 thf(fact_5046_case__prodD,axiom,
% 5.52/5.82 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.52/5.82 ( ( produc6590410687421337004_nat_o @ F @ ( produc6161850002892822231at_nat @ A @ B ) )
% 5.52/5.82 => ( F @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % case_prodD
% 5.52/5.82 thf(fact_5047_case__prodD,axiom,
% 5.52/5.82 ! [F: num > num > $o,A: num,B: num] :
% 5.52/5.82 ( ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) )
% 5.52/5.82 => ( F @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % case_prodD
% 5.52/5.82 thf(fact_5048_case__prodD,axiom,
% 5.52/5.82 ! [F: nat > num > $o,A: nat,B: num] :
% 5.52/5.82 ( ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) )
% 5.52/5.82 => ( F @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % case_prodD
% 5.52/5.82 thf(fact_5049_case__prodD,axiom,
% 5.52/5.82 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.52/5.82 ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.52/5.82 => ( F @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % case_prodD
% 5.52/5.82 thf(fact_5050_case__prodD,axiom,
% 5.52/5.82 ! [F: int > int > $o,A: int,B: int] :
% 5.52/5.82 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.52/5.82 => ( F @ A @ B ) ) ).
% 5.52/5.82
% 5.52/5.82 % case_prodD
% 5.52/5.82 thf(fact_5051_case__prodE,axiom,
% 5.52/5.82 ! [C: product_prod_nat_nat > product_prod_nat_nat > $o,P6: produc859450856879609959at_nat] :
% 5.52/5.82 ( ( produc6590410687421337004_nat_o @ C @ P6 )
% 5.52/5.82 => ~ ! [X4: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( produc6161850002892822231at_nat @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( C @ X4 @ Y3 ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % case_prodE
% 5.52/5.82 thf(fact_5052_case__prodE,axiom,
% 5.52/5.82 ! [C: num > num > $o,P6: product_prod_num_num] :
% 5.52/5.82 ( ( produc5703948589228662326_num_o @ C @ P6 )
% 5.52/5.82 => ~ ! [X4: num,Y3: num] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_num_num @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( C @ X4 @ Y3 ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % case_prodE
% 5.52/5.82 thf(fact_5053_case__prodE,axiom,
% 5.52/5.82 ! [C: nat > num > $o,P6: product_prod_nat_num] :
% 5.52/5.82 ( ( produc4927758841916487424_num_o @ C @ P6 )
% 5.52/5.82 => ~ ! [X4: nat,Y3: num] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_nat_num @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( C @ X4 @ Y3 ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % case_prodE
% 5.52/5.82 thf(fact_5054_case__prodE,axiom,
% 5.52/5.82 ! [C: nat > nat > $o,P6: product_prod_nat_nat] :
% 5.52/5.82 ( ( produc6081775807080527818_nat_o @ C @ P6 )
% 5.52/5.82 => ~ ! [X4: nat,Y3: nat] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_nat_nat @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( C @ X4 @ Y3 ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % case_prodE
% 5.52/5.82 thf(fact_5055_case__prodE,axiom,
% 5.52/5.82 ! [C: int > int > $o,P6: product_prod_int_int] :
% 5.52/5.82 ( ( produc4947309494688390418_int_o @ C @ P6 )
% 5.52/5.82 => ~ ! [X4: int,Y3: int] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_int_int @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( C @ X4 @ Y3 ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % case_prodE
% 5.52/5.82 thf(fact_5056_case__prodD_H,axiom,
% 5.52/5.82 ! [R2: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 5.52/5.82 ( ( produc8739625826339149834_nat_o @ R2 @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 5.52/5.82 => ( R2 @ A @ B @ C ) ) ).
% 5.52/5.82
% 5.52/5.82 % case_prodD'
% 5.52/5.82 thf(fact_5057_case__prodE_H,axiom,
% 5.52/5.82 ! [C: nat > nat > product_prod_nat_nat > $o,P6: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.52/5.82 ( ( produc8739625826339149834_nat_o @ C @ P6 @ Z )
% 5.52/5.82 => ~ ! [X4: nat,Y3: nat] :
% 5.52/5.82 ( ( P6
% 5.52/5.82 = ( product_Pair_nat_nat @ X4 @ Y3 ) )
% 5.52/5.82 => ~ ( C @ X4 @ Y3 @ Z ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % case_prodE'
% 5.52/5.82 thf(fact_5058_zero__less__eq__of__bool,axiom,
% 5.52/5.82 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.52/5.82
% 5.52/5.82 % zero_less_eq_of_bool
% 5.52/5.82 thf(fact_5059_zero__less__eq__of__bool,axiom,
% 5.52/5.82 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.52/5.82
% 5.52/5.82 % zero_less_eq_of_bool
% 5.52/5.82 thf(fact_5060_zero__less__eq__of__bool,axiom,
% 5.52/5.82 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.52/5.82
% 5.52/5.82 % zero_less_eq_of_bool
% 5.52/5.82 thf(fact_5061_zero__less__eq__of__bool,axiom,
% 5.52/5.82 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.52/5.82
% 5.52/5.82 % zero_less_eq_of_bool
% 5.52/5.82 thf(fact_5062_zero__less__eq__of__bool,axiom,
% 5.52/5.82 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.52/5.82
% 5.52/5.82 % zero_less_eq_of_bool
% 5.52/5.82 thf(fact_5063_of__bool__less__eq__one,axiom,
% 5.52/5.82 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_less_eq_one
% 5.52/5.82 thf(fact_5064_of__bool__less__eq__one,axiom,
% 5.52/5.82 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_less_eq_one
% 5.52/5.82 thf(fact_5065_of__bool__less__eq__one,axiom,
% 5.52/5.82 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_less_eq_one
% 5.52/5.82 thf(fact_5066_of__bool__less__eq__one,axiom,
% 5.52/5.82 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_less_eq_one
% 5.52/5.82 thf(fact_5067_of__bool__less__eq__one,axiom,
% 5.52/5.82 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_less_eq_one
% 5.52/5.82 thf(fact_5068_split__of__bool__asm,axiom,
% 5.52/5.82 ! [P: complex > $o,P6: $o] :
% 5.52/5.82 ( ( P @ ( zero_n1201886186963655149omplex @ P6 ) )
% 5.52/5.82 = ( ~ ( ( P6
% 5.52/5.82 & ~ ( P @ one_one_complex ) )
% 5.52/5.82 | ( ~ P6
% 5.52/5.82 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % split_of_bool_asm
% 5.52/5.82 thf(fact_5069_split__of__bool__asm,axiom,
% 5.52/5.82 ! [P: real > $o,P6: $o] :
% 5.52/5.82 ( ( P @ ( zero_n3304061248610475627l_real @ P6 ) )
% 5.52/5.82 = ( ~ ( ( P6
% 5.52/5.82 & ~ ( P @ one_one_real ) )
% 5.52/5.82 | ( ~ P6
% 5.52/5.82 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % split_of_bool_asm
% 5.52/5.82 thf(fact_5070_split__of__bool__asm,axiom,
% 5.52/5.82 ! [P: rat > $o,P6: $o] :
% 5.52/5.82 ( ( P @ ( zero_n2052037380579107095ol_rat @ P6 ) )
% 5.52/5.82 = ( ~ ( ( P6
% 5.52/5.82 & ~ ( P @ one_one_rat ) )
% 5.52/5.82 | ( ~ P6
% 5.52/5.82 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % split_of_bool_asm
% 5.52/5.82 thf(fact_5071_split__of__bool__asm,axiom,
% 5.52/5.82 ! [P: nat > $o,P6: $o] :
% 5.52/5.82 ( ( P @ ( zero_n2687167440665602831ol_nat @ P6 ) )
% 5.52/5.82 = ( ~ ( ( P6
% 5.52/5.82 & ~ ( P @ one_one_nat ) )
% 5.52/5.82 | ( ~ P6
% 5.52/5.82 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % split_of_bool_asm
% 5.52/5.82 thf(fact_5072_split__of__bool__asm,axiom,
% 5.52/5.82 ! [P: int > $o,P6: $o] :
% 5.52/5.82 ( ( P @ ( zero_n2684676970156552555ol_int @ P6 ) )
% 5.52/5.82 = ( ~ ( ( P6
% 5.52/5.82 & ~ ( P @ one_one_int ) )
% 5.52/5.82 | ( ~ P6
% 5.52/5.82 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % split_of_bool_asm
% 5.52/5.82 thf(fact_5073_split__of__bool__asm,axiom,
% 5.52/5.82 ! [P: code_integer > $o,P6: $o] :
% 5.52/5.82 ( ( P @ ( zero_n356916108424825756nteger @ P6 ) )
% 5.52/5.82 = ( ~ ( ( P6
% 5.52/5.82 & ~ ( P @ one_one_Code_integer ) )
% 5.52/5.82 | ( ~ P6
% 5.52/5.82 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % split_of_bool_asm
% 5.52/5.82 thf(fact_5074_split__of__bool,axiom,
% 5.52/5.82 ! [P: complex > $o,P6: $o] :
% 5.52/5.82 ( ( P @ ( zero_n1201886186963655149omplex @ P6 ) )
% 5.52/5.82 = ( ( P6
% 5.52/5.82 => ( P @ one_one_complex ) )
% 5.52/5.82 & ( ~ P6
% 5.52/5.82 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % split_of_bool
% 5.52/5.82 thf(fact_5075_split__of__bool,axiom,
% 5.52/5.82 ! [P: real > $o,P6: $o] :
% 5.52/5.82 ( ( P @ ( zero_n3304061248610475627l_real @ P6 ) )
% 5.52/5.82 = ( ( P6
% 5.52/5.82 => ( P @ one_one_real ) )
% 5.52/5.82 & ( ~ P6
% 5.52/5.82 => ( P @ zero_zero_real ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % split_of_bool
% 5.52/5.82 thf(fact_5076_split__of__bool,axiom,
% 5.52/5.82 ! [P: rat > $o,P6: $o] :
% 5.52/5.82 ( ( P @ ( zero_n2052037380579107095ol_rat @ P6 ) )
% 5.52/5.82 = ( ( P6
% 5.52/5.82 => ( P @ one_one_rat ) )
% 5.52/5.82 & ( ~ P6
% 5.52/5.82 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % split_of_bool
% 5.52/5.82 thf(fact_5077_split__of__bool,axiom,
% 5.52/5.82 ! [P: nat > $o,P6: $o] :
% 5.52/5.82 ( ( P @ ( zero_n2687167440665602831ol_nat @ P6 ) )
% 5.52/5.82 = ( ( P6
% 5.52/5.82 => ( P @ one_one_nat ) )
% 5.52/5.82 & ( ~ P6
% 5.52/5.82 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % split_of_bool
% 5.52/5.82 thf(fact_5078_split__of__bool,axiom,
% 5.52/5.82 ! [P: int > $o,P6: $o] :
% 5.52/5.82 ( ( P @ ( zero_n2684676970156552555ol_int @ P6 ) )
% 5.52/5.82 = ( ( P6
% 5.52/5.82 => ( P @ one_one_int ) )
% 5.52/5.82 & ( ~ P6
% 5.52/5.82 => ( P @ zero_zero_int ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % split_of_bool
% 5.52/5.82 thf(fact_5079_split__of__bool,axiom,
% 5.52/5.82 ! [P: code_integer > $o,P6: $o] :
% 5.52/5.82 ( ( P @ ( zero_n356916108424825756nteger @ P6 ) )
% 5.52/5.82 = ( ( P6
% 5.52/5.82 => ( P @ one_one_Code_integer ) )
% 5.52/5.82 & ( ~ P6
% 5.52/5.82 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % split_of_bool
% 5.52/5.82 thf(fact_5080_of__bool__def,axiom,
% 5.52/5.82 ( zero_n1201886186963655149omplex
% 5.52/5.82 = ( ^ [P4: $o] : ( if_complex @ P4 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_def
% 5.52/5.82 thf(fact_5081_of__bool__def,axiom,
% 5.52/5.82 ( zero_n3304061248610475627l_real
% 5.52/5.82 = ( ^ [P4: $o] : ( if_real @ P4 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_def
% 5.52/5.82 thf(fact_5082_of__bool__def,axiom,
% 5.52/5.82 ( zero_n2052037380579107095ol_rat
% 5.52/5.82 = ( ^ [P4: $o] : ( if_rat @ P4 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_def
% 5.52/5.82 thf(fact_5083_of__bool__def,axiom,
% 5.52/5.82 ( zero_n2687167440665602831ol_nat
% 5.52/5.82 = ( ^ [P4: $o] : ( if_nat @ P4 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_def
% 5.52/5.82 thf(fact_5084_of__bool__def,axiom,
% 5.52/5.82 ( zero_n2684676970156552555ol_int
% 5.52/5.82 = ( ^ [P4: $o] : ( if_int @ P4 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_def
% 5.52/5.82 thf(fact_5085_of__bool__def,axiom,
% 5.52/5.82 ( zero_n356916108424825756nteger
% 5.52/5.82 = ( ^ [P4: $o] : ( if_Code_integer @ P4 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % of_bool_def
% 5.52/5.82 thf(fact_5086_neg__numeral__le__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_le_numeral
% 5.52/5.82 thf(fact_5087_neg__numeral__le__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_le_numeral
% 5.52/5.82 thf(fact_5088_neg__numeral__le__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_le_numeral
% 5.52/5.82 thf(fact_5089_neg__numeral__le__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_le_numeral
% 5.52/5.82 thf(fact_5090_not__numeral__le__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % not_numeral_le_neg_numeral
% 5.52/5.82 thf(fact_5091_not__numeral__le__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % not_numeral_le_neg_numeral
% 5.52/5.82 thf(fact_5092_not__numeral__le__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % not_numeral_le_neg_numeral
% 5.52/5.82 thf(fact_5093_not__numeral__le__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % not_numeral_le_neg_numeral
% 5.52/5.82 thf(fact_5094_zero__neq__neg__numeral,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( zero_zero_int
% 5.52/5.82 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % zero_neq_neg_numeral
% 5.52/5.82 thf(fact_5095_zero__neq__neg__numeral,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( zero_zero_real
% 5.52/5.82 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % zero_neq_neg_numeral
% 5.52/5.82 thf(fact_5096_zero__neq__neg__numeral,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( zero_zero_complex
% 5.52/5.82 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % zero_neq_neg_numeral
% 5.52/5.82 thf(fact_5097_zero__neq__neg__numeral,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( zero_z3403309356797280102nteger
% 5.52/5.82 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % zero_neq_neg_numeral
% 5.52/5.82 thf(fact_5098_zero__neq__neg__numeral,axiom,
% 5.52/5.82 ! [N: num] :
% 5.52/5.82 ( zero_zero_rat
% 5.52/5.82 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % zero_neq_neg_numeral
% 5.52/5.82 thf(fact_5099_not__numeral__less__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % not_numeral_less_neg_numeral
% 5.52/5.82 thf(fact_5100_not__numeral__less__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % not_numeral_less_neg_numeral
% 5.52/5.82 thf(fact_5101_not__numeral__less__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % not_numeral_less_neg_numeral
% 5.52/5.82 thf(fact_5102_not__numeral__less__neg__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] :
% 5.52/5.82 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.52/5.82
% 5.52/5.82 % not_numeral_less_neg_numeral
% 5.52/5.82 thf(fact_5103_neg__numeral__less__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_less_numeral
% 5.52/5.82 thf(fact_5104_neg__numeral__less__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_less_numeral
% 5.52/5.82 thf(fact_5105_neg__numeral__less__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_less_numeral
% 5.52/5.82 thf(fact_5106_neg__numeral__less__numeral,axiom,
% 5.52/5.82 ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.52/5.82
% 5.52/5.82 % neg_numeral_less_numeral
% 5.52/5.82 thf(fact_5107_le__minus__one__simps_I4_J,axiom,
% 5.52/5.82 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_minus_one_simps(4)
% 5.52/5.82 thf(fact_5108_le__minus__one__simps_I4_J,axiom,
% 5.52/5.82 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_minus_one_simps(4)
% 5.52/5.82 thf(fact_5109_le__minus__one__simps_I4_J,axiom,
% 5.52/5.82 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_minus_one_simps(4)
% 5.52/5.82 thf(fact_5110_le__minus__one__simps_I4_J,axiom,
% 5.52/5.82 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.82
% 5.52/5.82 % le_minus_one_simps(4)
% 5.52/5.82 thf(fact_5111_le__minus__one__simps_I2_J,axiom,
% 5.52/5.82 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.52/5.82
% 5.52/5.82 % le_minus_one_simps(2)
% 5.52/5.82 thf(fact_5112_le__minus__one__simps_I2_J,axiom,
% 5.52/5.82 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.52/5.83
% 5.52/5.83 % le_minus_one_simps(2)
% 5.52/5.83 thf(fact_5113_le__minus__one__simps_I2_J,axiom,
% 5.52/5.83 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.52/5.83
% 5.52/5.83 % le_minus_one_simps(2)
% 5.52/5.83 thf(fact_5114_le__minus__one__simps_I2_J,axiom,
% 5.52/5.83 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.52/5.83
% 5.52/5.83 % le_minus_one_simps(2)
% 5.52/5.83 thf(fact_5115_zero__neq__neg__one,axiom,
% 5.52/5.83 ( zero_zero_int
% 5.52/5.83 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % zero_neq_neg_one
% 5.52/5.83 thf(fact_5116_zero__neq__neg__one,axiom,
% 5.52/5.83 ( zero_zero_real
% 5.52/5.83 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % zero_neq_neg_one
% 5.52/5.83 thf(fact_5117_zero__neq__neg__one,axiom,
% 5.52/5.83 ( zero_zero_complex
% 5.52/5.83 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.52/5.83
% 5.52/5.83 % zero_neq_neg_one
% 5.52/5.83 thf(fact_5118_zero__neq__neg__one,axiom,
% 5.52/5.83 ( zero_z3403309356797280102nteger
% 5.52/5.83 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.83
% 5.52/5.83 % zero_neq_neg_one
% 5.52/5.83 thf(fact_5119_zero__neq__neg__one,axiom,
% 5.52/5.83 ( zero_zero_rat
% 5.52/5.83 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % zero_neq_neg_one
% 5.52/5.83 thf(fact_5120_add__eq__0__iff,axiom,
% 5.52/5.83 ! [A: int,B: int] :
% 5.52/5.83 ( ( ( plus_plus_int @ A @ B )
% 5.52/5.83 = zero_zero_int )
% 5.52/5.83 = ( B
% 5.52/5.83 = ( uminus_uminus_int @ A ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_eq_0_iff
% 5.52/5.83 thf(fact_5121_add__eq__0__iff,axiom,
% 5.52/5.83 ! [A: real,B: real] :
% 5.52/5.83 ( ( ( plus_plus_real @ A @ B )
% 5.52/5.83 = zero_zero_real )
% 5.52/5.83 = ( B
% 5.52/5.83 = ( uminus_uminus_real @ A ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_eq_0_iff
% 5.52/5.83 thf(fact_5122_add__eq__0__iff,axiom,
% 5.52/5.83 ! [A: complex,B: complex] :
% 5.52/5.83 ( ( ( plus_plus_complex @ A @ B )
% 5.52/5.83 = zero_zero_complex )
% 5.52/5.83 = ( B
% 5.52/5.83 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_eq_0_iff
% 5.52/5.83 thf(fact_5123_add__eq__0__iff,axiom,
% 5.52/5.83 ! [A: code_integer,B: code_integer] :
% 5.52/5.83 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.52/5.83 = zero_z3403309356797280102nteger )
% 5.52/5.83 = ( B
% 5.52/5.83 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_eq_0_iff
% 5.52/5.83 thf(fact_5124_add__eq__0__iff,axiom,
% 5.52/5.83 ! [A: rat,B: rat] :
% 5.52/5.83 ( ( ( plus_plus_rat @ A @ B )
% 5.52/5.83 = zero_zero_rat )
% 5.52/5.83 = ( B
% 5.52/5.83 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_eq_0_iff
% 5.52/5.83 thf(fact_5125_ab__group__add__class_Oab__left__minus,axiom,
% 5.52/5.83 ! [A: int] :
% 5.52/5.83 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.52/5.83 = zero_zero_int ) ).
% 5.52/5.83
% 5.52/5.83 % ab_group_add_class.ab_left_minus
% 5.52/5.83 thf(fact_5126_ab__group__add__class_Oab__left__minus,axiom,
% 5.52/5.83 ! [A: real] :
% 5.52/5.83 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.52/5.83 = zero_zero_real ) ).
% 5.52/5.83
% 5.52/5.83 % ab_group_add_class.ab_left_minus
% 5.52/5.83 thf(fact_5127_ab__group__add__class_Oab__left__minus,axiom,
% 5.52/5.83 ! [A: complex] :
% 5.52/5.83 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.52/5.83 = zero_zero_complex ) ).
% 5.52/5.83
% 5.52/5.83 % ab_group_add_class.ab_left_minus
% 5.52/5.83 thf(fact_5128_ab__group__add__class_Oab__left__minus,axiom,
% 5.52/5.83 ! [A: code_integer] :
% 5.52/5.83 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.52/5.83 = zero_z3403309356797280102nteger ) ).
% 5.52/5.83
% 5.52/5.83 % ab_group_add_class.ab_left_minus
% 5.52/5.83 thf(fact_5129_ab__group__add__class_Oab__left__minus,axiom,
% 5.52/5.83 ! [A: rat] :
% 5.52/5.83 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.52/5.83 = zero_zero_rat ) ).
% 5.52/5.83
% 5.52/5.83 % ab_group_add_class.ab_left_minus
% 5.52/5.83 thf(fact_5130_add_Oinverse__unique,axiom,
% 5.52/5.83 ! [A: int,B: int] :
% 5.52/5.83 ( ( ( plus_plus_int @ A @ B )
% 5.52/5.83 = zero_zero_int )
% 5.52/5.83 => ( ( uminus_uminus_int @ A )
% 5.52/5.83 = B ) ) ).
% 5.52/5.83
% 5.52/5.83 % add.inverse_unique
% 5.52/5.83 thf(fact_5131_add_Oinverse__unique,axiom,
% 5.52/5.83 ! [A: real,B: real] :
% 5.52/5.83 ( ( ( plus_plus_real @ A @ B )
% 5.52/5.83 = zero_zero_real )
% 5.52/5.83 => ( ( uminus_uminus_real @ A )
% 5.52/5.83 = B ) ) ).
% 5.52/5.83
% 5.52/5.83 % add.inverse_unique
% 5.52/5.83 thf(fact_5132_add_Oinverse__unique,axiom,
% 5.52/5.83 ! [A: complex,B: complex] :
% 5.52/5.83 ( ( ( plus_plus_complex @ A @ B )
% 5.52/5.83 = zero_zero_complex )
% 5.52/5.83 => ( ( uminus1482373934393186551omplex @ A )
% 5.52/5.83 = B ) ) ).
% 5.52/5.83
% 5.52/5.83 % add.inverse_unique
% 5.52/5.83 thf(fact_5133_add_Oinverse__unique,axiom,
% 5.52/5.83 ! [A: code_integer,B: code_integer] :
% 5.52/5.83 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.52/5.83 = zero_z3403309356797280102nteger )
% 5.52/5.83 => ( ( uminus1351360451143612070nteger @ A )
% 5.52/5.83 = B ) ) ).
% 5.52/5.83
% 5.52/5.83 % add.inverse_unique
% 5.52/5.83 thf(fact_5134_add_Oinverse__unique,axiom,
% 5.52/5.83 ! [A: rat,B: rat] :
% 5.52/5.83 ( ( ( plus_plus_rat @ A @ B )
% 5.52/5.83 = zero_zero_rat )
% 5.52/5.83 => ( ( uminus_uminus_rat @ A )
% 5.52/5.83 = B ) ) ).
% 5.52/5.83
% 5.52/5.83 % add.inverse_unique
% 5.52/5.83 thf(fact_5135_eq__neg__iff__add__eq__0,axiom,
% 5.52/5.83 ! [A: int,B: int] :
% 5.52/5.83 ( ( A
% 5.52/5.83 = ( uminus_uminus_int @ B ) )
% 5.52/5.83 = ( ( plus_plus_int @ A @ B )
% 5.52/5.83 = zero_zero_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % eq_neg_iff_add_eq_0
% 5.52/5.83 thf(fact_5136_eq__neg__iff__add__eq__0,axiom,
% 5.52/5.83 ! [A: real,B: real] :
% 5.52/5.83 ( ( A
% 5.52/5.83 = ( uminus_uminus_real @ B ) )
% 5.52/5.83 = ( ( plus_plus_real @ A @ B )
% 5.52/5.83 = zero_zero_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % eq_neg_iff_add_eq_0
% 5.52/5.83 thf(fact_5137_eq__neg__iff__add__eq__0,axiom,
% 5.52/5.83 ! [A: complex,B: complex] :
% 5.52/5.83 ( ( A
% 5.52/5.83 = ( uminus1482373934393186551omplex @ B ) )
% 5.52/5.83 = ( ( plus_plus_complex @ A @ B )
% 5.52/5.83 = zero_zero_complex ) ) ).
% 5.52/5.83
% 5.52/5.83 % eq_neg_iff_add_eq_0
% 5.52/5.83 thf(fact_5138_eq__neg__iff__add__eq__0,axiom,
% 5.52/5.83 ! [A: code_integer,B: code_integer] :
% 5.52/5.83 ( ( A
% 5.52/5.83 = ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.83 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.52/5.83 = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.83
% 5.52/5.83 % eq_neg_iff_add_eq_0
% 5.52/5.83 thf(fact_5139_eq__neg__iff__add__eq__0,axiom,
% 5.52/5.83 ! [A: rat,B: rat] :
% 5.52/5.83 ( ( A
% 5.52/5.83 = ( uminus_uminus_rat @ B ) )
% 5.52/5.83 = ( ( plus_plus_rat @ A @ B )
% 5.52/5.83 = zero_zero_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % eq_neg_iff_add_eq_0
% 5.52/5.83 thf(fact_5140_neg__eq__iff__add__eq__0,axiom,
% 5.52/5.83 ! [A: int,B: int] :
% 5.52/5.83 ( ( ( uminus_uminus_int @ A )
% 5.52/5.83 = B )
% 5.52/5.83 = ( ( plus_plus_int @ A @ B )
% 5.52/5.83 = zero_zero_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_eq_iff_add_eq_0
% 5.52/5.83 thf(fact_5141_neg__eq__iff__add__eq__0,axiom,
% 5.52/5.83 ! [A: real,B: real] :
% 5.52/5.83 ( ( ( uminus_uminus_real @ A )
% 5.52/5.83 = B )
% 5.52/5.83 = ( ( plus_plus_real @ A @ B )
% 5.52/5.83 = zero_zero_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_eq_iff_add_eq_0
% 5.52/5.83 thf(fact_5142_neg__eq__iff__add__eq__0,axiom,
% 5.52/5.83 ! [A: complex,B: complex] :
% 5.52/5.83 ( ( ( uminus1482373934393186551omplex @ A )
% 5.52/5.83 = B )
% 5.52/5.83 = ( ( plus_plus_complex @ A @ B )
% 5.52/5.83 = zero_zero_complex ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_eq_iff_add_eq_0
% 5.52/5.83 thf(fact_5143_neg__eq__iff__add__eq__0,axiom,
% 5.52/5.83 ! [A: code_integer,B: code_integer] :
% 5.52/5.83 ( ( ( uminus1351360451143612070nteger @ A )
% 5.52/5.83 = B )
% 5.52/5.83 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.52/5.83 = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_eq_iff_add_eq_0
% 5.52/5.83 thf(fact_5144_neg__eq__iff__add__eq__0,axiom,
% 5.52/5.83 ! [A: rat,B: rat] :
% 5.52/5.83 ( ( ( uminus_uminus_rat @ A )
% 5.52/5.83 = B )
% 5.52/5.83 = ( ( plus_plus_rat @ A @ B )
% 5.52/5.83 = zero_zero_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_eq_iff_add_eq_0
% 5.52/5.83 thf(fact_5145_less__minus__one__simps_I2_J,axiom,
% 5.52/5.83 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(2)
% 5.52/5.83 thf(fact_5146_less__minus__one__simps_I2_J,axiom,
% 5.52/5.83 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(2)
% 5.52/5.83 thf(fact_5147_less__minus__one__simps_I2_J,axiom,
% 5.52/5.83 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(2)
% 5.52/5.83 thf(fact_5148_less__minus__one__simps_I2_J,axiom,
% 5.52/5.83 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(2)
% 5.52/5.83 thf(fact_5149_less__minus__one__simps_I4_J,axiom,
% 5.52/5.83 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(4)
% 5.52/5.83 thf(fact_5150_less__minus__one__simps_I4_J,axiom,
% 5.52/5.83 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(4)
% 5.52/5.83 thf(fact_5151_less__minus__one__simps_I4_J,axiom,
% 5.52/5.83 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(4)
% 5.52/5.83 thf(fact_5152_less__minus__one__simps_I4_J,axiom,
% 5.52/5.83 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(4)
% 5.52/5.83 thf(fact_5153_numeral__times__minus__swap,axiom,
% 5.52/5.83 ! [W: num,X2: int] :
% 5.52/5.83 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X2 ) )
% 5.52/5.83 = ( times_times_int @ X2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_times_minus_swap
% 5.52/5.83 thf(fact_5154_numeral__times__minus__swap,axiom,
% 5.52/5.83 ! [W: num,X2: real] :
% 5.52/5.83 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X2 ) )
% 5.52/5.83 = ( times_times_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_times_minus_swap
% 5.52/5.83 thf(fact_5155_numeral__times__minus__swap,axiom,
% 5.52/5.83 ! [W: num,X2: complex] :
% 5.52/5.83 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.52/5.83 = ( times_times_complex @ X2 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_times_minus_swap
% 5.52/5.83 thf(fact_5156_numeral__times__minus__swap,axiom,
% 5.52/5.83 ! [W: num,X2: code_integer] :
% 5.52/5.83 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X2 ) )
% 5.52/5.83 = ( times_3573771949741848930nteger @ X2 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_times_minus_swap
% 5.52/5.83 thf(fact_5157_numeral__times__minus__swap,axiom,
% 5.52/5.83 ! [W: num,X2: rat] :
% 5.52/5.83 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X2 ) )
% 5.52/5.83 = ( times_times_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_times_minus_swap
% 5.52/5.83 thf(fact_5158_numeral__neq__neg__one,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ( ( numeral_numeral_int @ N )
% 5.52/5.83 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_neq_neg_one
% 5.52/5.83 thf(fact_5159_numeral__neq__neg__one,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ( ( numeral_numeral_real @ N )
% 5.52/5.83 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_neq_neg_one
% 5.52/5.83 thf(fact_5160_numeral__neq__neg__one,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ( ( numera6690914467698888265omplex @ N )
% 5.52/5.83 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_neq_neg_one
% 5.52/5.83 thf(fact_5161_numeral__neq__neg__one,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ( ( numera6620942414471956472nteger @ N )
% 5.52/5.83 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_neq_neg_one
% 5.52/5.83 thf(fact_5162_numeral__neq__neg__one,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ( ( numeral_numeral_rat @ N )
% 5.52/5.83 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_neq_neg_one
% 5.52/5.83 thf(fact_5163_one__neq__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ( one_one_int
% 5.52/5.83 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % one_neq_neg_numeral
% 5.52/5.83 thf(fact_5164_one__neq__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ( one_one_real
% 5.52/5.83 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % one_neq_neg_numeral
% 5.52/5.83 thf(fact_5165_one__neq__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ( one_one_complex
% 5.52/5.83 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % one_neq_neg_numeral
% 5.52/5.83 thf(fact_5166_one__neq__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ( one_one_Code_integer
% 5.52/5.83 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % one_neq_neg_numeral
% 5.52/5.83 thf(fact_5167_one__neq__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ( one_one_rat
% 5.52/5.83 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % one_neq_neg_numeral
% 5.52/5.83 thf(fact_5168_nonzero__minus__divide__divide,axiom,
% 5.52/5.83 ! [B: real,A: real] :
% 5.52/5.83 ( ( B != zero_zero_real )
% 5.52/5.83 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.52/5.83 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % nonzero_minus_divide_divide
% 5.52/5.83 thf(fact_5169_nonzero__minus__divide__divide,axiom,
% 5.52/5.83 ! [B: complex,A: complex] :
% 5.52/5.83 ( ( B != zero_zero_complex )
% 5.52/5.83 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.52/5.83 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % nonzero_minus_divide_divide
% 5.52/5.83 thf(fact_5170_nonzero__minus__divide__divide,axiom,
% 5.52/5.83 ! [B: rat,A: rat] :
% 5.52/5.83 ( ( B != zero_zero_rat )
% 5.52/5.83 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.52/5.83 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % nonzero_minus_divide_divide
% 5.52/5.83 thf(fact_5171_nonzero__minus__divide__right,axiom,
% 5.52/5.83 ! [B: real,A: real] :
% 5.52/5.83 ( ( B != zero_zero_real )
% 5.52/5.83 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.52/5.83 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % nonzero_minus_divide_right
% 5.52/5.83 thf(fact_5172_nonzero__minus__divide__right,axiom,
% 5.52/5.83 ! [B: complex,A: complex] :
% 5.52/5.83 ( ( B != zero_zero_complex )
% 5.52/5.83 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.52/5.83 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % nonzero_minus_divide_right
% 5.52/5.83 thf(fact_5173_nonzero__minus__divide__right,axiom,
% 5.52/5.83 ! [B: rat,A: rat] :
% 5.52/5.83 ( ( B != zero_zero_rat )
% 5.52/5.83 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.52/5.83 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % nonzero_minus_divide_right
% 5.52/5.83 thf(fact_5174_square__eq__1__iff,axiom,
% 5.52/5.83 ! [X2: int] :
% 5.52/5.83 ( ( ( times_times_int @ X2 @ X2 )
% 5.52/5.83 = one_one_int )
% 5.52/5.83 = ( ( X2 = one_one_int )
% 5.52/5.83 | ( X2
% 5.52/5.83 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % square_eq_1_iff
% 5.52/5.83 thf(fact_5175_square__eq__1__iff,axiom,
% 5.52/5.83 ! [X2: real] :
% 5.52/5.83 ( ( ( times_times_real @ X2 @ X2 )
% 5.52/5.83 = one_one_real )
% 5.52/5.83 = ( ( X2 = one_one_real )
% 5.52/5.83 | ( X2
% 5.52/5.83 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % square_eq_1_iff
% 5.52/5.83 thf(fact_5176_square__eq__1__iff,axiom,
% 5.52/5.83 ! [X2: complex] :
% 5.52/5.83 ( ( ( times_times_complex @ X2 @ X2 )
% 5.52/5.83 = one_one_complex )
% 5.52/5.83 = ( ( X2 = one_one_complex )
% 5.52/5.83 | ( X2
% 5.52/5.83 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % square_eq_1_iff
% 5.52/5.83 thf(fact_5177_square__eq__1__iff,axiom,
% 5.52/5.83 ! [X2: code_integer] :
% 5.52/5.83 ( ( ( times_3573771949741848930nteger @ X2 @ X2 )
% 5.52/5.83 = one_one_Code_integer )
% 5.52/5.83 = ( ( X2 = one_one_Code_integer )
% 5.52/5.83 | ( X2
% 5.52/5.83 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % square_eq_1_iff
% 5.52/5.83 thf(fact_5178_square__eq__1__iff,axiom,
% 5.52/5.83 ! [X2: rat] :
% 5.52/5.83 ( ( ( times_times_rat @ X2 @ X2 )
% 5.52/5.83 = one_one_rat )
% 5.52/5.83 = ( ( X2 = one_one_rat )
% 5.52/5.83 | ( X2
% 5.52/5.83 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % square_eq_1_iff
% 5.52/5.83 thf(fact_5179_group__cancel_Osub2,axiom,
% 5.52/5.83 ! [B4: int,K: int,B: int,A: int] :
% 5.52/5.83 ( ( B4
% 5.52/5.83 = ( plus_plus_int @ K @ B ) )
% 5.52/5.83 => ( ( minus_minus_int @ A @ B4 )
% 5.52/5.83 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % group_cancel.sub2
% 5.52/5.83 thf(fact_5180_group__cancel_Osub2,axiom,
% 5.52/5.83 ! [B4: real,K: real,B: real,A: real] :
% 5.52/5.83 ( ( B4
% 5.52/5.83 = ( plus_plus_real @ K @ B ) )
% 5.52/5.83 => ( ( minus_minus_real @ A @ B4 )
% 5.52/5.83 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % group_cancel.sub2
% 5.52/5.83 thf(fact_5181_group__cancel_Osub2,axiom,
% 5.52/5.83 ! [B4: complex,K: complex,B: complex,A: complex] :
% 5.52/5.83 ( ( B4
% 5.52/5.83 = ( plus_plus_complex @ K @ B ) )
% 5.52/5.83 => ( ( minus_minus_complex @ A @ B4 )
% 5.52/5.83 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % group_cancel.sub2
% 5.52/5.83 thf(fact_5182_group__cancel_Osub2,axiom,
% 5.52/5.83 ! [B4: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.52/5.83 ( ( B4
% 5.52/5.83 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.52/5.83 => ( ( minus_8373710615458151222nteger @ A @ B4 )
% 5.52/5.83 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % group_cancel.sub2
% 5.52/5.83 thf(fact_5183_group__cancel_Osub2,axiom,
% 5.52/5.83 ! [B4: rat,K: rat,B: rat,A: rat] :
% 5.52/5.83 ( ( B4
% 5.52/5.83 = ( plus_plus_rat @ K @ B ) )
% 5.52/5.83 => ( ( minus_minus_rat @ A @ B4 )
% 5.52/5.83 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % group_cancel.sub2
% 5.52/5.83 thf(fact_5184_diff__conv__add__uminus,axiom,
% 5.52/5.83 ( minus_minus_int
% 5.52/5.83 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % diff_conv_add_uminus
% 5.52/5.83 thf(fact_5185_diff__conv__add__uminus,axiom,
% 5.52/5.83 ( minus_minus_real
% 5.52/5.83 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % diff_conv_add_uminus
% 5.52/5.83 thf(fact_5186_diff__conv__add__uminus,axiom,
% 5.52/5.83 ( minus_minus_complex
% 5.52/5.83 = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % diff_conv_add_uminus
% 5.52/5.83 thf(fact_5187_diff__conv__add__uminus,axiom,
% 5.52/5.83 ( minus_8373710615458151222nteger
% 5.52/5.83 = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % diff_conv_add_uminus
% 5.52/5.83 thf(fact_5188_diff__conv__add__uminus,axiom,
% 5.52/5.83 ( minus_minus_rat
% 5.52/5.83 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % diff_conv_add_uminus
% 5.52/5.83 thf(fact_5189_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.52/5.83 ( minus_minus_int
% 5.52/5.83 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.52/5.83 thf(fact_5190_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.52/5.83 ( minus_minus_real
% 5.52/5.83 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.52/5.83 thf(fact_5191_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.52/5.83 ( minus_minus_complex
% 5.52/5.83 = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.52/5.83 thf(fact_5192_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.52/5.83 ( minus_8373710615458151222nteger
% 5.52/5.83 = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.52/5.83 thf(fact_5193_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.52/5.83 ( minus_minus_rat
% 5.52/5.83 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.52/5.83 thf(fact_5194_replicate__length__same,axiom,
% 5.52/5.83 ! [Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.52/5.83 ( ! [X4: vEBT_VEBT] :
% 5.52/5.83 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.52/5.83 => ( X4 = X2 ) )
% 5.52/5.83 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X2 )
% 5.52/5.83 = Xs2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % replicate_length_same
% 5.52/5.83 thf(fact_5195_replicate__length__same,axiom,
% 5.52/5.83 ! [Xs2: list_o,X2: $o] :
% 5.52/5.83 ( ! [X4: $o] :
% 5.52/5.83 ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 5.52/5.83 => ( X4 = X2 ) )
% 5.52/5.83 => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X2 )
% 5.52/5.83 = Xs2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % replicate_length_same
% 5.52/5.83 thf(fact_5196_replicate__length__same,axiom,
% 5.52/5.83 ! [Xs2: list_nat,X2: nat] :
% 5.52/5.83 ( ! [X4: nat] :
% 5.52/5.83 ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 5.52/5.83 => ( X4 = X2 ) )
% 5.52/5.83 => ( ( replicate_nat @ ( size_size_list_nat @ Xs2 ) @ X2 )
% 5.52/5.83 = Xs2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % replicate_length_same
% 5.52/5.83 thf(fact_5197_replicate__eqI,axiom,
% 5.52/5.83 ! [Xs2: list_option_nat,N: nat,X2: option_nat] :
% 5.52/5.83 ( ( ( size_s6086282163384603972on_nat @ Xs2 )
% 5.52/5.83 = N )
% 5.52/5.83 => ( ! [Y3: option_nat] :
% 5.52/5.83 ( ( member_option_nat @ Y3 @ ( set_option_nat2 @ Xs2 ) )
% 5.52/5.83 => ( Y3 = X2 ) )
% 5.52/5.83 => ( Xs2
% 5.52/5.83 = ( replicate_option_nat @ N @ X2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % replicate_eqI
% 5.52/5.83 thf(fact_5198_replicate__eqI,axiom,
% 5.52/5.83 ! [Xs2: list_real,N: nat,X2: real] :
% 5.52/5.83 ( ( ( size_size_list_real @ Xs2 )
% 5.52/5.83 = N )
% 5.52/5.83 => ( ! [Y3: real] :
% 5.52/5.83 ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 5.52/5.83 => ( Y3 = X2 ) )
% 5.52/5.83 => ( Xs2
% 5.52/5.83 = ( replicate_real @ N @ X2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % replicate_eqI
% 5.52/5.83 thf(fact_5199_replicate__eqI,axiom,
% 5.52/5.83 ! [Xs2: list_set_nat_rat,N: nat,X2: set_nat_rat] :
% 5.52/5.83 ( ( ( size_s3959913991096427681at_rat @ Xs2 )
% 5.52/5.83 = N )
% 5.52/5.83 => ( ! [Y3: set_nat_rat] :
% 5.52/5.83 ( ( member_set_nat_rat @ Y3 @ ( set_set_nat_rat2 @ Xs2 ) )
% 5.52/5.83 => ( Y3 = X2 ) )
% 5.52/5.83 => ( Xs2
% 5.52/5.83 = ( replic5516892415368941373at_rat @ N @ X2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % replicate_eqI
% 5.52/5.83 thf(fact_5200_replicate__eqI,axiom,
% 5.52/5.83 ! [Xs2: list_int,N: nat,X2: int] :
% 5.52/5.83 ( ( ( size_size_list_int @ Xs2 )
% 5.52/5.83 = N )
% 5.52/5.83 => ( ! [Y3: int] :
% 5.52/5.83 ( ( member_int @ Y3 @ ( set_int2 @ Xs2 ) )
% 5.52/5.83 => ( Y3 = X2 ) )
% 5.52/5.83 => ( Xs2
% 5.52/5.83 = ( replicate_int @ N @ X2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % replicate_eqI
% 5.52/5.83 thf(fact_5201_replicate__eqI,axiom,
% 5.52/5.83 ! [Xs2: list_VEBT_VEBT,N: nat,X2: vEBT_VEBT] :
% 5.52/5.83 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.52/5.83 = N )
% 5.52/5.83 => ( ! [Y3: vEBT_VEBT] :
% 5.52/5.83 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.52/5.83 => ( Y3 = X2 ) )
% 5.52/5.83 => ( Xs2
% 5.52/5.83 = ( replicate_VEBT_VEBT @ N @ X2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % replicate_eqI
% 5.52/5.83 thf(fact_5202_replicate__eqI,axiom,
% 5.52/5.83 ! [Xs2: list_o,N: nat,X2: $o] :
% 5.52/5.83 ( ( ( size_size_list_o @ Xs2 )
% 5.52/5.83 = N )
% 5.52/5.83 => ( ! [Y3: $o] :
% 5.52/5.83 ( ( member_o @ Y3 @ ( set_o2 @ Xs2 ) )
% 5.52/5.83 => ( Y3 = X2 ) )
% 5.52/5.83 => ( Xs2
% 5.52/5.83 = ( replicate_o @ N @ X2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % replicate_eqI
% 5.52/5.83 thf(fact_5203_replicate__eqI,axiom,
% 5.52/5.83 ! [Xs2: list_nat,N: nat,X2: nat] :
% 5.52/5.83 ( ( ( size_size_list_nat @ Xs2 )
% 5.52/5.83 = N )
% 5.52/5.83 => ( ! [Y3: nat] :
% 5.52/5.83 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 5.52/5.83 => ( Y3 = X2 ) )
% 5.52/5.83 => ( Xs2
% 5.52/5.83 = ( replicate_nat @ N @ X2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % replicate_eqI
% 5.52/5.83 thf(fact_5204_dvd__div__neg,axiom,
% 5.52/5.83 ! [B: int,A: int] :
% 5.52/5.83 ( ( dvd_dvd_int @ B @ A )
% 5.52/5.83 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.52/5.83 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dvd_div_neg
% 5.52/5.83 thf(fact_5205_dvd__div__neg,axiom,
% 5.52/5.83 ! [B: real,A: real] :
% 5.52/5.83 ( ( dvd_dvd_real @ B @ A )
% 5.52/5.83 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.52/5.83 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dvd_div_neg
% 5.52/5.83 thf(fact_5206_dvd__div__neg,axiom,
% 5.52/5.83 ! [B: complex,A: complex] :
% 5.52/5.83 ( ( dvd_dvd_complex @ B @ A )
% 5.52/5.83 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dvd_div_neg
% 5.52/5.83 thf(fact_5207_dvd__div__neg,axiom,
% 5.52/5.83 ! [B: code_integer,A: code_integer] :
% 5.52/5.83 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.52/5.83 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dvd_div_neg
% 5.52/5.83 thf(fact_5208_dvd__div__neg,axiom,
% 5.52/5.83 ! [B: rat,A: rat] :
% 5.52/5.83 ( ( dvd_dvd_rat @ B @ A )
% 5.52/5.83 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.52/5.83 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dvd_div_neg
% 5.52/5.83 thf(fact_5209_dvd__neg__div,axiom,
% 5.52/5.83 ! [B: int,A: int] :
% 5.52/5.83 ( ( dvd_dvd_int @ B @ A )
% 5.52/5.83 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.52/5.83 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dvd_neg_div
% 5.52/5.83 thf(fact_5210_dvd__neg__div,axiom,
% 5.52/5.83 ! [B: real,A: real] :
% 5.52/5.83 ( ( dvd_dvd_real @ B @ A )
% 5.52/5.83 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.52/5.83 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dvd_neg_div
% 5.52/5.83 thf(fact_5211_dvd__neg__div,axiom,
% 5.52/5.83 ! [B: complex,A: complex] :
% 5.52/5.83 ( ( dvd_dvd_complex @ B @ A )
% 5.52/5.83 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dvd_neg_div
% 5.52/5.83 thf(fact_5212_dvd__neg__div,axiom,
% 5.52/5.83 ! [B: code_integer,A: code_integer] :
% 5.52/5.83 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.52/5.83 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dvd_neg_div
% 5.52/5.83 thf(fact_5213_dvd__neg__div,axiom,
% 5.52/5.83 ! [B: rat,A: rat] :
% 5.52/5.83 ( ( dvd_dvd_rat @ B @ A )
% 5.52/5.83 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.52/5.83 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dvd_neg_div
% 5.52/5.83 thf(fact_5214_real__minus__mult__self__le,axiom,
% 5.52/5.83 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X2 @ X2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % real_minus_mult_self_le
% 5.52/5.83 thf(fact_5215_numeral__eq__Suc,axiom,
% 5.52/5.83 ( numeral_numeral_nat
% 5.52/5.83 = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_eq_Suc
% 5.52/5.83 thf(fact_5216_zmod__zminus1__not__zero,axiom,
% 5.52/5.83 ! [K: int,L: int] :
% 5.52/5.83 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.52/5.83 != zero_zero_int )
% 5.52/5.83 => ( ( modulo_modulo_int @ K @ L )
% 5.52/5.83 != zero_zero_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % zmod_zminus1_not_zero
% 5.52/5.83 thf(fact_5217_zmod__zminus2__not__zero,axiom,
% 5.52/5.83 ! [K: int,L: int] :
% 5.52/5.83 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 5.52/5.83 != zero_zero_int )
% 5.52/5.83 => ( ( modulo_modulo_int @ K @ L )
% 5.52/5.83 != zero_zero_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % zmod_zminus2_not_zero
% 5.52/5.83 thf(fact_5218_minus__real__def,axiom,
% 5.52/5.83 ( minus_minus_real
% 5.52/5.83 = ( ^ [X: real,Y: real] : ( plus_plus_real @ X @ ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_real_def
% 5.52/5.83 thf(fact_5219_neg__numeral__le__zero,axiom,
% 5.52/5.83 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_le_zero
% 5.52/5.83 thf(fact_5220_neg__numeral__le__zero,axiom,
% 5.52/5.83 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_le_zero
% 5.52/5.83 thf(fact_5221_neg__numeral__le__zero,axiom,
% 5.52/5.83 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_le_zero
% 5.52/5.83 thf(fact_5222_neg__numeral__le__zero,axiom,
% 5.52/5.83 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_le_zero
% 5.52/5.83 thf(fact_5223_not__zero__le__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_zero_le_neg_numeral
% 5.52/5.83 thf(fact_5224_not__zero__le__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_zero_le_neg_numeral
% 5.52/5.83 thf(fact_5225_not__zero__le__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_zero_le_neg_numeral
% 5.52/5.83 thf(fact_5226_not__zero__le__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_zero_le_neg_numeral
% 5.52/5.83 thf(fact_5227_neg__numeral__less__zero,axiom,
% 5.52/5.83 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_less_zero
% 5.52/5.83 thf(fact_5228_neg__numeral__less__zero,axiom,
% 5.52/5.83 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_less_zero
% 5.52/5.83 thf(fact_5229_neg__numeral__less__zero,axiom,
% 5.52/5.83 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_less_zero
% 5.52/5.83 thf(fact_5230_neg__numeral__less__zero,axiom,
% 5.52/5.83 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_less_zero
% 5.52/5.83 thf(fact_5231_not__zero__less__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_zero_less_neg_numeral
% 5.52/5.83 thf(fact_5232_not__zero__less__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_zero_less_neg_numeral
% 5.52/5.83 thf(fact_5233_not__zero__less__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_zero_less_neg_numeral
% 5.52/5.83 thf(fact_5234_not__zero__less__neg__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_zero_less_neg_numeral
% 5.52/5.83 thf(fact_5235_le__minus__one__simps_I3_J,axiom,
% 5.52/5.83 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % le_minus_one_simps(3)
% 5.52/5.83 thf(fact_5236_le__minus__one__simps_I3_J,axiom,
% 5.52/5.83 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.83
% 5.52/5.83 % le_minus_one_simps(3)
% 5.52/5.83 thf(fact_5237_le__minus__one__simps_I3_J,axiom,
% 5.52/5.83 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % le_minus_one_simps(3)
% 5.52/5.83 thf(fact_5238_le__minus__one__simps_I3_J,axiom,
% 5.52/5.83 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % le_minus_one_simps(3)
% 5.52/5.83 thf(fact_5239_le__minus__one__simps_I1_J,axiom,
% 5.52/5.83 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.52/5.83
% 5.52/5.83 % le_minus_one_simps(1)
% 5.52/5.83 thf(fact_5240_le__minus__one__simps_I1_J,axiom,
% 5.52/5.83 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.52/5.83
% 5.52/5.83 % le_minus_one_simps(1)
% 5.52/5.83 thf(fact_5241_le__minus__one__simps_I1_J,axiom,
% 5.52/5.83 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.52/5.83
% 5.52/5.83 % le_minus_one_simps(1)
% 5.52/5.83 thf(fact_5242_le__minus__one__simps_I1_J,axiom,
% 5.52/5.83 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.52/5.83
% 5.52/5.83 % le_minus_one_simps(1)
% 5.52/5.83 thf(fact_5243_less__minus__one__simps_I3_J,axiom,
% 5.52/5.83 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(3)
% 5.52/5.83 thf(fact_5244_less__minus__one__simps_I3_J,axiom,
% 5.52/5.83 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(3)
% 5.52/5.83 thf(fact_5245_less__minus__one__simps_I3_J,axiom,
% 5.52/5.83 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(3)
% 5.52/5.83 thf(fact_5246_less__minus__one__simps_I3_J,axiom,
% 5.52/5.83 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(3)
% 5.52/5.83 thf(fact_5247_less__minus__one__simps_I1_J,axiom,
% 5.52/5.83 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(1)
% 5.52/5.83 thf(fact_5248_less__minus__one__simps_I1_J,axiom,
% 5.52/5.83 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(1)
% 5.52/5.83 thf(fact_5249_less__minus__one__simps_I1_J,axiom,
% 5.52/5.83 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(1)
% 5.52/5.83 thf(fact_5250_less__minus__one__simps_I1_J,axiom,
% 5.52/5.83 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.52/5.83
% 5.52/5.83 % less_minus_one_simps(1)
% 5.52/5.83 thf(fact_5251_neg__numeral__le__one,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_le_one
% 5.52/5.83 thf(fact_5252_neg__numeral__le__one,axiom,
% 5.52/5.83 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_le_one
% 5.52/5.83 thf(fact_5253_neg__numeral__le__one,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_le_one
% 5.52/5.83 thf(fact_5254_neg__numeral__le__one,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_le_one
% 5.52/5.83 thf(fact_5255_neg__one__le__numeral,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_le_numeral
% 5.52/5.83 thf(fact_5256_neg__one__le__numeral,axiom,
% 5.52/5.83 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_le_numeral
% 5.52/5.83 thf(fact_5257_neg__one__le__numeral,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_le_numeral
% 5.52/5.83 thf(fact_5258_neg__one__le__numeral,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_le_numeral
% 5.52/5.83 thf(fact_5259_neg__numeral__le__neg__one,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_le_neg_one
% 5.52/5.83 thf(fact_5260_neg__numeral__le__neg__one,axiom,
% 5.52/5.83 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_le_neg_one
% 5.52/5.83 thf(fact_5261_neg__numeral__le__neg__one,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_le_neg_one
% 5.52/5.83 thf(fact_5262_neg__numeral__le__neg__one,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_le_neg_one
% 5.52/5.83 thf(fact_5263_not__numeral__le__neg__one,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_numeral_le_neg_one
% 5.52/5.83 thf(fact_5264_not__numeral__le__neg__one,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_numeral_le_neg_one
% 5.52/5.83 thf(fact_5265_not__numeral__le__neg__one,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_numeral_le_neg_one
% 5.52/5.83 thf(fact_5266_not__numeral__le__neg__one,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_numeral_le_neg_one
% 5.52/5.83 thf(fact_5267_not__one__le__neg__numeral,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_one_le_neg_numeral
% 5.52/5.83 thf(fact_5268_not__one__le__neg__numeral,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_one_le_neg_numeral
% 5.52/5.83 thf(fact_5269_not__one__le__neg__numeral,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_one_le_neg_numeral
% 5.52/5.83 thf(fact_5270_not__one__le__neg__numeral,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_one_le_neg_numeral
% 5.52/5.83 thf(fact_5271_neg__numeral__less__one,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_less_one
% 5.52/5.83 thf(fact_5272_neg__numeral__less__one,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_less_one
% 5.52/5.83 thf(fact_5273_neg__numeral__less__one,axiom,
% 5.52/5.83 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_less_one
% 5.52/5.83 thf(fact_5274_neg__numeral__less__one,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.52/5.83
% 5.52/5.83 % neg_numeral_less_one
% 5.52/5.83 thf(fact_5275_neg__one__less__numeral,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_less_numeral
% 5.52/5.83 thf(fact_5276_neg__one__less__numeral,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_less_numeral
% 5.52/5.83 thf(fact_5277_neg__one__less__numeral,axiom,
% 5.52/5.83 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_less_numeral
% 5.52/5.83 thf(fact_5278_neg__one__less__numeral,axiom,
% 5.52/5.83 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_less_numeral
% 5.52/5.83 thf(fact_5279_not__numeral__less__neg__one,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_numeral_less_neg_one
% 5.52/5.83 thf(fact_5280_not__numeral__less__neg__one,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_numeral_less_neg_one
% 5.52/5.83 thf(fact_5281_not__numeral__less__neg__one,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_numeral_less_neg_one
% 5.52/5.83 thf(fact_5282_not__numeral__less__neg__one,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_numeral_less_neg_one
% 5.52/5.83 thf(fact_5283_not__one__less__neg__numeral,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_one_less_neg_numeral
% 5.52/5.83 thf(fact_5284_not__one__less__neg__numeral,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_one_less_neg_numeral
% 5.52/5.83 thf(fact_5285_not__one__less__neg__numeral,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_one_less_neg_numeral
% 5.52/5.83 thf(fact_5286_not__one__less__neg__numeral,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_one_less_neg_numeral
% 5.52/5.83 thf(fact_5287_not__neg__one__less__neg__numeral,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_neg_one_less_neg_numeral
% 5.52/5.83 thf(fact_5288_not__neg__one__less__neg__numeral,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_neg_one_less_neg_numeral
% 5.52/5.83 thf(fact_5289_not__neg__one__less__neg__numeral,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_neg_one_less_neg_numeral
% 5.52/5.83 thf(fact_5290_not__neg__one__less__neg__numeral,axiom,
% 5.52/5.83 ! [M: num] :
% 5.52/5.83 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % not_neg_one_less_neg_numeral
% 5.52/5.83 thf(fact_5291_nonzero__neg__divide__eq__eq2,axiom,
% 5.52/5.83 ! [B: real,C: real,A: real] :
% 5.52/5.83 ( ( B != zero_zero_real )
% 5.52/5.83 => ( ( C
% 5.52/5.83 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.52/5.83 = ( ( times_times_real @ C @ B )
% 5.52/5.83 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % nonzero_neg_divide_eq_eq2
% 5.52/5.83 thf(fact_5292_nonzero__neg__divide__eq__eq2,axiom,
% 5.52/5.83 ! [B: complex,C: complex,A: complex] :
% 5.52/5.83 ( ( B != zero_zero_complex )
% 5.52/5.83 => ( ( C
% 5.52/5.83 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.52/5.83 = ( ( times_times_complex @ C @ B )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % nonzero_neg_divide_eq_eq2
% 5.52/5.83 thf(fact_5293_nonzero__neg__divide__eq__eq2,axiom,
% 5.52/5.83 ! [B: rat,C: rat,A: rat] :
% 5.52/5.83 ( ( B != zero_zero_rat )
% 5.52/5.83 => ( ( C
% 5.52/5.83 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.52/5.83 = ( ( times_times_rat @ C @ B )
% 5.52/5.83 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % nonzero_neg_divide_eq_eq2
% 5.52/5.83 thf(fact_5294_nonzero__neg__divide__eq__eq,axiom,
% 5.52/5.83 ! [B: real,A: real,C: real] :
% 5.52/5.83 ( ( B != zero_zero_real )
% 5.52/5.83 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.52/5.83 = C )
% 5.52/5.83 = ( ( uminus_uminus_real @ A )
% 5.52/5.83 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % nonzero_neg_divide_eq_eq
% 5.52/5.83 thf(fact_5295_nonzero__neg__divide__eq__eq,axiom,
% 5.52/5.83 ! [B: complex,A: complex,C: complex] :
% 5.52/5.83 ( ( B != zero_zero_complex )
% 5.52/5.83 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.52/5.83 = C )
% 5.52/5.83 = ( ( uminus1482373934393186551omplex @ A )
% 5.52/5.83 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % nonzero_neg_divide_eq_eq
% 5.52/5.83 thf(fact_5296_nonzero__neg__divide__eq__eq,axiom,
% 5.52/5.83 ! [B: rat,A: rat,C: rat] :
% 5.52/5.83 ( ( B != zero_zero_rat )
% 5.52/5.83 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.52/5.83 = C )
% 5.52/5.83 = ( ( uminus_uminus_rat @ A )
% 5.52/5.83 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % nonzero_neg_divide_eq_eq
% 5.52/5.83 thf(fact_5297_minus__divide__eq__eq,axiom,
% 5.52/5.83 ! [B: real,C: real,A: real] :
% 5.52/5.83 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.52/5.83 = A )
% 5.52/5.83 = ( ( ( C != zero_zero_real )
% 5.52/5.83 => ( ( uminus_uminus_real @ B )
% 5.52/5.83 = ( times_times_real @ A @ C ) ) )
% 5.52/5.83 & ( ( C = zero_zero_real )
% 5.52/5.83 => ( A = zero_zero_real ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_eq_eq
% 5.52/5.83 thf(fact_5298_minus__divide__eq__eq,axiom,
% 5.52/5.83 ! [B: complex,C: complex,A: complex] :
% 5.52/5.83 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.52/5.83 = A )
% 5.52/5.83 = ( ( ( C != zero_zero_complex )
% 5.52/5.83 => ( ( uminus1482373934393186551omplex @ B )
% 5.52/5.83 = ( times_times_complex @ A @ C ) ) )
% 5.52/5.83 & ( ( C = zero_zero_complex )
% 5.52/5.83 => ( A = zero_zero_complex ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_eq_eq
% 5.52/5.83 thf(fact_5299_minus__divide__eq__eq,axiom,
% 5.52/5.83 ! [B: rat,C: rat,A: rat] :
% 5.52/5.83 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.83 = A )
% 5.52/5.83 = ( ( ( C != zero_zero_rat )
% 5.52/5.83 => ( ( uminus_uminus_rat @ B )
% 5.52/5.83 = ( times_times_rat @ A @ C ) ) )
% 5.52/5.83 & ( ( C = zero_zero_rat )
% 5.52/5.83 => ( A = zero_zero_rat ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_eq_eq
% 5.52/5.83 thf(fact_5300_eq__minus__divide__eq,axiom,
% 5.52/5.83 ! [A: real,B: real,C: real] :
% 5.52/5.83 ( ( A
% 5.52/5.83 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.52/5.83 = ( ( ( C != zero_zero_real )
% 5.52/5.83 => ( ( times_times_real @ A @ C )
% 5.52/5.83 = ( uminus_uminus_real @ B ) ) )
% 5.52/5.83 & ( ( C = zero_zero_real )
% 5.52/5.83 => ( A = zero_zero_real ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % eq_minus_divide_eq
% 5.52/5.83 thf(fact_5301_eq__minus__divide__eq,axiom,
% 5.52/5.83 ! [A: complex,B: complex,C: complex] :
% 5.52/5.83 ( ( A
% 5.52/5.83 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.52/5.83 = ( ( ( C != zero_zero_complex )
% 5.52/5.83 => ( ( times_times_complex @ A @ C )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.52/5.83 & ( ( C = zero_zero_complex )
% 5.52/5.83 => ( A = zero_zero_complex ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % eq_minus_divide_eq
% 5.52/5.83 thf(fact_5302_eq__minus__divide__eq,axiom,
% 5.52/5.83 ! [A: rat,B: rat,C: rat] :
% 5.52/5.83 ( ( A
% 5.52/5.83 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.52/5.83 = ( ( ( C != zero_zero_rat )
% 5.52/5.83 => ( ( times_times_rat @ A @ C )
% 5.52/5.83 = ( uminus_uminus_rat @ B ) ) )
% 5.52/5.83 & ( ( C = zero_zero_rat )
% 5.52/5.83 => ( A = zero_zero_rat ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % eq_minus_divide_eq
% 5.52/5.83 thf(fact_5303_divide__eq__minus__1__iff,axiom,
% 5.52/5.83 ! [A: real,B: real] :
% 5.52/5.83 ( ( ( divide_divide_real @ A @ B )
% 5.52/5.83 = ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.83 = ( ( B != zero_zero_real )
% 5.52/5.83 & ( A
% 5.52/5.83 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % divide_eq_minus_1_iff
% 5.52/5.83 thf(fact_5304_divide__eq__minus__1__iff,axiom,
% 5.52/5.83 ! [A: complex,B: complex] :
% 5.52/5.83 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.83 = ( ( B != zero_zero_complex )
% 5.52/5.83 & ( A
% 5.52/5.83 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % divide_eq_minus_1_iff
% 5.52/5.83 thf(fact_5305_divide__eq__minus__1__iff,axiom,
% 5.52/5.83 ! [A: rat,B: rat] :
% 5.52/5.83 ( ( ( divide_divide_rat @ A @ B )
% 5.52/5.83 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.83 = ( ( B != zero_zero_rat )
% 5.52/5.83 & ( A
% 5.52/5.83 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % divide_eq_minus_1_iff
% 5.52/5.83 thf(fact_5306_mult__1s__ring__1_I2_J,axiom,
% 5.52/5.83 ! [B: int] :
% 5.52/5.83 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.52/5.83 = ( uminus_uminus_int @ B ) ) ).
% 5.52/5.83
% 5.52/5.83 % mult_1s_ring_1(2)
% 5.52/5.83 thf(fact_5307_mult__1s__ring__1_I2_J,axiom,
% 5.52/5.83 ! [B: real] :
% 5.52/5.83 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.52/5.83 = ( uminus_uminus_real @ B ) ) ).
% 5.52/5.83
% 5.52/5.83 % mult_1s_ring_1(2)
% 5.52/5.83 thf(fact_5308_mult__1s__ring__1_I2_J,axiom,
% 5.52/5.83 ! [B: complex] :
% 5.52/5.83 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.52/5.83
% 5.52/5.83 % mult_1s_ring_1(2)
% 5.52/5.83 thf(fact_5309_mult__1s__ring__1_I2_J,axiom,
% 5.52/5.83 ! [B: code_integer] :
% 5.52/5.83 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.52/5.83
% 5.52/5.83 % mult_1s_ring_1(2)
% 5.52/5.83 thf(fact_5310_mult__1s__ring__1_I2_J,axiom,
% 5.52/5.83 ! [B: rat] :
% 5.52/5.83 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.52/5.83 = ( uminus_uminus_rat @ B ) ) ).
% 5.52/5.83
% 5.52/5.83 % mult_1s_ring_1(2)
% 5.52/5.83 thf(fact_5311_mult__1s__ring__1_I1_J,axiom,
% 5.52/5.83 ! [B: int] :
% 5.52/5.83 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.52/5.83 = ( uminus_uminus_int @ B ) ) ).
% 5.52/5.83
% 5.52/5.83 % mult_1s_ring_1(1)
% 5.52/5.83 thf(fact_5312_mult__1s__ring__1_I1_J,axiom,
% 5.52/5.83 ! [B: real] :
% 5.52/5.83 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.52/5.83 = ( uminus_uminus_real @ B ) ) ).
% 5.52/5.83
% 5.52/5.83 % mult_1s_ring_1(1)
% 5.52/5.83 thf(fact_5313_mult__1s__ring__1_I1_J,axiom,
% 5.52/5.83 ! [B: complex] :
% 5.52/5.83 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.52/5.83
% 5.52/5.83 % mult_1s_ring_1(1)
% 5.52/5.83 thf(fact_5314_mult__1s__ring__1_I1_J,axiom,
% 5.52/5.83 ! [B: code_integer] :
% 5.52/5.83 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.52/5.83
% 5.52/5.83 % mult_1s_ring_1(1)
% 5.52/5.83 thf(fact_5315_mult__1s__ring__1_I1_J,axiom,
% 5.52/5.83 ! [B: rat] :
% 5.52/5.83 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.52/5.83 = ( uminus_uminus_rat @ B ) ) ).
% 5.52/5.83
% 5.52/5.83 % mult_1s_ring_1(1)
% 5.52/5.83 thf(fact_5316_uminus__numeral__One,axiom,
% 5.52/5.83 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.52/5.83 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % uminus_numeral_One
% 5.52/5.83 thf(fact_5317_uminus__numeral__One,axiom,
% 5.52/5.83 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.52/5.83 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % uminus_numeral_One
% 5.52/5.83 thf(fact_5318_uminus__numeral__One,axiom,
% 5.52/5.83 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.52/5.83
% 5.52/5.83 % uminus_numeral_One
% 5.52/5.83 thf(fact_5319_uminus__numeral__One,axiom,
% 5.52/5.83 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.83
% 5.52/5.83 % uminus_numeral_One
% 5.52/5.83 thf(fact_5320_uminus__numeral__One,axiom,
% 5.52/5.83 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.52/5.83 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % uminus_numeral_One
% 5.52/5.83 thf(fact_5321_power__minus,axiom,
% 5.52/5.83 ! [A: int,N: nat] :
% 5.52/5.83 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.52/5.83 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus
% 5.52/5.83 thf(fact_5322_power__minus,axiom,
% 5.52/5.83 ! [A: real,N: nat] :
% 5.52/5.83 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.52/5.83 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus
% 5.52/5.83 thf(fact_5323_power__minus,axiom,
% 5.52/5.83 ! [A: complex,N: nat] :
% 5.52/5.83 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.52/5.83 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus
% 5.52/5.83 thf(fact_5324_power__minus,axiom,
% 5.52/5.83 ! [A: code_integer,N: nat] :
% 5.52/5.83 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.52/5.83 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus
% 5.52/5.83 thf(fact_5325_power__minus,axiom,
% 5.52/5.83 ! [A: rat,N: nat] :
% 5.52/5.83 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.52/5.83 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus
% 5.52/5.83 thf(fact_5326_power__minus__Bit0,axiom,
% 5.52/5.83 ! [X2: int,K: num] :
% 5.52/5.83 ( ( power_power_int @ ( uminus_uminus_int @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.52/5.83 = ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus_Bit0
% 5.52/5.83 thf(fact_5327_power__minus__Bit0,axiom,
% 5.52/5.83 ! [X2: real,K: num] :
% 5.52/5.83 ( ( power_power_real @ ( uminus_uminus_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.52/5.83 = ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus_Bit0
% 5.52/5.83 thf(fact_5328_power__minus__Bit0,axiom,
% 5.52/5.83 ! [X2: complex,K: num] :
% 5.52/5.83 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.52/5.83 = ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus_Bit0
% 5.52/5.83 thf(fact_5329_power__minus__Bit0,axiom,
% 5.52/5.83 ! [X2: code_integer,K: num] :
% 5.52/5.83 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.52/5.83 = ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus_Bit0
% 5.52/5.83 thf(fact_5330_power__minus__Bit0,axiom,
% 5.52/5.83 ! [X2: rat,K: num] :
% 5.52/5.83 ( ( power_power_rat @ ( uminus_uminus_rat @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.52/5.83 = ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus_Bit0
% 5.52/5.83 thf(fact_5331_power__minus__Bit1,axiom,
% 5.52/5.83 ! [X2: int,K: num] :
% 5.52/5.83 ( ( power_power_int @ ( uminus_uminus_int @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.52/5.83 = ( uminus_uminus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus_Bit1
% 5.52/5.83 thf(fact_5332_power__minus__Bit1,axiom,
% 5.52/5.83 ! [X2: real,K: num] :
% 5.52/5.83 ( ( power_power_real @ ( uminus_uminus_real @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.52/5.83 = ( uminus_uminus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus_Bit1
% 5.52/5.83 thf(fact_5333_power__minus__Bit1,axiom,
% 5.52/5.83 ! [X2: complex,K: num] :
% 5.52/5.83 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus_Bit1
% 5.52/5.83 thf(fact_5334_power__minus__Bit1,axiom,
% 5.52/5.83 ! [X2: code_integer,K: num] :
% 5.52/5.83 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus_Bit1
% 5.52/5.83 thf(fact_5335_power__minus__Bit1,axiom,
% 5.52/5.83 ! [X2: rat,K: num] :
% 5.52/5.83 ( ( power_power_rat @ ( uminus_uminus_rat @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.52/5.83 = ( uminus_uminus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus_Bit1
% 5.52/5.83 thf(fact_5336_real__add__less__0__iff,axiom,
% 5.52/5.83 ! [X2: real,Y2: real] :
% 5.52/5.83 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y2 ) @ zero_zero_real )
% 5.52/5.83 = ( ord_less_real @ Y2 @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % real_add_less_0_iff
% 5.52/5.83 thf(fact_5337_real__0__less__add__iff,axiom,
% 5.52/5.83 ! [X2: real,Y2: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.52/5.83 = ( ord_less_real @ ( uminus_uminus_real @ X2 ) @ Y2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % real_0_less_add_iff
% 5.52/5.83 thf(fact_5338_real__0__le__add__iff,axiom,
% 5.52/5.83 ! [X2: real,Y2: real] :
% 5.52/5.83 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.52/5.83 = ( ord_less_eq_real @ ( uminus_uminus_real @ X2 ) @ Y2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % real_0_le_add_iff
% 5.52/5.83 thf(fact_5339_real__add__le__0__iff,axiom,
% 5.52/5.83 ! [X2: real,Y2: real] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( plus_plus_real @ X2 @ Y2 ) @ zero_zero_real )
% 5.52/5.83 = ( ord_less_eq_real @ Y2 @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % real_add_le_0_iff
% 5.52/5.83 thf(fact_5340_pred__numeral__def,axiom,
% 5.52/5.83 ( pred_numeral
% 5.52/5.83 = ( ^ [K2: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ one_one_nat ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % pred_numeral_def
% 5.52/5.83 thf(fact_5341_zmod__zminus2__eq__if,axiom,
% 5.52/5.83 ! [A: int,B: int] :
% 5.52/5.83 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.52/5.83 = zero_zero_int )
% 5.52/5.83 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.52/5.83 = zero_zero_int ) )
% 5.52/5.83 & ( ( ( modulo_modulo_int @ A @ B )
% 5.52/5.83 != zero_zero_int )
% 5.52/5.83 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.52/5.83 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % zmod_zminus2_eq_if
% 5.52/5.83 thf(fact_5342_zmod__zminus1__eq__if,axiom,
% 5.52/5.83 ! [A: int,B: int] :
% 5.52/5.83 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.52/5.83 = zero_zero_int )
% 5.52/5.83 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.52/5.83 = zero_zero_int ) )
% 5.52/5.83 & ( ( ( modulo_modulo_int @ A @ B )
% 5.52/5.83 != zero_zero_int )
% 5.52/5.83 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.52/5.83 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % zmod_zminus1_eq_if
% 5.52/5.83 thf(fact_5343_pos__minus__divide__less__eq,axiom,
% 5.52/5.83 ! [C: real,B: real,A: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.52/5.83 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % pos_minus_divide_less_eq
% 5.52/5.83 thf(fact_5344_pos__minus__divide__less__eq,axiom,
% 5.52/5.83 ! [C: rat,B: rat,A: rat] :
% 5.52/5.83 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.52/5.83 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % pos_minus_divide_less_eq
% 5.52/5.83 thf(fact_5345_pos__less__minus__divide__eq,axiom,
% 5.52/5.83 ! [C: real,A: real,B: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.52/5.83 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % pos_less_minus_divide_eq
% 5.52/5.83 thf(fact_5346_pos__less__minus__divide__eq,axiom,
% 5.52/5.83 ! [C: rat,A: rat,B: rat] :
% 5.52/5.83 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.52/5.83 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % pos_less_minus_divide_eq
% 5.52/5.83 thf(fact_5347_neg__minus__divide__less__eq,axiom,
% 5.52/5.83 ! [C: real,B: real,A: real] :
% 5.52/5.83 ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.52/5.83 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_minus_divide_less_eq
% 5.52/5.83 thf(fact_5348_neg__minus__divide__less__eq,axiom,
% 5.52/5.83 ! [C: rat,B: rat,A: rat] :
% 5.52/5.83 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.52/5.83 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_minus_divide_less_eq
% 5.52/5.83 thf(fact_5349_neg__less__minus__divide__eq,axiom,
% 5.52/5.83 ! [C: real,A: real,B: real] :
% 5.52/5.83 ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.52/5.83 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_less_minus_divide_eq
% 5.52/5.83 thf(fact_5350_neg__less__minus__divide__eq,axiom,
% 5.52/5.83 ! [C: rat,A: rat,B: rat] :
% 5.52/5.83 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.52/5.83 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_less_minus_divide_eq
% 5.52/5.83 thf(fact_5351_minus__divide__less__eq,axiom,
% 5.52/5.83 ! [B: real,C: real,A: real] :
% 5.52/5.83 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.52/5.83 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_less_eq
% 5.52/5.83 thf(fact_5352_minus__divide__less__eq,axiom,
% 5.52/5.83 ! [B: rat,C: rat,A: rat] :
% 5.52/5.83 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.52/5.83 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_less_eq
% 5.52/5.83 thf(fact_5353_less__minus__divide__eq,axiom,
% 5.52/5.83 ! [A: real,B: real,C: real] :
% 5.52/5.83 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.52/5.83 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % less_minus_divide_eq
% 5.52/5.83 thf(fact_5354_less__minus__divide__eq,axiom,
% 5.52/5.83 ! [A: rat,B: rat,C: rat] :
% 5.52/5.83 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.52/5.83 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % less_minus_divide_eq
% 5.52/5.83 thf(fact_5355_divide__eq__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [B: real,C: real,W: num] :
% 5.52/5.83 ( ( ( divide_divide_real @ B @ C )
% 5.52/5.83 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.52/5.83 = ( ( ( C != zero_zero_real )
% 5.52/5.83 => ( B
% 5.52/5.83 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.52/5.83 & ( ( C = zero_zero_real )
% 5.52/5.83 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.52/5.83 = zero_zero_real ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % divide_eq_eq_numeral(2)
% 5.52/5.83 thf(fact_5356_divide__eq__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [B: complex,C: complex,W: num] :
% 5.52/5.83 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.52/5.83 = ( ( ( C != zero_zero_complex )
% 5.52/5.83 => ( B
% 5.52/5.83 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.52/5.83 & ( ( C = zero_zero_complex )
% 5.52/5.83 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.52/5.83 = zero_zero_complex ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % divide_eq_eq_numeral(2)
% 5.52/5.83 thf(fact_5357_divide__eq__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [B: rat,C: rat,W: num] :
% 5.52/5.83 ( ( ( divide_divide_rat @ B @ C )
% 5.52/5.83 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.52/5.83 = ( ( ( C != zero_zero_rat )
% 5.52/5.83 => ( B
% 5.52/5.83 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.52/5.83 & ( ( C = zero_zero_rat )
% 5.52/5.83 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.52/5.83 = zero_zero_rat ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % divide_eq_eq_numeral(2)
% 5.52/5.83 thf(fact_5358_eq__divide__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [W: num,B: real,C: real] :
% 5.52/5.83 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.52/5.83 = ( divide_divide_real @ B @ C ) )
% 5.52/5.83 = ( ( ( C != zero_zero_real )
% 5.52/5.83 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.52/5.83 = B ) )
% 5.52/5.83 & ( ( C = zero_zero_real )
% 5.52/5.83 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.52/5.83 = zero_zero_real ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % eq_divide_eq_numeral(2)
% 5.52/5.83 thf(fact_5359_eq__divide__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [W: num,B: complex,C: complex] :
% 5.52/5.83 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.52/5.83 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.52/5.83 = ( ( ( C != zero_zero_complex )
% 5.52/5.83 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.52/5.83 = B ) )
% 5.52/5.83 & ( ( C = zero_zero_complex )
% 5.52/5.83 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.52/5.83 = zero_zero_complex ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % eq_divide_eq_numeral(2)
% 5.52/5.83 thf(fact_5360_eq__divide__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [W: num,B: rat,C: rat] :
% 5.52/5.83 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.52/5.83 = ( divide_divide_rat @ B @ C ) )
% 5.52/5.83 = ( ( ( C != zero_zero_rat )
% 5.52/5.83 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.52/5.83 = B ) )
% 5.52/5.83 & ( ( C = zero_zero_rat )
% 5.52/5.83 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.52/5.83 = zero_zero_rat ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % eq_divide_eq_numeral(2)
% 5.52/5.83 thf(fact_5361_add__divide__eq__if__simps_I3_J,axiom,
% 5.52/5.83 ! [Z: real,A: real,B: real] :
% 5.52/5.83 ( ( ( Z = zero_zero_real )
% 5.52/5.83 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.52/5.83 = B ) )
% 5.52/5.83 & ( ( Z != zero_zero_real )
% 5.52/5.83 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.52/5.83 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_divide_eq_if_simps(3)
% 5.52/5.83 thf(fact_5362_add__divide__eq__if__simps_I3_J,axiom,
% 5.52/5.83 ! [Z: complex,A: complex,B: complex] :
% 5.52/5.83 ( ( ( Z = zero_zero_complex )
% 5.52/5.83 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.52/5.83 = B ) )
% 5.52/5.83 & ( ( Z != zero_zero_complex )
% 5.52/5.83 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.52/5.83 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_divide_eq_if_simps(3)
% 5.52/5.83 thf(fact_5363_add__divide__eq__if__simps_I3_J,axiom,
% 5.52/5.83 ! [Z: rat,A: rat,B: rat] :
% 5.52/5.83 ( ( ( Z = zero_zero_rat )
% 5.52/5.83 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.52/5.83 = B ) )
% 5.52/5.83 & ( ( Z != zero_zero_rat )
% 5.52/5.83 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.52/5.83 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_divide_eq_if_simps(3)
% 5.52/5.83 thf(fact_5364_minus__divide__add__eq__iff,axiom,
% 5.52/5.83 ! [Z: real,X2: real,Y2: real] :
% 5.52/5.83 ( ( Z != zero_zero_real )
% 5.52/5.83 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X2 @ Z ) ) @ Y2 )
% 5.52/5.83 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_add_eq_iff
% 5.52/5.83 thf(fact_5365_minus__divide__add__eq__iff,axiom,
% 5.52/5.83 ! [Z: complex,X2: complex,Y2: complex] :
% 5.52/5.83 ( ( Z != zero_zero_complex )
% 5.52/5.83 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X2 @ Z ) ) @ Y2 )
% 5.52/5.83 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_add_eq_iff
% 5.52/5.83 thf(fact_5366_minus__divide__add__eq__iff,axiom,
% 5.52/5.83 ! [Z: rat,X2: rat,Y2: rat] :
% 5.52/5.83 ( ( Z != zero_zero_rat )
% 5.52/5.83 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z ) ) @ Y2 )
% 5.52/5.83 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_add_eq_iff
% 5.52/5.83 thf(fact_5367_subset__decode__imp__le,axiom,
% 5.52/5.83 ! [M: nat,N: nat] :
% 5.52/5.83 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 5.52/5.83 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.83
% 5.52/5.83 % subset_decode_imp_le
% 5.52/5.83 thf(fact_5368_minus__divide__diff__eq__iff,axiom,
% 5.52/5.83 ! [Z: real,X2: real,Y2: real] :
% 5.52/5.83 ( ( Z != zero_zero_real )
% 5.52/5.83 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X2 @ Z ) ) @ Y2 )
% 5.52/5.83 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_diff_eq_iff
% 5.52/5.83 thf(fact_5369_minus__divide__diff__eq__iff,axiom,
% 5.52/5.83 ! [Z: complex,X2: complex,Y2: complex] :
% 5.52/5.83 ( ( Z != zero_zero_complex )
% 5.52/5.83 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X2 @ Z ) ) @ Y2 )
% 5.52/5.83 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_diff_eq_iff
% 5.52/5.83 thf(fact_5370_minus__divide__diff__eq__iff,axiom,
% 5.52/5.83 ! [Z: rat,X2: rat,Y2: rat] :
% 5.52/5.83 ( ( Z != zero_zero_rat )
% 5.52/5.83 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z ) ) @ Y2 )
% 5.52/5.83 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_diff_eq_iff
% 5.52/5.83 thf(fact_5371_add__divide__eq__if__simps_I5_J,axiom,
% 5.52/5.83 ! [Z: real,A: real,B: real] :
% 5.52/5.83 ( ( ( Z = zero_zero_real )
% 5.52/5.83 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.52/5.83 = ( uminus_uminus_real @ B ) ) )
% 5.52/5.83 & ( ( Z != zero_zero_real )
% 5.52/5.83 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.52/5.83 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_divide_eq_if_simps(5)
% 5.52/5.83 thf(fact_5372_add__divide__eq__if__simps_I5_J,axiom,
% 5.52/5.83 ! [Z: complex,A: complex,B: complex] :
% 5.52/5.83 ( ( ( Z = zero_zero_complex )
% 5.52/5.83 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.52/5.83 & ( ( Z != zero_zero_complex )
% 5.52/5.83 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.52/5.83 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_divide_eq_if_simps(5)
% 5.52/5.83 thf(fact_5373_add__divide__eq__if__simps_I5_J,axiom,
% 5.52/5.83 ! [Z: rat,A: rat,B: rat] :
% 5.52/5.83 ( ( ( Z = zero_zero_rat )
% 5.52/5.83 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.52/5.83 = ( uminus_uminus_rat @ B ) ) )
% 5.52/5.83 & ( ( Z != zero_zero_rat )
% 5.52/5.83 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.52/5.83 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_divide_eq_if_simps(5)
% 5.52/5.83 thf(fact_5374_add__divide__eq__if__simps_I6_J,axiom,
% 5.52/5.83 ! [Z: real,A: real,B: real] :
% 5.52/5.83 ( ( ( Z = zero_zero_real )
% 5.52/5.83 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.52/5.83 = ( uminus_uminus_real @ B ) ) )
% 5.52/5.83 & ( ( Z != zero_zero_real )
% 5.52/5.83 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.52/5.83 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_divide_eq_if_simps(6)
% 5.52/5.83 thf(fact_5375_add__divide__eq__if__simps_I6_J,axiom,
% 5.52/5.83 ! [Z: complex,A: complex,B: complex] :
% 5.52/5.83 ( ( ( Z = zero_zero_complex )
% 5.52/5.83 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.52/5.83 & ( ( Z != zero_zero_complex )
% 5.52/5.83 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.52/5.83 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_divide_eq_if_simps(6)
% 5.52/5.83 thf(fact_5376_add__divide__eq__if__simps_I6_J,axiom,
% 5.52/5.83 ! [Z: rat,A: rat,B: rat] :
% 5.52/5.83 ( ( ( Z = zero_zero_rat )
% 5.52/5.83 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.52/5.83 = ( uminus_uminus_rat @ B ) ) )
% 5.52/5.83 & ( ( Z != zero_zero_rat )
% 5.52/5.83 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.52/5.83 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % add_divide_eq_if_simps(6)
% 5.52/5.83 thf(fact_5377_even__minus,axiom,
% 5.52/5.83 ! [A: int] :
% 5.52/5.83 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.52/5.83 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.52/5.83
% 5.52/5.83 % even_minus
% 5.52/5.83 thf(fact_5378_even__minus,axiom,
% 5.52/5.83 ! [A: code_integer] :
% 5.52/5.83 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.83 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.52/5.83
% 5.52/5.83 % even_minus
% 5.52/5.83 thf(fact_5379_power2__eq__iff,axiom,
% 5.52/5.83 ! [X2: int,Y2: int] :
% 5.52/5.83 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.83 = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.83 = ( ( X2 = Y2 )
% 5.52/5.83 | ( X2
% 5.52/5.83 = ( uminus_uminus_int @ Y2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power2_eq_iff
% 5.52/5.83 thf(fact_5380_power2__eq__iff,axiom,
% 5.52/5.83 ! [X2: real,Y2: real] :
% 5.52/5.83 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.83 = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.83 = ( ( X2 = Y2 )
% 5.52/5.83 | ( X2
% 5.52/5.83 = ( uminus_uminus_real @ Y2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power2_eq_iff
% 5.52/5.83 thf(fact_5381_power2__eq__iff,axiom,
% 5.52/5.83 ! [X2: complex,Y2: complex] :
% 5.52/5.83 ( ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.83 = ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.83 = ( ( X2 = Y2 )
% 5.52/5.83 | ( X2
% 5.52/5.83 = ( uminus1482373934393186551omplex @ Y2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power2_eq_iff
% 5.52/5.83 thf(fact_5382_power2__eq__iff,axiom,
% 5.52/5.83 ! [X2: code_integer,Y2: code_integer] :
% 5.52/5.83 ( ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.83 = ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.83 = ( ( X2 = Y2 )
% 5.52/5.83 | ( X2
% 5.52/5.83 = ( uminus1351360451143612070nteger @ Y2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power2_eq_iff
% 5.52/5.83 thf(fact_5383_power2__eq__iff,axiom,
% 5.52/5.83 ! [X2: rat,Y2: rat] :
% 5.52/5.83 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.83 = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.83 = ( ( X2 = Y2 )
% 5.52/5.83 | ( X2
% 5.52/5.83 = ( uminus_uminus_rat @ Y2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power2_eq_iff
% 5.52/5.83 thf(fact_5384_uminus__power__if,axiom,
% 5.52/5.83 ! [N: nat,A: int] :
% 5.52/5.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.52/5.83 = ( power_power_int @ A @ N ) ) )
% 5.52/5.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.52/5.83 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % uminus_power_if
% 5.52/5.83 thf(fact_5385_uminus__power__if,axiom,
% 5.52/5.83 ! [N: nat,A: real] :
% 5.52/5.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.52/5.83 = ( power_power_real @ A @ N ) ) )
% 5.52/5.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.52/5.83 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % uminus_power_if
% 5.52/5.83 thf(fact_5386_uminus__power__if,axiom,
% 5.52/5.83 ! [N: nat,A: complex] :
% 5.52/5.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.52/5.83 = ( power_power_complex @ A @ N ) ) )
% 5.52/5.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % uminus_power_if
% 5.52/5.83 thf(fact_5387_uminus__power__if,axiom,
% 5.52/5.83 ! [N: nat,A: code_integer] :
% 5.52/5.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.52/5.83 = ( power_8256067586552552935nteger @ A @ N ) ) )
% 5.52/5.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % uminus_power_if
% 5.52/5.83 thf(fact_5388_uminus__power__if,axiom,
% 5.52/5.83 ! [N: nat,A: rat] :
% 5.52/5.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.52/5.83 = ( power_power_rat @ A @ N ) ) )
% 5.52/5.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.52/5.83 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % uminus_power_if
% 5.52/5.83 thf(fact_5389_verit__less__mono__div__int2,axiom,
% 5.52/5.83 ! [A2: int,B4: int,N: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ A2 @ B4 )
% 5.52/5.83 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.52/5.83 => ( ord_less_eq_int @ ( divide_divide_int @ B4 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % verit_less_mono_div_int2
% 5.52/5.83 thf(fact_5390_div__eq__minus1,axiom,
% 5.52/5.83 ! [B: int] :
% 5.52/5.83 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.83 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.52/5.83 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % div_eq_minus1
% 5.52/5.83 thf(fact_5391_of__bool__odd__eq__mod__2,axiom,
% 5.52/5.83 ! [A: nat] :
% 5.52/5.83 ( ( zero_n2687167440665602831ol_nat
% 5.52/5.83 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.83 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_bool_odd_eq_mod_2
% 5.52/5.83 thf(fact_5392_of__bool__odd__eq__mod__2,axiom,
% 5.52/5.83 ! [A: int] :
% 5.52/5.83 ( ( zero_n2684676970156552555ol_int
% 5.52/5.83 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.83 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_bool_odd_eq_mod_2
% 5.52/5.83 thf(fact_5393_of__bool__odd__eq__mod__2,axiom,
% 5.52/5.83 ! [A: code_integer] :
% 5.52/5.83 ( ( zero_n356916108424825756nteger
% 5.52/5.83 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.83 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_bool_odd_eq_mod_2
% 5.52/5.83 thf(fact_5394_pos__minus__divide__le__eq,axiom,
% 5.52/5.83 ! [C: real,B: real,A: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.52/5.83 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % pos_minus_divide_le_eq
% 5.52/5.83 thf(fact_5395_pos__minus__divide__le__eq,axiom,
% 5.52/5.83 ! [C: rat,B: rat,A: rat] :
% 5.52/5.83 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.52/5.83 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % pos_minus_divide_le_eq
% 5.52/5.83 thf(fact_5396_pos__le__minus__divide__eq,axiom,
% 5.52/5.83 ! [C: real,A: real,B: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.52/5.83 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % pos_le_minus_divide_eq
% 5.52/5.83 thf(fact_5397_pos__le__minus__divide__eq,axiom,
% 5.52/5.83 ! [C: rat,A: rat,B: rat] :
% 5.52/5.83 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.52/5.83 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % pos_le_minus_divide_eq
% 5.52/5.83 thf(fact_5398_neg__minus__divide__le__eq,axiom,
% 5.52/5.83 ! [C: real,B: real,A: real] :
% 5.52/5.83 ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.52/5.83 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_minus_divide_le_eq
% 5.52/5.83 thf(fact_5399_neg__minus__divide__le__eq,axiom,
% 5.52/5.83 ! [C: rat,B: rat,A: rat] :
% 5.52/5.83 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.52/5.83 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_minus_divide_le_eq
% 5.52/5.83 thf(fact_5400_neg__le__minus__divide__eq,axiom,
% 5.52/5.83 ! [C: real,A: real,B: real] :
% 5.52/5.83 ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.52/5.83 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_le_minus_divide_eq
% 5.52/5.83 thf(fact_5401_neg__le__minus__divide__eq,axiom,
% 5.52/5.83 ! [C: rat,A: rat,B: rat] :
% 5.52/5.83 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.52/5.83 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_le_minus_divide_eq
% 5.52/5.83 thf(fact_5402_minus__divide__le__eq,axiom,
% 5.52/5.83 ! [B: real,C: real,A: real] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.52/5.83 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_le_eq
% 5.52/5.83 thf(fact_5403_minus__divide__le__eq,axiom,
% 5.52/5.83 ! [B: rat,C: rat,A: rat] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.52/5.83 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_divide_le_eq
% 5.52/5.83 thf(fact_5404_le__minus__divide__eq,axiom,
% 5.52/5.83 ! [A: real,B: real,C: real] :
% 5.52/5.83 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.52/5.83 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % le_minus_divide_eq
% 5.52/5.83 thf(fact_5405_le__minus__divide__eq,axiom,
% 5.52/5.83 ! [A: rat,B: rat,C: rat] :
% 5.52/5.83 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.52/5.83 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % le_minus_divide_eq
% 5.52/5.83 thf(fact_5406_less__divide__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [W: num,B: real,C: real] :
% 5.52/5.83 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.52/5.83 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % less_divide_eq_numeral(2)
% 5.52/5.83 thf(fact_5407_less__divide__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [W: num,B: rat,C: rat] :
% 5.52/5.83 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.83 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % less_divide_eq_numeral(2)
% 5.52/5.83 thf(fact_5408_divide__less__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [B: real,C: real,W: num] :
% 5.52/5.83 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.52/5.83 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % divide_less_eq_numeral(2)
% 5.52/5.83 thf(fact_5409_divide__less__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [B: rat,C: rat,W: num] :
% 5.52/5.83 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.52/5.83 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % divide_less_eq_numeral(2)
% 5.52/5.83 thf(fact_5410_power2__eq__1__iff,axiom,
% 5.52/5.83 ! [A: int] :
% 5.52/5.83 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.83 = one_one_int )
% 5.52/5.83 = ( ( A = one_one_int )
% 5.52/5.83 | ( A
% 5.52/5.83 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power2_eq_1_iff
% 5.52/5.83 thf(fact_5411_power2__eq__1__iff,axiom,
% 5.52/5.83 ! [A: real] :
% 5.52/5.83 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.83 = one_one_real )
% 5.52/5.83 = ( ( A = one_one_real )
% 5.52/5.83 | ( A
% 5.52/5.83 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power2_eq_1_iff
% 5.52/5.83 thf(fact_5412_power2__eq__1__iff,axiom,
% 5.52/5.83 ! [A: complex] :
% 5.52/5.83 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.83 = one_one_complex )
% 5.52/5.83 = ( ( A = one_one_complex )
% 5.52/5.83 | ( A
% 5.52/5.83 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power2_eq_1_iff
% 5.52/5.83 thf(fact_5413_power2__eq__1__iff,axiom,
% 5.52/5.83 ! [A: code_integer] :
% 5.52/5.83 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.83 = one_one_Code_integer )
% 5.52/5.83 = ( ( A = one_one_Code_integer )
% 5.52/5.83 | ( A
% 5.52/5.83 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power2_eq_1_iff
% 5.52/5.83 thf(fact_5414_power2__eq__1__iff,axiom,
% 5.52/5.83 ! [A: rat] :
% 5.52/5.83 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.83 = one_one_rat )
% 5.52/5.83 = ( ( A = one_one_rat )
% 5.52/5.83 | ( A
% 5.52/5.83 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % power2_eq_1_iff
% 5.52/5.83 thf(fact_5415_minus__one__power__iff,axiom,
% 5.52/5.83 ! [N: nat] :
% 5.52/5.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.52/5.83 = one_one_int ) )
% 5.52/5.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.52/5.83 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_one_power_iff
% 5.52/5.83 thf(fact_5416_minus__one__power__iff,axiom,
% 5.52/5.83 ! [N: nat] :
% 5.52/5.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.52/5.83 = one_one_real ) )
% 5.52/5.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.52/5.83 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_one_power_iff
% 5.52/5.83 thf(fact_5417_minus__one__power__iff,axiom,
% 5.52/5.83 ! [N: nat] :
% 5.52/5.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.52/5.83 = one_one_complex ) )
% 5.52/5.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_one_power_iff
% 5.52/5.83 thf(fact_5418_minus__one__power__iff,axiom,
% 5.52/5.83 ! [N: nat] :
% 5.52/5.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.52/5.83 = one_one_Code_integer ) )
% 5.52/5.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_one_power_iff
% 5.52/5.83 thf(fact_5419_minus__one__power__iff,axiom,
% 5.52/5.83 ! [N: nat] :
% 5.52/5.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.52/5.83 = one_one_rat ) )
% 5.52/5.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.83 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.52/5.83 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_one_power_iff
% 5.52/5.83 thf(fact_5420_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.52/5.83 ! [K: nat,N: nat] :
% 5.52/5.83 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.83 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 5.52/5.83 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_power_add_eq_neg_one_power_diff
% 5.52/5.83 thf(fact_5421_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.52/5.83 ! [K: nat,N: nat] :
% 5.52/5.83 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.83 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 5.52/5.83 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_power_add_eq_neg_one_power_diff
% 5.52/5.83 thf(fact_5422_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.52/5.83 ! [K: nat,N: nat] :
% 5.52/5.83 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.83 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 5.52/5.83 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_power_add_eq_neg_one_power_diff
% 5.52/5.83 thf(fact_5423_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.52/5.83 ! [K: nat,N: nat] :
% 5.52/5.83 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.83 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 5.52/5.83 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_power_add_eq_neg_one_power_diff
% 5.52/5.83 thf(fact_5424_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.52/5.83 ! [K: nat,N: nat] :
% 5.52/5.83 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.83 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 5.52/5.83 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % neg_one_power_add_eq_neg_one_power_diff
% 5.52/5.83 thf(fact_5425_realpow__square__minus__le,axiom,
% 5.52/5.83 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % realpow_square_minus_le
% 5.52/5.83 thf(fact_5426_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.52/5.83 ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 5.52/5.83
% 5.52/5.83 % signed_take_bit_int_greater_eq_minus_exp
% 5.52/5.83 thf(fact_5427_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.52/5.83 ! [N: nat,K: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.52/5.83 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.52/5.83
% 5.52/5.83 % signed_take_bit_int_less_eq_self_iff
% 5.52/5.83 thf(fact_5428_signed__take__bit__int__greater__self__iff,axiom,
% 5.52/5.83 ! [K: int,N: nat] :
% 5.52/5.83 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.52/5.83 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % signed_take_bit_int_greater_self_iff
% 5.52/5.83 thf(fact_5429_minus__mod__int__eq,axiom,
% 5.52/5.83 ! [L: int,K: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.52/5.83 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.52/5.83 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_mod_int_eq
% 5.52/5.83 thf(fact_5430_zmod__minus1,axiom,
% 5.52/5.83 ! [B: int] :
% 5.52/5.83 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.83 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.52/5.83 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % zmod_minus1
% 5.52/5.83 thf(fact_5431_zdiv__zminus2__eq__if,axiom,
% 5.52/5.83 ! [B: int,A: int] :
% 5.52/5.83 ( ( B != zero_zero_int )
% 5.52/5.83 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.52/5.83 = zero_zero_int )
% 5.52/5.83 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.52/5.83 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.52/5.83 & ( ( ( modulo_modulo_int @ A @ B )
% 5.52/5.83 != zero_zero_int )
% 5.52/5.83 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.52/5.83 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % zdiv_zminus2_eq_if
% 5.52/5.83 thf(fact_5432_zdiv__zminus1__eq__if,axiom,
% 5.52/5.83 ! [B: int,A: int] :
% 5.52/5.83 ( ( B != zero_zero_int )
% 5.52/5.83 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.52/5.83 = zero_zero_int )
% 5.52/5.83 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.52/5.83 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.52/5.83 & ( ( ( modulo_modulo_int @ A @ B )
% 5.52/5.83 != zero_zero_int )
% 5.52/5.83 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.52/5.83 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % zdiv_zminus1_eq_if
% 5.52/5.83 thf(fact_5433_zminus1__lemma,axiom,
% 5.52/5.83 ! [A: int,B: int,Q2: int,R: int] :
% 5.52/5.83 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.52/5.83 => ( ( B != zero_zero_int )
% 5.52/5.83 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % zminus1_lemma
% 5.52/5.83 thf(fact_5434_bits__induct,axiom,
% 5.52/5.83 ! [P: nat > $o,A: nat] :
% 5.52/5.83 ( ! [A3: nat] :
% 5.52/5.83 ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.83 = A3 )
% 5.52/5.83 => ( P @ A3 ) )
% 5.52/5.83 => ( ! [A3: nat,B2: $o] :
% 5.52/5.83 ( ( P @ A3 )
% 5.52/5.83 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.83 = A3 )
% 5.52/5.83 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.52/5.83 => ( P @ A ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % bits_induct
% 5.52/5.83 thf(fact_5435_bits__induct,axiom,
% 5.52/5.83 ! [P: int > $o,A: int] :
% 5.52/5.83 ( ! [A3: int] :
% 5.52/5.83 ( ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.83 = A3 )
% 5.52/5.83 => ( P @ A3 ) )
% 5.52/5.83 => ( ! [A3: int,B2: $o] :
% 5.52/5.83 ( ( P @ A3 )
% 5.52/5.83 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.83 = A3 )
% 5.52/5.83 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.52/5.83 => ( P @ A ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % bits_induct
% 5.52/5.83 thf(fact_5436_bits__induct,axiom,
% 5.52/5.83 ! [P: code_integer > $o,A: code_integer] :
% 5.52/5.83 ( ! [A3: code_integer] :
% 5.52/5.83 ( ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.83 = A3 )
% 5.52/5.83 => ( P @ A3 ) )
% 5.52/5.83 => ( ! [A3: code_integer,B2: $o] :
% 5.52/5.83 ( ( P @ A3 )
% 5.52/5.83 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.83 = A3 )
% 5.52/5.83 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.52/5.83 => ( P @ A ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % bits_induct
% 5.52/5.83 thf(fact_5437_divide__le__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [B: real,C: real,W: num] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.52/5.83 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % divide_le_eq_numeral(2)
% 5.52/5.83 thf(fact_5438_divide__le__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [B: rat,C: rat,W: num] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.52/5.83 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % divide_le_eq_numeral(2)
% 5.52/5.83 thf(fact_5439_le__divide__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [W: num,B: real,C: real] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.52/5.83 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.83 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.52/5.83 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % le_divide_eq_numeral(2)
% 5.52/5.83 thf(fact_5440_le__divide__eq__numeral_I2_J,axiom,
% 5.52/5.83 ! [W: num,B: rat,C: rat] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.52/5.83 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.52/5.83 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.52/5.83 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.52/5.83 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % le_divide_eq_numeral(2)
% 5.52/5.83 thf(fact_5441_square__le__1,axiom,
% 5.52/5.83 ! [X2: real] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.83 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.52/5.83 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % square_le_1
% 5.52/5.83 thf(fact_5442_square__le__1,axiom,
% 5.52/5.83 ! [X2: code_integer] :
% 5.52/5.83 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X2 )
% 5.52/5.83 => ( ( ord_le3102999989581377725nteger @ X2 @ one_one_Code_integer )
% 5.52/5.83 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % square_le_1
% 5.52/5.83 thf(fact_5443_square__le__1,axiom,
% 5.52/5.83 ! [X2: rat] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 )
% 5.52/5.83 => ( ( ord_less_eq_rat @ X2 @ one_one_rat )
% 5.52/5.83 => ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % square_le_1
% 5.52/5.83 thf(fact_5444_square__le__1,axiom,
% 5.52/5.83 ! [X2: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X2 )
% 5.52/5.83 => ( ( ord_less_eq_int @ X2 @ one_one_int )
% 5.52/5.83 => ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % square_le_1
% 5.52/5.83 thf(fact_5445_minus__power__mult__self,axiom,
% 5.52/5.83 ! [A: int,N: nat] :
% 5.52/5.83 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.52/5.83 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_power_mult_self
% 5.52/5.83 thf(fact_5446_minus__power__mult__self,axiom,
% 5.52/5.83 ! [A: real,N: nat] :
% 5.52/5.83 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.52/5.83 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_power_mult_self
% 5.52/5.83 thf(fact_5447_minus__power__mult__self,axiom,
% 5.52/5.83 ! [A: complex,N: nat] :
% 5.52/5.83 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 5.52/5.83 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_power_mult_self
% 5.52/5.83 thf(fact_5448_minus__power__mult__self,axiom,
% 5.52/5.83 ! [A: code_integer,N: nat] :
% 5.52/5.83 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.52/5.83 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_power_mult_self
% 5.52/5.83 thf(fact_5449_minus__power__mult__self,axiom,
% 5.52/5.83 ! [A: rat,N: nat] :
% 5.52/5.83 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.52/5.83 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_power_mult_self
% 5.52/5.83 thf(fact_5450_signed__take__bit__int__eq__self,axiom,
% 5.52/5.83 ! [N: nat,K: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.52/5.83 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.83 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.52/5.83 = K ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % signed_take_bit_int_eq_self
% 5.52/5.83 thf(fact_5451_signed__take__bit__int__eq__self__iff,axiom,
% 5.52/5.83 ! [N: nat,K: int] :
% 5.52/5.83 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.52/5.83 = K )
% 5.52/5.83 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.52/5.83 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % signed_take_bit_int_eq_self_iff
% 5.52/5.83 thf(fact_5452_minus__1__div__exp__eq__int,axiom,
% 5.52/5.83 ! [N: nat] :
% 5.52/5.83 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.83 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_1_div_exp_eq_int
% 5.52/5.83 thf(fact_5453_div__pos__neg__trivial,axiom,
% 5.52/5.83 ! [K: int,L: int] :
% 5.52/5.83 ( ( ord_less_int @ zero_zero_int @ K )
% 5.52/5.83 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.52/5.83 => ( ( divide_divide_int @ K @ L )
% 5.52/5.83 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % div_pos_neg_trivial
% 5.52/5.83 thf(fact_5454_exp__mod__exp,axiom,
% 5.52/5.83 ! [M: nat,N: nat] :
% 5.52/5.83 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.83 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % exp_mod_exp
% 5.52/5.83 thf(fact_5455_exp__mod__exp,axiom,
% 5.52/5.83 ! [M: nat,N: nat] :
% 5.52/5.83 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.83 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % exp_mod_exp
% 5.52/5.83 thf(fact_5456_exp__mod__exp,axiom,
% 5.52/5.83 ! [M: nat,N: nat] :
% 5.52/5.83 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.83 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % exp_mod_exp
% 5.52/5.83 thf(fact_5457_divmod__nat__def,axiom,
% 5.52/5.83 ( divmod_nat
% 5.52/5.83 = ( ^ [M3: nat,N3: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M3 @ N3 ) @ ( modulo_modulo_nat @ M3 @ N3 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % divmod_nat_def
% 5.52/5.83 thf(fact_5458_power__minus1__odd,axiom,
% 5.52/5.83 ! [N: nat] :
% 5.52/5.83 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.83 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus1_odd
% 5.52/5.83 thf(fact_5459_power__minus1__odd,axiom,
% 5.52/5.83 ! [N: nat] :
% 5.52/5.83 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.83 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus1_odd
% 5.52/5.83 thf(fact_5460_power__minus1__odd,axiom,
% 5.52/5.83 ! [N: nat] :
% 5.52/5.83 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus1_odd
% 5.52/5.83 thf(fact_5461_power__minus1__odd,axiom,
% 5.52/5.83 ! [N: nat] :
% 5.52/5.83 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus1_odd
% 5.52/5.83 thf(fact_5462_power__minus1__odd,axiom,
% 5.52/5.83 ! [N: nat] :
% 5.52/5.83 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.83 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % power_minus1_odd
% 5.52/5.83 thf(fact_5463_int__bit__induct,axiom,
% 5.52/5.83 ! [P: int > $o,K: int] :
% 5.52/5.83 ( ( P @ zero_zero_int )
% 5.52/5.83 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.83 => ( ! [K3: int] :
% 5.52/5.83 ( ( P @ K3 )
% 5.52/5.83 => ( ( K3 != zero_zero_int )
% 5.52/5.83 => ( P @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.83 => ( ! [K3: int] :
% 5.52/5.83 ( ( P @ K3 )
% 5.52/5.83 => ( ( K3
% 5.52/5.83 != ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.83 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.52/5.83 => ( P @ K ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % int_bit_induct
% 5.52/5.83 thf(fact_5464_signed__take__bit__int__greater__eq,axiom,
% 5.52/5.83 ! [K: int,N: nat] :
% 5.52/5.83 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.83 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % signed_take_bit_int_greater_eq
% 5.52/5.83 thf(fact_5465_set__decode__def,axiom,
% 5.52/5.83 ( nat_set_decode
% 5.52/5.83 = ( ^ [X: nat] :
% 5.52/5.83 ( collect_nat
% 5.52/5.83 @ ^ [N3: nat] :
% 5.52/5.83 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % set_decode_def
% 5.52/5.83 thf(fact_5466_exp__div__exp__eq,axiom,
% 5.52/5.83 ! [M: nat,N: nat] :
% 5.52/5.83 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.83 = ( times_times_nat
% 5.52/5.83 @ ( zero_n2687167440665602831ol_nat
% 5.52/5.83 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.52/5.83 != zero_zero_nat )
% 5.52/5.83 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.52/5.83 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % exp_div_exp_eq
% 5.52/5.83 thf(fact_5467_exp__div__exp__eq,axiom,
% 5.52/5.83 ! [M: nat,N: nat] :
% 5.52/5.83 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.83 = ( times_times_int
% 5.52/5.83 @ ( zero_n2684676970156552555ol_int
% 5.52/5.83 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.52/5.83 != zero_zero_int )
% 5.52/5.83 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.52/5.83 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % exp_div_exp_eq
% 5.52/5.83 thf(fact_5468_exp__div__exp__eq,axiom,
% 5.52/5.83 ! [M: nat,N: nat] :
% 5.52/5.83 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.83 = ( times_3573771949741848930nteger
% 5.52/5.83 @ ( zero_n356916108424825756nteger
% 5.52/5.83 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.52/5.83 != zero_z3403309356797280102nteger )
% 5.52/5.83 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.52/5.83 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % exp_div_exp_eq
% 5.52/5.83 thf(fact_5469_vebt__buildup_Osimps_I3_J,axiom,
% 5.52/5.83 ! [Va: nat] :
% 5.52/5.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.52/5.83 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.52/5.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.52/5.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.52/5.83 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.52/5.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % vebt_buildup.simps(3)
% 5.52/5.83 thf(fact_5470_one__div__minus__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.83 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % one_div_minus_numeral
% 5.52/5.83 thf(fact_5471_minus__one__div__numeral,axiom,
% 5.52/5.83 ! [N: num] :
% 5.52/5.83 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.83 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_one_div_numeral
% 5.52/5.83 thf(fact_5472_compl__le__compl__iff,axiom,
% 5.52/5.83 ! [X2: set_nat,Y2: set_nat] :
% 5.52/5.83 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ ( uminus5710092332889474511et_nat @ Y2 ) )
% 5.52/5.83 = ( ord_less_eq_set_nat @ Y2 @ X2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % compl_le_compl_iff
% 5.52/5.83 thf(fact_5473_numeral__div__minus__numeral,axiom,
% 5.52/5.83 ! [M: num,N: num] :
% 5.52/5.83 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.83 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_div_minus_numeral
% 5.52/5.83 thf(fact_5474_minus__numeral__div__numeral,axiom,
% 5.52/5.83 ! [M: num,N: num] :
% 5.52/5.83 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.83 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % minus_numeral_div_numeral
% 5.52/5.83 thf(fact_5475_dbl__dec__simps_I4_J,axiom,
% 5.52/5.83 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.83 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(4)
% 5.52/5.83 thf(fact_5476_dbl__dec__simps_I4_J,axiom,
% 5.52/5.83 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.83 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(4)
% 5.52/5.83 thf(fact_5477_dbl__dec__simps_I4_J,axiom,
% 5.52/5.83 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(4)
% 5.52/5.83 thf(fact_5478_dbl__dec__simps_I4_J,axiom,
% 5.52/5.83 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(4)
% 5.52/5.83 thf(fact_5479_dbl__dec__simps_I4_J,axiom,
% 5.52/5.83 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.83 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(4)
% 5.52/5.83 thf(fact_5480_dbl__dec__simps_I3_J,axiom,
% 5.52/5.83 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.52/5.83 = one_one_complex ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(3)
% 5.52/5.83 thf(fact_5481_dbl__dec__simps_I3_J,axiom,
% 5.52/5.83 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.52/5.83 = one_one_real ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(3)
% 5.52/5.83 thf(fact_5482_dbl__dec__simps_I3_J,axiom,
% 5.52/5.83 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.52/5.83 = one_one_rat ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(3)
% 5.52/5.83 thf(fact_5483_dbl__dec__simps_I3_J,axiom,
% 5.52/5.83 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.52/5.83 = one_one_int ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(3)
% 5.52/5.83 thf(fact_5484_dbl__dec__simps_I5_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.52/5.83 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(5)
% 5.52/5.83 thf(fact_5485_dbl__dec__simps_I5_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.52/5.83 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(5)
% 5.52/5.83 thf(fact_5486_dbl__dec__simps_I5_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 5.52/5.83 = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(5)
% 5.52/5.83 thf(fact_5487_dbl__dec__simps_I5_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.52/5.83 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(5)
% 5.52/5.83 thf(fact_5488_dbl__dec__simps_I2_J,axiom,
% 5.52/5.83 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.52/5.83 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(2)
% 5.52/5.83 thf(fact_5489_dbl__dec__simps_I2_J,axiom,
% 5.52/5.83 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.52/5.83 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(2)
% 5.52/5.83 thf(fact_5490_dbl__dec__simps_I2_J,axiom,
% 5.52/5.83 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(2)
% 5.52/5.83 thf(fact_5491_dbl__dec__simps_I2_J,axiom,
% 5.52/5.83 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(2)
% 5.52/5.83 thf(fact_5492_dbl__dec__simps_I2_J,axiom,
% 5.52/5.83 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.52/5.83 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(2)
% 5.52/5.83 thf(fact_5493_Divides_Oadjust__div__eq,axiom,
% 5.52/5.83 ! [Q2: int,R: int] :
% 5.52/5.83 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.52/5.83 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % Divides.adjust_div_eq
% 5.52/5.83 thf(fact_5494_dbl__inc__simps_I1_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.52/5.83 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_inc_simps(1)
% 5.52/5.83 thf(fact_5495_dbl__inc__simps_I1_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.52/5.83 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_inc_simps(1)
% 5.52/5.83 thf(fact_5496_dbl__inc__simps_I1_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_inc_simps(1)
% 5.52/5.83 thf(fact_5497_dbl__inc__simps_I1_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_inc_simps(1)
% 5.52/5.83 thf(fact_5498_dbl__inc__simps_I1_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.52/5.83 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_inc_simps(1)
% 5.52/5.83 thf(fact_5499_dbl__dec__simps_I1_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.52/5.83 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(1)
% 5.52/5.83 thf(fact_5500_dbl__dec__simps_I1_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.52/5.83 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(1)
% 5.52/5.83 thf(fact_5501_dbl__dec__simps_I1_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.52/5.83 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(1)
% 5.52/5.83 thf(fact_5502_dbl__dec__simps_I1_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.52/5.83 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(1)
% 5.52/5.83 thf(fact_5503_dbl__dec__simps_I1_J,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.52/5.83 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_simps(1)
% 5.52/5.83 thf(fact_5504_Divides_Oadjust__div__def,axiom,
% 5.52/5.83 ( adjust_div
% 5.52/5.83 = ( produc8211389475949308722nt_int
% 5.52/5.83 @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % Divides.adjust_div_def
% 5.52/5.83 thf(fact_5505_dbl__dec__def,axiom,
% 5.52/5.83 ( neg_nu6511756317524482435omplex
% 5.52/5.83 = ( ^ [X: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_def
% 5.52/5.83 thf(fact_5506_dbl__dec__def,axiom,
% 5.52/5.83 ( neg_nu6075765906172075777c_real
% 5.52/5.83 = ( ^ [X: real] : ( minus_minus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_def
% 5.52/5.83 thf(fact_5507_dbl__dec__def,axiom,
% 5.52/5.83 ( neg_nu3179335615603231917ec_rat
% 5.52/5.83 = ( ^ [X: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_def
% 5.52/5.83 thf(fact_5508_dbl__dec__def,axiom,
% 5.52/5.83 ( neg_nu3811975205180677377ec_int
% 5.52/5.83 = ( ^ [X: int] : ( minus_minus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % dbl_dec_def
% 5.52/5.83 thf(fact_5509_compl__mono,axiom,
% 5.52/5.83 ! [X2: set_nat,Y2: set_nat] :
% 5.52/5.83 ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 5.52/5.83 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y2 ) @ ( uminus5710092332889474511et_nat @ X2 ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % compl_mono
% 5.52/5.83 thf(fact_5510_compl__le__swap1,axiom,
% 5.52/5.83 ! [Y2: set_nat,X2: set_nat] :
% 5.52/5.83 ( ( ord_less_eq_set_nat @ Y2 @ ( uminus5710092332889474511et_nat @ X2 ) )
% 5.52/5.83 => ( ord_less_eq_set_nat @ X2 @ ( uminus5710092332889474511et_nat @ Y2 ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % compl_le_swap1
% 5.52/5.83 thf(fact_5511_compl__le__swap2,axiom,
% 5.52/5.83 ! [Y2: set_nat,X2: set_nat] :
% 5.52/5.83 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y2 ) @ X2 )
% 5.52/5.83 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ Y2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % compl_le_swap2
% 5.52/5.83 thf(fact_5512_diff__shunt__var,axiom,
% 5.52/5.83 ! [X2: set_int,Y2: set_int] :
% 5.52/5.83 ( ( ( minus_minus_set_int @ X2 @ Y2 )
% 5.52/5.83 = bot_bot_set_int )
% 5.52/5.83 = ( ord_less_eq_set_int @ X2 @ Y2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % diff_shunt_var
% 5.52/5.83 thf(fact_5513_diff__shunt__var,axiom,
% 5.52/5.83 ! [X2: set_Extended_enat,Y2: set_Extended_enat] :
% 5.52/5.83 ( ( ( minus_925952699566721837d_enat @ X2 @ Y2 )
% 5.52/5.83 = bot_bo7653980558646680370d_enat )
% 5.52/5.83 = ( ord_le7203529160286727270d_enat @ X2 @ Y2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % diff_shunt_var
% 5.52/5.83 thf(fact_5514_diff__shunt__var,axiom,
% 5.52/5.83 ! [X2: set_nat,Y2: set_nat] :
% 5.52/5.83 ( ( ( minus_minus_set_nat @ X2 @ Y2 )
% 5.52/5.83 = bot_bot_set_nat )
% 5.52/5.83 = ( ord_less_eq_set_nat @ X2 @ Y2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % diff_shunt_var
% 5.52/5.83 thf(fact_5515_ln__one__minus__pos__lower__bound,axiom,
% 5.52/5.83 ! [X2: real] :
% 5.52/5.83 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.83 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.83 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ln_one_minus_pos_lower_bound
% 5.52/5.83 thf(fact_5516_of__int__code__if,axiom,
% 5.52/5.83 ( ring_1_of_int_int
% 5.52/5.83 = ( ^ [K2: int] :
% 5.52/5.83 ( if_int @ ( K2 = zero_zero_int ) @ zero_zero_int
% 5.52/5.83 @ ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K2 ) ) )
% 5.52/5.83 @ ( if_int
% 5.52/5.83 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.83 = zero_zero_int )
% 5.52/5.83 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.52/5.83 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_code_if
% 5.52/5.83 thf(fact_5517_of__int__code__if,axiom,
% 5.52/5.83 ( ring_1_of_int_real
% 5.52/5.83 = ( ^ [K2: int] :
% 5.52/5.83 ( if_real @ ( K2 = zero_zero_int ) @ zero_zero_real
% 5.52/5.83 @ ( if_real @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K2 ) ) )
% 5.52/5.83 @ ( if_real
% 5.52/5.83 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.83 = zero_zero_int )
% 5.52/5.83 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.52/5.83 @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_code_if
% 5.52/5.83 thf(fact_5518_of__int__code__if,axiom,
% 5.52/5.83 ( ring_17405671764205052669omplex
% 5.52/5.83 = ( ^ [K2: int] :
% 5.52/5.83 ( if_complex @ ( K2 = zero_zero_int ) @ zero_zero_complex
% 5.52/5.83 @ ( if_complex @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K2 ) ) )
% 5.52/5.83 @ ( if_complex
% 5.52/5.83 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.83 = zero_zero_int )
% 5.52/5.83 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.52/5.83 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_code_if
% 5.52/5.83 thf(fact_5519_of__int__code__if,axiom,
% 5.52/5.83 ( ring_18347121197199848620nteger
% 5.52/5.83 = ( ^ [K2: int] :
% 5.52/5.83 ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.52/5.83 @ ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K2 ) ) )
% 5.52/5.83 @ ( if_Code_integer
% 5.52/5.83 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.83 = zero_zero_int )
% 5.52/5.83 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.52/5.83 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_code_if
% 5.52/5.83 thf(fact_5520_of__int__code__if,axiom,
% 5.52/5.83 ( ring_1_of_int_rat
% 5.52/5.83 = ( ^ [K2: int] :
% 5.52/5.83 ( if_rat @ ( K2 = zero_zero_int ) @ zero_zero_rat
% 5.52/5.83 @ ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K2 ) ) )
% 5.52/5.83 @ ( if_rat
% 5.52/5.83 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.83 = zero_zero_int )
% 5.52/5.83 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.52/5.83 @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_code_if
% 5.52/5.83 thf(fact_5521_vebt__buildup_Opelims,axiom,
% 5.52/5.83 ! [X2: nat,Y2: vEBT_VEBT] :
% 5.52/5.83 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.52/5.83 = Y2 )
% 5.52/5.83 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X2 )
% 5.52/5.83 => ( ( ( X2 = zero_zero_nat )
% 5.52/5.83 => ( ( Y2
% 5.52/5.83 = ( vEBT_Leaf @ $false @ $false ) )
% 5.52/5.83 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.52/5.83 => ( ( ( X2
% 5.52/5.83 = ( suc @ zero_zero_nat ) )
% 5.52/5.83 => ( ( Y2
% 5.52/5.83 = ( vEBT_Leaf @ $false @ $false ) )
% 5.52/5.83 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.52/5.83 => ~ ! [Va3: nat] :
% 5.52/5.83 ( ( X2
% 5.52/5.83 = ( suc @ ( suc @ Va3 ) ) )
% 5.52/5.83 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.52/5.83 => ( Y2
% 5.52/5.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.52/5.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.52/5.83 => ( Y2
% 5.52/5.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.52/5.83 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % vebt_buildup.pelims
% 5.52/5.83 thf(fact_5522_int__ge__less__than__def,axiom,
% 5.52/5.83 ( int_ge_less_than
% 5.52/5.83 = ( ^ [D: int] :
% 5.52/5.83 ( collec213857154873943460nt_int
% 5.52/5.83 @ ( produc4947309494688390418_int_o
% 5.52/5.83 @ ^ [Z6: int,Z2: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ D @ Z6 )
% 5.52/5.83 & ( ord_less_int @ Z6 @ Z2 ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % int_ge_less_than_def
% 5.52/5.83 thf(fact_5523_int__ge__less__than2__def,axiom,
% 5.52/5.83 ( int_ge_less_than2
% 5.52/5.83 = ( ^ [D: int] :
% 5.52/5.83 ( collec213857154873943460nt_int
% 5.52/5.83 @ ( produc4947309494688390418_int_o
% 5.52/5.83 @ ^ [Z6: int,Z2: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ D @ Z2 )
% 5.52/5.83 & ( ord_less_int @ Z6 @ Z2 ) ) ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % int_ge_less_than2_def
% 5.52/5.83 thf(fact_5524_of__int__numeral,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.52/5.83 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_numeral
% 5.52/5.83 thf(fact_5525_of__int__numeral,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.52/5.83 = ( numeral_numeral_real @ K ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_numeral
% 5.52/5.83 thf(fact_5526_of__int__numeral,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.52/5.83 = ( numeral_numeral_rat @ K ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_numeral
% 5.52/5.83 thf(fact_5527_of__int__numeral,axiom,
% 5.52/5.83 ! [K: num] :
% 5.52/5.83 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.52/5.83 = ( numeral_numeral_int @ K ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_numeral
% 5.52/5.83 thf(fact_5528_of__int__eq__numeral__iff,axiom,
% 5.52/5.83 ! [Z: int,N: num] :
% 5.52/5.83 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.52/5.83 = ( numera6690914467698888265omplex @ N ) )
% 5.52/5.83 = ( Z
% 5.52/5.83 = ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_numeral_iff
% 5.52/5.83 thf(fact_5529_of__int__eq__numeral__iff,axiom,
% 5.52/5.83 ! [Z: int,N: num] :
% 5.52/5.83 ( ( ( ring_1_of_int_real @ Z )
% 5.52/5.83 = ( numeral_numeral_real @ N ) )
% 5.52/5.83 = ( Z
% 5.52/5.83 = ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_numeral_iff
% 5.52/5.83 thf(fact_5530_of__int__eq__numeral__iff,axiom,
% 5.52/5.83 ! [Z: int,N: num] :
% 5.52/5.83 ( ( ( ring_1_of_int_rat @ Z )
% 5.52/5.83 = ( numeral_numeral_rat @ N ) )
% 5.52/5.83 = ( Z
% 5.52/5.83 = ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_numeral_iff
% 5.52/5.83 thf(fact_5531_of__int__eq__numeral__iff,axiom,
% 5.52/5.83 ! [Z: int,N: num] :
% 5.52/5.83 ( ( ( ring_1_of_int_int @ Z )
% 5.52/5.83 = ( numeral_numeral_int @ N ) )
% 5.52/5.83 = ( Z
% 5.52/5.83 = ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_numeral_iff
% 5.52/5.83 thf(fact_5532_of__int__le__iff,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.52/5.83 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_iff
% 5.52/5.83 thf(fact_5533_of__int__le__iff,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.52/5.83 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_iff
% 5.52/5.83 thf(fact_5534_of__int__le__iff,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.52/5.83 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_iff
% 5.52/5.83 thf(fact_5535_ln__one,axiom,
% 5.52/5.83 ( ( ln_ln_real @ one_one_real )
% 5.52/5.83 = zero_zero_real ) ).
% 5.52/5.83
% 5.52/5.83 % ln_one
% 5.52/5.83 thf(fact_5536_of__int__less__iff,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.52/5.83 = ( ord_less_int @ W @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_iff
% 5.52/5.83 thf(fact_5537_of__int__less__iff,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.52/5.83 = ( ord_less_int @ W @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_iff
% 5.52/5.83 thf(fact_5538_of__int__less__iff,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.52/5.83 = ( ord_less_int @ W @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_iff
% 5.52/5.83 thf(fact_5539_of__int__1,axiom,
% 5.52/5.83 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.52/5.83 = one_one_complex ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_1
% 5.52/5.83 thf(fact_5540_of__int__1,axiom,
% 5.52/5.83 ( ( ring_1_of_int_int @ one_one_int )
% 5.52/5.83 = one_one_int ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_1
% 5.52/5.83 thf(fact_5541_of__int__1,axiom,
% 5.52/5.83 ( ( ring_1_of_int_real @ one_one_int )
% 5.52/5.83 = one_one_real ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_1
% 5.52/5.83 thf(fact_5542_of__int__1,axiom,
% 5.52/5.83 ( ( ring_1_of_int_rat @ one_one_int )
% 5.52/5.83 = one_one_rat ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_1
% 5.52/5.83 thf(fact_5543_of__int__eq__1__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.52/5.83 = one_one_complex )
% 5.52/5.83 = ( Z = one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_1_iff
% 5.52/5.83 thf(fact_5544_of__int__eq__1__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ( ring_1_of_int_int @ Z )
% 5.52/5.83 = one_one_int )
% 5.52/5.83 = ( Z = one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_1_iff
% 5.52/5.83 thf(fact_5545_of__int__eq__1__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ( ring_1_of_int_real @ Z )
% 5.52/5.83 = one_one_real )
% 5.52/5.83 = ( Z = one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_1_iff
% 5.52/5.83 thf(fact_5546_of__int__eq__1__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ( ring_1_of_int_rat @ Z )
% 5.52/5.83 = one_one_rat )
% 5.52/5.83 = ( Z = one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_1_iff
% 5.52/5.83 thf(fact_5547_of__int__mult,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.52/5.83 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_mult
% 5.52/5.83 thf(fact_5548_of__int__mult,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 5.52/5.83 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_mult
% 5.52/5.83 thf(fact_5549_of__int__mult,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.52/5.83 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_mult
% 5.52/5.83 thf(fact_5550_of__int__add,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.52/5.83 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_add
% 5.52/5.83 thf(fact_5551_of__int__add,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 5.52/5.83 = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_add
% 5.52/5.83 thf(fact_5552_of__int__add,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.52/5.83 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_add
% 5.52/5.83 thf(fact_5553_of__int__add,axiom,
% 5.52/5.83 ! [W: int,Z: int] :
% 5.52/5.83 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.52/5.83 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_add
% 5.52/5.83 thf(fact_5554_ln__less__cancel__iff,axiom,
% 5.52/5.83 ! [X2: real,Y2: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.83 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.83 => ( ( ord_less_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y2 ) )
% 5.52/5.83 = ( ord_less_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ln_less_cancel_iff
% 5.52/5.83 thf(fact_5555_ln__inj__iff,axiom,
% 5.52/5.83 ! [X2: real,Y2: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.83 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.83 => ( ( ( ln_ln_real @ X2 )
% 5.52/5.83 = ( ln_ln_real @ Y2 ) )
% 5.52/5.83 = ( X2 = Y2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ln_inj_iff
% 5.52/5.83 thf(fact_5556_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: int,B: int,W: nat] :
% 5.52/5.83 ( ( ( ring_1_of_int_rat @ X2 )
% 5.52/5.83 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.52/5.83 = ( X2
% 5.52/5.83 = ( power_power_int @ B @ W ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power_eq_of_int_cancel_iff
% 5.52/5.83 thf(fact_5557_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: int,B: int,W: nat] :
% 5.52/5.83 ( ( ( ring_1_of_int_real @ X2 )
% 5.52/5.83 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.52/5.83 = ( X2
% 5.52/5.83 = ( power_power_int @ B @ W ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power_eq_of_int_cancel_iff
% 5.52/5.83 thf(fact_5558_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: int,B: int,W: nat] :
% 5.52/5.83 ( ( ( ring_1_of_int_int @ X2 )
% 5.52/5.83 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.52/5.83 = ( X2
% 5.52/5.83 = ( power_power_int @ B @ W ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power_eq_of_int_cancel_iff
% 5.52/5.83 thf(fact_5559_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: int,B: int,W: nat] :
% 5.52/5.83 ( ( ( ring_17405671764205052669omplex @ X2 )
% 5.52/5.83 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.52/5.83 = ( X2
% 5.52/5.83 = ( power_power_int @ B @ W ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power_eq_of_int_cancel_iff
% 5.52/5.83 thf(fact_5560_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.52/5.83 ! [B: int,W: nat,X2: int] :
% 5.52/5.83 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 5.52/5.83 = ( ring_1_of_int_rat @ X2 ) )
% 5.52/5.83 = ( ( power_power_int @ B @ W )
% 5.52/5.83 = X2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_of_int_power_cancel_iff
% 5.52/5.83 thf(fact_5561_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.52/5.83 ! [B: int,W: nat,X2: int] :
% 5.52/5.83 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.52/5.83 = ( ring_1_of_int_real @ X2 ) )
% 5.52/5.83 = ( ( power_power_int @ B @ W )
% 5.52/5.83 = X2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_of_int_power_cancel_iff
% 5.52/5.83 thf(fact_5562_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.52/5.83 ! [B: int,W: nat,X2: int] :
% 5.52/5.83 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.52/5.83 = ( ring_1_of_int_int @ X2 ) )
% 5.52/5.83 = ( ( power_power_int @ B @ W )
% 5.52/5.83 = X2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_of_int_power_cancel_iff
% 5.52/5.83 thf(fact_5563_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.52/5.83 ! [B: int,W: nat,X2: int] :
% 5.52/5.83 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.52/5.83 = ( ring_17405671764205052669omplex @ X2 ) )
% 5.52/5.83 = ( ( power_power_int @ B @ W )
% 5.52/5.83 = X2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_of_int_power_cancel_iff
% 5.52/5.83 thf(fact_5564_of__int__power,axiom,
% 5.52/5.83 ! [Z: int,N: nat] :
% 5.52/5.83 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 5.52/5.83 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power
% 5.52/5.83 thf(fact_5565_of__int__power,axiom,
% 5.52/5.83 ! [Z: int,N: nat] :
% 5.52/5.83 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 5.52/5.83 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power
% 5.52/5.83 thf(fact_5566_of__int__power,axiom,
% 5.52/5.83 ! [Z: int,N: nat] :
% 5.52/5.83 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 5.52/5.83 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power
% 5.52/5.83 thf(fact_5567_of__int__power,axiom,
% 5.52/5.83 ! [Z: int,N: nat] :
% 5.52/5.83 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 5.52/5.83 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power
% 5.52/5.83 thf(fact_5568_ln__le__cancel__iff,axiom,
% 5.52/5.83 ! [X2: real,Y2: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.83 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.83 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y2 ) )
% 5.52/5.83 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ln_le_cancel_iff
% 5.52/5.83 thf(fact_5569_ln__eq__zero__iff,axiom,
% 5.52/5.83 ! [X2: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.83 => ( ( ( ln_ln_real @ X2 )
% 5.52/5.83 = zero_zero_real )
% 5.52/5.83 = ( X2 = one_one_real ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ln_eq_zero_iff
% 5.52/5.83 thf(fact_5570_ln__gt__zero__iff,axiom,
% 5.52/5.83 ! [X2: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.83 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.52/5.83 = ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ln_gt_zero_iff
% 5.52/5.83 thf(fact_5571_ln__less__zero__iff,axiom,
% 5.52/5.83 ! [X2: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.83 => ( ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.52/5.83 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ln_less_zero_iff
% 5.52/5.83 thf(fact_5572_of__int__0__le__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.52/5.83 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_0_le_iff
% 5.52/5.83 thf(fact_5573_of__int__0__le__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.52/5.83 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_0_le_iff
% 5.52/5.83 thf(fact_5574_of__int__0__le__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.52/5.83 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_0_le_iff
% 5.52/5.83 thf(fact_5575_of__int__le__0__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.52/5.83 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_0_iff
% 5.52/5.83 thf(fact_5576_of__int__le__0__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.52/5.83 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_0_iff
% 5.52/5.83 thf(fact_5577_of__int__le__0__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.52/5.83 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_0_iff
% 5.52/5.83 thf(fact_5578_of__int__less__0__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.52/5.83 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_0_iff
% 5.52/5.83 thf(fact_5579_of__int__less__0__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.52/5.83 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_0_iff
% 5.52/5.83 thf(fact_5580_of__int__less__0__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.52/5.83 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_0_iff
% 5.52/5.83 thf(fact_5581_of__int__0__less__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.52/5.83 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_0_less_iff
% 5.52/5.83 thf(fact_5582_of__int__0__less__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.52/5.83 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_0_less_iff
% 5.52/5.83 thf(fact_5583_of__int__0__less__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.52/5.83 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_0_less_iff
% 5.52/5.83 thf(fact_5584_of__int__le__numeral__iff,axiom,
% 5.52/5.83 ! [Z: int,N: num] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.52/5.83 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_numeral_iff
% 5.52/5.83 thf(fact_5585_of__int__le__numeral__iff,axiom,
% 5.52/5.83 ! [Z: int,N: num] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.52/5.83 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_numeral_iff
% 5.52/5.83 thf(fact_5586_of__int__le__numeral__iff,axiom,
% 5.52/5.83 ! [Z: int,N: num] :
% 5.52/5.83 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.83 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_numeral_iff
% 5.52/5.83 thf(fact_5587_of__int__numeral__le__iff,axiom,
% 5.52/5.83 ! [N: num,Z: int] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.52/5.83 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_numeral_le_iff
% 5.52/5.83 thf(fact_5588_of__int__numeral__le__iff,axiom,
% 5.52/5.83 ! [N: num,Z: int] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.52/5.83 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_numeral_le_iff
% 5.52/5.83 thf(fact_5589_of__int__numeral__le__iff,axiom,
% 5.52/5.83 ! [N: num,Z: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.52/5.83 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_numeral_le_iff
% 5.52/5.83 thf(fact_5590_of__int__less__numeral__iff,axiom,
% 5.52/5.83 ! [Z: int,N: num] :
% 5.52/5.83 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.52/5.83 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_numeral_iff
% 5.52/5.83 thf(fact_5591_of__int__less__numeral__iff,axiom,
% 5.52/5.83 ! [Z: int,N: num] :
% 5.52/5.83 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.52/5.83 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_numeral_iff
% 5.52/5.83 thf(fact_5592_of__int__less__numeral__iff,axiom,
% 5.52/5.83 ! [Z: int,N: num] :
% 5.52/5.83 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.83 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_numeral_iff
% 5.52/5.83 thf(fact_5593_of__int__numeral__less__iff,axiom,
% 5.52/5.83 ! [N: num,Z: int] :
% 5.52/5.83 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.52/5.83 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_numeral_less_iff
% 5.52/5.83 thf(fact_5594_of__int__numeral__less__iff,axiom,
% 5.52/5.83 ! [N: num,Z: int] :
% 5.52/5.83 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.52/5.83 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_numeral_less_iff
% 5.52/5.83 thf(fact_5595_of__int__numeral__less__iff,axiom,
% 5.52/5.83 ! [N: num,Z: int] :
% 5.52/5.83 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.52/5.83 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_numeral_less_iff
% 5.52/5.83 thf(fact_5596_of__int__1__le__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.52/5.83 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_1_le_iff
% 5.52/5.83 thf(fact_5597_of__int__1__le__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.52/5.83 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_1_le_iff
% 5.52/5.83 thf(fact_5598_of__int__1__le__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.52/5.83 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_1_le_iff
% 5.52/5.83 thf(fact_5599_of__int__le__1__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.52/5.83 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_1_iff
% 5.52/5.83 thf(fact_5600_of__int__le__1__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.52/5.83 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_1_iff
% 5.52/5.83 thf(fact_5601_of__int__le__1__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.52/5.83 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_1_iff
% 5.52/5.83 thf(fact_5602_of__int__1__less__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.52/5.83 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_1_less_iff
% 5.52/5.83 thf(fact_5603_of__int__1__less__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.52/5.83 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_1_less_iff
% 5.52/5.83 thf(fact_5604_of__int__1__less__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.52/5.83 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_1_less_iff
% 5.52/5.83 thf(fact_5605_of__int__less__1__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.52/5.83 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_1_iff
% 5.52/5.83 thf(fact_5606_of__int__less__1__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.52/5.83 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_1_iff
% 5.52/5.83 thf(fact_5607_of__int__less__1__iff,axiom,
% 5.52/5.83 ! [Z: int] :
% 5.52/5.83 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.52/5.83 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_1_iff
% 5.52/5.83 thf(fact_5608_ln__le__zero__iff,axiom,
% 5.52/5.83 ! [X2: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.83 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.52/5.83 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ln_le_zero_iff
% 5.52/5.83 thf(fact_5609_ln__ge__zero__iff,axiom,
% 5.52/5.83 ! [X2: real] :
% 5.52/5.83 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.83 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.52/5.83 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % ln_ge_zero_iff
% 5.52/5.83 thf(fact_5610_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: num,N: nat,Y2: int] :
% 5.52/5.83 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N )
% 5.52/5.83 = ( ring_17405671764205052669omplex @ Y2 ) )
% 5.52/5.83 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.52/5.83 = Y2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_power_eq_of_int_cancel_iff
% 5.52/5.83 thf(fact_5611_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: num,N: nat,Y2: int] :
% 5.52/5.83 ( ( ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N )
% 5.52/5.83 = ( ring_1_of_int_real @ Y2 ) )
% 5.52/5.83 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.52/5.83 = Y2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_power_eq_of_int_cancel_iff
% 5.52/5.83 thf(fact_5612_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: num,N: nat,Y2: int] :
% 5.52/5.83 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 5.52/5.83 = ( ring_1_of_int_rat @ Y2 ) )
% 5.52/5.83 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.52/5.83 = Y2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_power_eq_of_int_cancel_iff
% 5.52/5.83 thf(fact_5613_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: num,N: nat,Y2: int] :
% 5.52/5.83 ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.52/5.83 = ( ring_1_of_int_int @ Y2 ) )
% 5.52/5.83 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.52/5.83 = Y2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_power_eq_of_int_cancel_iff
% 5.52/5.83 thf(fact_5614_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [Y2: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ( ring_17405671764205052669omplex @ Y2 )
% 5.52/5.83 = ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N ) )
% 5.52/5.83 = ( Y2
% 5.52/5.83 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5615_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [Y2: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ( ring_1_of_int_real @ Y2 )
% 5.52/5.83 = ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.52/5.83 = ( Y2
% 5.52/5.83 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5616_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [Y2: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ( ring_1_of_int_rat @ Y2 )
% 5.52/5.83 = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.52/5.83 = ( Y2
% 5.52/5.83 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5617_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [Y2: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ( ring_1_of_int_int @ Y2 )
% 5.52/5.83 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.52/5.83 = ( Y2
% 5.52/5.83 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5618_of__int__power__le__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: int,B: int,W: nat] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.52/5.83 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power_le_of_int_cancel_iff
% 5.52/5.83 thf(fact_5619_of__int__power__le__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: int,B: int,W: nat] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.52/5.83 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power_le_of_int_cancel_iff
% 5.52/5.83 thf(fact_5620_of__int__power__le__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: int,B: int,W: nat] :
% 5.52/5.83 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.52/5.83 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power_le_of_int_cancel_iff
% 5.52/5.83 thf(fact_5621_of__int__le__of__int__power__cancel__iff,axiom,
% 5.52/5.83 ! [B: int,W: nat,X2: int] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X2 ) )
% 5.52/5.83 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_of_int_power_cancel_iff
% 5.52/5.83 thf(fact_5622_of__int__le__of__int__power__cancel__iff,axiom,
% 5.52/5.83 ! [B: int,W: nat,X2: int] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.52/5.83 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_of_int_power_cancel_iff
% 5.52/5.83 thf(fact_5623_of__int__le__of__int__power__cancel__iff,axiom,
% 5.52/5.83 ! [B: int,W: nat,X2: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X2 ) )
% 5.52/5.83 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_of_int_power_cancel_iff
% 5.52/5.83 thf(fact_5624_of__int__less__of__int__power__cancel__iff,axiom,
% 5.52/5.83 ! [B: int,W: nat,X2: int] :
% 5.52/5.83 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X2 ) )
% 5.52/5.83 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_of_int_power_cancel_iff
% 5.52/5.83 thf(fact_5625_of__int__less__of__int__power__cancel__iff,axiom,
% 5.52/5.83 ! [B: int,W: nat,X2: int] :
% 5.52/5.83 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.52/5.83 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_of_int_power_cancel_iff
% 5.52/5.83 thf(fact_5626_of__int__less__of__int__power__cancel__iff,axiom,
% 5.52/5.83 ! [B: int,W: nat,X2: int] :
% 5.52/5.83 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X2 ) )
% 5.52/5.83 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_of_int_power_cancel_iff
% 5.52/5.83 thf(fact_5627_of__int__power__less__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: int,B: int,W: nat] :
% 5.52/5.83 ( ( ord_less_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.52/5.83 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power_less_of_int_cancel_iff
% 5.52/5.83 thf(fact_5628_of__int__power__less__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: int,B: int,W: nat] :
% 5.52/5.83 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.52/5.83 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power_less_of_int_cancel_iff
% 5.52/5.83 thf(fact_5629_of__int__power__less__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: int,B: int,W: nat] :
% 5.52/5.83 ( ( ord_less_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.52/5.83 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_power_less_of_int_cancel_iff
% 5.52/5.83 thf(fact_5630_numeral__power__le__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: num,N: nat,A: int] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.52/5.83 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_power_le_of_int_cancel_iff
% 5.52/5.83 thf(fact_5631_numeral__power__le__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: num,N: nat,A: int] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.52/5.83 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_power_le_of_int_cancel_iff
% 5.52/5.83 thf(fact_5632_numeral__power__le__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: num,N: nat,A: int] :
% 5.52/5.83 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.52/5.83 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_power_le_of_int_cancel_iff
% 5.52/5.83 thf(fact_5633_of__int__le__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [A: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.52/5.83 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5634_of__int__le__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [A: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.52/5.83 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5635_of__int__le__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [A: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.52/5.83 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_le_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5636_numeral__power__less__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: num,N: nat,A: int] :
% 5.52/5.83 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.52/5.83 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_power_less_of_int_cancel_iff
% 5.52/5.83 thf(fact_5637_numeral__power__less__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: num,N: nat,A: int] :
% 5.52/5.83 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.52/5.83 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_power_less_of_int_cancel_iff
% 5.52/5.83 thf(fact_5638_numeral__power__less__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: num,N: nat,A: int] :
% 5.52/5.83 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.52/5.83 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.52/5.83
% 5.52/5.83 % numeral_power_less_of_int_cancel_iff
% 5.52/5.83 thf(fact_5639_of__int__less__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [A: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.52/5.83 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5640_of__int__less__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [A: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.52/5.83 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5641_of__int__less__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [A: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.52/5.83 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_less_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5642_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [Y2: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ( ring_1_of_int_int @ Y2 )
% 5.52/5.83 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.52/5.83 = ( Y2
% 5.52/5.83 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_neg_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5643_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [Y2: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ( ring_1_of_int_real @ Y2 )
% 5.52/5.83 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.52/5.83 = ( Y2
% 5.52/5.83 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_neg_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5644_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [Y2: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ( ring_17405671764205052669omplex @ Y2 )
% 5.52/5.83 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X2 ) ) @ N ) )
% 5.52/5.83 = ( Y2
% 5.52/5.83 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_neg_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5645_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [Y2: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ( ring_18347121197199848620nteger @ Y2 )
% 5.52/5.83 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.52/5.83 = ( Y2
% 5.52/5.83 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_neg_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5646_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.83 ! [Y2: int,X2: num,N: nat] :
% 5.52/5.83 ( ( ( ring_1_of_int_rat @ Y2 )
% 5.52/5.83 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.52/5.83 = ( Y2
% 5.52/5.83 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.83
% 5.52/5.83 % of_int_eq_neg_numeral_power_cancel_iff
% 5.52/5.83 thf(fact_5647_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.83 ! [X2: num,N: nat,Y2: int] :
% 5.52/5.84 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.52/5.84 = ( ring_1_of_int_int @ Y2 ) )
% 5.52/5.84 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.52/5.84 = Y2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_eq_of_int_cancel_iff
% 5.52/5.84 thf(fact_5648_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.84 ! [X2: num,N: nat,Y2: int] :
% 5.52/5.84 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N )
% 5.52/5.84 = ( ring_1_of_int_real @ Y2 ) )
% 5.52/5.84 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.52/5.84 = Y2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_eq_of_int_cancel_iff
% 5.52/5.84 thf(fact_5649_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.84 ! [X2: num,N: nat,Y2: int] :
% 5.52/5.84 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X2 ) ) @ N )
% 5.52/5.84 = ( ring_17405671764205052669omplex @ Y2 ) )
% 5.52/5.84 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.52/5.84 = Y2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_eq_of_int_cancel_iff
% 5.52/5.84 thf(fact_5650_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.84 ! [X2: num,N: nat,Y2: int] :
% 5.52/5.84 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N )
% 5.52/5.84 = ( ring_18347121197199848620nteger @ Y2 ) )
% 5.52/5.84 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.52/5.84 = Y2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_eq_of_int_cancel_iff
% 5.52/5.84 thf(fact_5651_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.52/5.84 ! [X2: num,N: nat,Y2: int] :
% 5.52/5.84 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N )
% 5.52/5.84 = ( ring_1_of_int_rat @ Y2 ) )
% 5.52/5.84 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.52/5.84 = Y2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_eq_of_int_cancel_iff
% 5.52/5.84 thf(fact_5652_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.84 ! [A: int,X2: num,N: nat] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.52/5.84 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_le_neg_numeral_power_cancel_iff
% 5.52/5.84 thf(fact_5653_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.84 ! [A: int,X2: num,N: nat] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.52/5.84 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_le_neg_numeral_power_cancel_iff
% 5.52/5.84 thf(fact_5654_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.84 ! [A: int,X2: num,N: nat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.52/5.84 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_le_neg_numeral_power_cancel_iff
% 5.52/5.84 thf(fact_5655_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.84 ! [A: int,X2: num,N: nat] :
% 5.52/5.84 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.52/5.84 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_le_neg_numeral_power_cancel_iff
% 5.52/5.84 thf(fact_5656_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.52/5.84 ! [X2: num,N: nat,A: int] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.52/5.84 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_le_of_int_cancel_iff
% 5.52/5.84 thf(fact_5657_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.52/5.84 ! [X2: num,N: nat,A: int] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.52/5.84 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_le_of_int_cancel_iff
% 5.52/5.84 thf(fact_5658_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.52/5.84 ! [X2: num,N: nat,A: int] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.52/5.84 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_le_of_int_cancel_iff
% 5.52/5.84 thf(fact_5659_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.52/5.84 ! [X2: num,N: nat,A: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.52/5.84 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_le_of_int_cancel_iff
% 5.52/5.84 thf(fact_5660_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.84 ! [A: int,X2: num,N: nat] :
% 5.52/5.84 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.52/5.84 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_less_neg_numeral_power_cancel_iff
% 5.52/5.84 thf(fact_5661_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.84 ! [A: int,X2: num,N: nat] :
% 5.52/5.84 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.52/5.84 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_less_neg_numeral_power_cancel_iff
% 5.52/5.84 thf(fact_5662_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.84 ! [A: int,X2: num,N: nat] :
% 5.52/5.84 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.52/5.84 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_less_neg_numeral_power_cancel_iff
% 5.52/5.84 thf(fact_5663_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.52/5.84 ! [A: int,X2: num,N: nat] :
% 5.52/5.84 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.52/5.84 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_less_neg_numeral_power_cancel_iff
% 5.52/5.84 thf(fact_5664_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.52/5.84 ! [X2: num,N: nat,A: int] :
% 5.52/5.84 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.52/5.84 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_less_of_int_cancel_iff
% 5.52/5.84 thf(fact_5665_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.52/5.84 ! [X2: num,N: nat,A: int] :
% 5.52/5.84 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.52/5.84 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_less_of_int_cancel_iff
% 5.52/5.84 thf(fact_5666_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.52/5.84 ! [X2: num,N: nat,A: int] :
% 5.52/5.84 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.52/5.84 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_less_of_int_cancel_iff
% 5.52/5.84 thf(fact_5667_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.52/5.84 ! [X2: num,N: nat,A: int] :
% 5.52/5.84 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.52/5.84 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % neg_numeral_power_less_of_int_cancel_iff
% 5.52/5.84 thf(fact_5668_mult__of__int__commute,axiom,
% 5.52/5.84 ! [X2: int,Y2: real] :
% 5.52/5.84 ( ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ Y2 )
% 5.52/5.84 = ( times_times_real @ Y2 @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % mult_of_int_commute
% 5.52/5.84 thf(fact_5669_mult__of__int__commute,axiom,
% 5.52/5.84 ! [X2: int,Y2: rat] :
% 5.52/5.84 ( ( times_times_rat @ ( ring_1_of_int_rat @ X2 ) @ Y2 )
% 5.52/5.84 = ( times_times_rat @ Y2 @ ( ring_1_of_int_rat @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % mult_of_int_commute
% 5.52/5.84 thf(fact_5670_mult__of__int__commute,axiom,
% 5.52/5.84 ! [X2: int,Y2: int] :
% 5.52/5.84 ( ( times_times_int @ ( ring_1_of_int_int @ X2 ) @ Y2 )
% 5.52/5.84 = ( times_times_int @ Y2 @ ( ring_1_of_int_int @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % mult_of_int_commute
% 5.52/5.84 thf(fact_5671_bot__nat__def,axiom,
% 5.52/5.84 bot_bot_nat = zero_zero_nat ).
% 5.52/5.84
% 5.52/5.84 % bot_nat_def
% 5.52/5.84 thf(fact_5672_bot__enat__def,axiom,
% 5.52/5.84 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.52/5.84
% 5.52/5.84 % bot_enat_def
% 5.52/5.84 thf(fact_5673_ln__less__self,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ord_less_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_less_self
% 5.52/5.84 thf(fact_5674_ln__bound,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_bound
% 5.52/5.84 thf(fact_5675_ln__gt__zero,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ one_one_real @ X2 )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_gt_zero
% 5.52/5.84 thf(fact_5676_ln__less__zero,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.52/5.84 => ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_less_zero
% 5.52/5.84 thf(fact_5677_ln__gt__zero__imp__gt__one,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_gt_zero_imp_gt_one
% 5.52/5.84 thf(fact_5678_real__of__int__div4,axiom,
% 5.52/5.84 ! [N: int,X2: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % real_of_int_div4
% 5.52/5.84 thf(fact_5679_real__of__int__div,axiom,
% 5.52/5.84 ! [D2: int,N: int] :
% 5.52/5.84 ( ( dvd_dvd_int @ D2 @ N )
% 5.52/5.84 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D2 ) )
% 5.52/5.84 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % real_of_int_div
% 5.52/5.84 thf(fact_5680_ln__ge__zero__imp__ge__one,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_ge_zero_imp_ge_one
% 5.52/5.84 thf(fact_5681_ln__mult,axiom,
% 5.52/5.84 ! [X2: real,Y2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.84 => ( ( ln_ln_real @ ( times_times_real @ X2 @ Y2 ) )
% 5.52/5.84 = ( plus_plus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_mult
% 5.52/5.84 thf(fact_5682_ln__eq__minus__one,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ( ( ln_ln_real @ X2 )
% 5.52/5.84 = ( minus_minus_real @ X2 @ one_one_real ) )
% 5.52/5.84 => ( X2 = one_one_real ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_eq_minus_one
% 5.52/5.84 thf(fact_5683_ln__div,axiom,
% 5.52/5.84 ! [X2: real,Y2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.84 => ( ( ln_ln_real @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.52/5.84 = ( minus_minus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_div
% 5.52/5.84 thf(fact_5684_of__int__nonneg,axiom,
% 5.52/5.84 ! [Z: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_nonneg
% 5.52/5.84 thf(fact_5685_of__int__nonneg,axiom,
% 5.52/5.84 ! [Z: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_nonneg
% 5.52/5.84 thf(fact_5686_of__int__nonneg,axiom,
% 5.52/5.84 ! [Z: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.52/5.84 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_nonneg
% 5.52/5.84 thf(fact_5687_of__int__pos,axiom,
% 5.52/5.84 ! [Z: int] :
% 5.52/5.84 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_pos
% 5.52/5.84 thf(fact_5688_of__int__pos,axiom,
% 5.52/5.84 ! [Z: int] :
% 5.52/5.84 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_pos
% 5.52/5.84 thf(fact_5689_of__int__pos,axiom,
% 5.52/5.84 ! [Z: int] :
% 5.52/5.84 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.52/5.84 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_pos
% 5.52/5.84 thf(fact_5690_of__int__neg__numeral,axiom,
% 5.52/5.84 ! [K: num] :
% 5.52/5.84 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.52/5.84 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_neg_numeral
% 5.52/5.84 thf(fact_5691_of__int__neg__numeral,axiom,
% 5.52/5.84 ! [K: num] :
% 5.52/5.84 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.52/5.84 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_neg_numeral
% 5.52/5.84 thf(fact_5692_of__int__neg__numeral,axiom,
% 5.52/5.84 ! [K: num] :
% 5.52/5.84 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.52/5.84 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_neg_numeral
% 5.52/5.84 thf(fact_5693_of__int__neg__numeral,axiom,
% 5.52/5.84 ! [K: num] :
% 5.52/5.84 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.52/5.84 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_neg_numeral
% 5.52/5.84 thf(fact_5694_of__int__neg__numeral,axiom,
% 5.52/5.84 ! [K: num] :
% 5.52/5.84 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.52/5.84 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_neg_numeral
% 5.52/5.84 thf(fact_5695_int__le__real__less,axiom,
% 5.52/5.84 ( ord_less_eq_int
% 5.52/5.84 = ( ^ [N3: int,M3: int] : ( ord_less_real @ ( ring_1_of_int_real @ N3 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M3 ) @ one_one_real ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % int_le_real_less
% 5.52/5.84 thf(fact_5696_int__less__real__le,axiom,
% 5.52/5.84 ( ord_less_int
% 5.52/5.84 = ( ^ [N3: int,M3: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N3 ) @ one_one_real ) @ ( ring_1_of_int_real @ M3 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % int_less_real_le
% 5.52/5.84 thf(fact_5697_real__of__int__div__aux,axiom,
% 5.52/5.84 ! [X2: int,D2: int] :
% 5.52/5.84 ( ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ D2 ) )
% 5.52/5.84 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X2 @ D2 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X2 @ D2 ) ) @ ( ring_1_of_int_real @ D2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % real_of_int_div_aux
% 5.52/5.84 thf(fact_5698_ln__2__less__1,axiom,
% 5.52/5.84 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.52/5.84
% 5.52/5.84 % ln_2_less_1
% 5.52/5.84 thf(fact_5699_ln__le__minus__one,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_le_minus_one
% 5.52/5.84 thf(fact_5700_ln__diff__le,axiom,
% 5.52/5.84 ! [X2: real,Y2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.84 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y2 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X2 @ Y2 ) @ Y2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_diff_le
% 5.52/5.84 thf(fact_5701_ln__add__one__self__le__self2,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.84 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_add_one_self_le_self2
% 5.52/5.84 thf(fact_5702_real__of__int__div2,axiom,
% 5.52/5.84 ! [N: int,X2: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % real_of_int_div2
% 5.52/5.84 thf(fact_5703_real__of__int__div3,axiom,
% 5.52/5.84 ! [N: int,X2: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) ) @ one_one_real ) ).
% 5.52/5.84
% 5.52/5.84 % real_of_int_div3
% 5.52/5.84 thf(fact_5704_ln__one__minus__pos__upper__bound,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.52/5.84 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) @ ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_one_minus_pos_upper_bound
% 5.52/5.84 thf(fact_5705_even__of__int__iff,axiom,
% 5.52/5.84 ! [K: int] :
% 5.52/5.84 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.52/5.84 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % even_of_int_iff
% 5.52/5.84 thf(fact_5706_even__of__int__iff,axiom,
% 5.52/5.84 ! [K: int] :
% 5.52/5.84 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.52/5.84 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % even_of_int_iff
% 5.52/5.84 thf(fact_5707_ln__one__plus__pos__lower__bound,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.52/5.84 => ( ord_less_eq_real @ ( minus_minus_real @ X2 @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % ln_one_plus_pos_lower_bound
% 5.52/5.84 thf(fact_5708_artanh__def,axiom,
% 5.52/5.84 ( artanh_real
% 5.52/5.84 = ( ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X ) @ ( minus_minus_real @ one_one_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % artanh_def
% 5.52/5.84 thf(fact_5709_floor__exists,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ? [Z3: int] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X2 )
% 5.52/5.84 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % floor_exists
% 5.52/5.84 thf(fact_5710_floor__exists,axiom,
% 5.52/5.84 ! [X2: rat] :
% 5.52/5.84 ? [Z3: int] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X2 )
% 5.52/5.84 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % floor_exists
% 5.52/5.84 thf(fact_5711_floor__exists1,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ? [X4: int] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ X2 )
% 5.52/5.84 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 5.52/5.84 & ! [Y4: int] :
% 5.52/5.84 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X2 )
% 5.52/5.84 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.52/5.84 => ( Y4 = X4 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % floor_exists1
% 5.52/5.84 thf(fact_5712_floor__exists1,axiom,
% 5.52/5.84 ! [X2: rat] :
% 5.52/5.84 ? [X4: int] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ X2 )
% 5.52/5.84 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 5.52/5.84 & ! [Y4: int] :
% 5.52/5.84 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X2 )
% 5.52/5.84 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.52/5.84 => ( Y4 = X4 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % floor_exists1
% 5.52/5.84 thf(fact_5713_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.84 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.52/5.84 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.52/5.84 thf(fact_5714_tanh__ln__real,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ( tanh_real @ ( ln_ln_real @ X2 ) )
% 5.52/5.84 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % tanh_ln_real
% 5.52/5.84 thf(fact_5715_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ln_one_plus_x_minus_x_bound
% 5.52/5.84 thf(fact_5716_abs__idempotent,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.52/5.84 = ( abs_abs_real @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_idempotent
% 5.52/5.84 thf(fact_5717_abs__idempotent,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.52/5.84 = ( abs_abs_int @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_idempotent
% 5.52/5.84 thf(fact_5718_abs__idempotent,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.52/5.84 = ( abs_abs_Code_integer @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_idempotent
% 5.52/5.84 thf(fact_5719_abs__idempotent,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.52/5.84 = ( abs_abs_rat @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_idempotent
% 5.52/5.84 thf(fact_5720_abs__abs,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.52/5.84 = ( abs_abs_real @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_abs
% 5.52/5.84 thf(fact_5721_abs__abs,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.52/5.84 = ( abs_abs_int @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_abs
% 5.52/5.84 thf(fact_5722_abs__abs,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.52/5.84 = ( abs_abs_Code_integer @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_abs
% 5.52/5.84 thf(fact_5723_abs__abs,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.52/5.84 = ( abs_abs_rat @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_abs
% 5.52/5.84 thf(fact_5724_abs__zero,axiom,
% 5.52/5.84 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.52/5.84 = zero_z3403309356797280102nteger ) ).
% 5.52/5.84
% 5.52/5.84 % abs_zero
% 5.52/5.84 thf(fact_5725_abs__zero,axiom,
% 5.52/5.84 ( ( abs_abs_real @ zero_zero_real )
% 5.52/5.84 = zero_zero_real ) ).
% 5.52/5.84
% 5.52/5.84 % abs_zero
% 5.52/5.84 thf(fact_5726_abs__zero,axiom,
% 5.52/5.84 ( ( abs_abs_rat @ zero_zero_rat )
% 5.52/5.84 = zero_zero_rat ) ).
% 5.52/5.84
% 5.52/5.84 % abs_zero
% 5.52/5.84 thf(fact_5727_abs__zero,axiom,
% 5.52/5.84 ( ( abs_abs_int @ zero_zero_int )
% 5.52/5.84 = zero_zero_int ) ).
% 5.52/5.84
% 5.52/5.84 % abs_zero
% 5.52/5.84 thf(fact_5728_abs__eq__0,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( ( abs_abs_Code_integer @ A )
% 5.52/5.84 = zero_z3403309356797280102nteger )
% 5.52/5.84 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_0
% 5.52/5.84 thf(fact_5729_abs__eq__0,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( ( abs_abs_real @ A )
% 5.52/5.84 = zero_zero_real )
% 5.52/5.84 = ( A = zero_zero_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_0
% 5.52/5.84 thf(fact_5730_abs__eq__0,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( ( abs_abs_rat @ A )
% 5.52/5.84 = zero_zero_rat )
% 5.52/5.84 = ( A = zero_zero_rat ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_0
% 5.52/5.84 thf(fact_5731_abs__eq__0,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( ( abs_abs_int @ A )
% 5.52/5.84 = zero_zero_int )
% 5.52/5.84 = ( A = zero_zero_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_0
% 5.52/5.84 thf(fact_5732_abs__0__eq,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( zero_z3403309356797280102nteger
% 5.52/5.84 = ( abs_abs_Code_integer @ A ) )
% 5.52/5.84 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_0_eq
% 5.52/5.84 thf(fact_5733_abs__0__eq,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( zero_zero_real
% 5.52/5.84 = ( abs_abs_real @ A ) )
% 5.52/5.84 = ( A = zero_zero_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_0_eq
% 5.52/5.84 thf(fact_5734_abs__0__eq,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( zero_zero_rat
% 5.52/5.84 = ( abs_abs_rat @ A ) )
% 5.52/5.84 = ( A = zero_zero_rat ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_0_eq
% 5.52/5.84 thf(fact_5735_abs__0__eq,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( zero_zero_int
% 5.52/5.84 = ( abs_abs_int @ A ) )
% 5.52/5.84 = ( A = zero_zero_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_0_eq
% 5.52/5.84 thf(fact_5736_abs__0,axiom,
% 5.52/5.84 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.52/5.84 = zero_z3403309356797280102nteger ) ).
% 5.52/5.84
% 5.52/5.84 % abs_0
% 5.52/5.84 thf(fact_5737_abs__0,axiom,
% 5.52/5.84 ( ( abs_abs_real @ zero_zero_real )
% 5.52/5.84 = zero_zero_real ) ).
% 5.52/5.84
% 5.52/5.84 % abs_0
% 5.52/5.84 thf(fact_5738_abs__0,axiom,
% 5.52/5.84 ( ( abs_abs_rat @ zero_zero_rat )
% 5.52/5.84 = zero_zero_rat ) ).
% 5.52/5.84
% 5.52/5.84 % abs_0
% 5.52/5.84 thf(fact_5739_abs__0,axiom,
% 5.52/5.84 ( ( abs_abs_int @ zero_zero_int )
% 5.52/5.84 = zero_zero_int ) ).
% 5.52/5.84
% 5.52/5.84 % abs_0
% 5.52/5.84 thf(fact_5740_abs__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.52/5.84 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_numeral
% 5.52/5.84 thf(fact_5741_abs__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 5.52/5.84 = ( numeral_numeral_real @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_numeral
% 5.52/5.84 thf(fact_5742_abs__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 5.52/5.84 = ( numeral_numeral_rat @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_numeral
% 5.52/5.84 thf(fact_5743_abs__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 5.52/5.84 = ( numeral_numeral_int @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_numeral
% 5.52/5.84 thf(fact_5744_abs__mult__self__eq,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.52/5.84 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult_self_eq
% 5.52/5.84 thf(fact_5745_abs__mult__self__eq,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.52/5.84 = ( times_times_real @ A @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult_self_eq
% 5.52/5.84 thf(fact_5746_abs__mult__self__eq,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.52/5.84 = ( times_times_rat @ A @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult_self_eq
% 5.52/5.84 thf(fact_5747_abs__mult__self__eq,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.52/5.84 = ( times_times_int @ A @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult_self_eq
% 5.52/5.84 thf(fact_5748_abs__1,axiom,
% 5.52/5.84 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.52/5.84 = one_one_Code_integer ) ).
% 5.52/5.84
% 5.52/5.84 % abs_1
% 5.52/5.84 thf(fact_5749_abs__1,axiom,
% 5.52/5.84 ( ( abs_abs_complex @ one_one_complex )
% 5.52/5.84 = one_one_complex ) ).
% 5.52/5.84
% 5.52/5.84 % abs_1
% 5.52/5.84 thf(fact_5750_abs__1,axiom,
% 5.52/5.84 ( ( abs_abs_real @ one_one_real )
% 5.52/5.84 = one_one_real ) ).
% 5.52/5.84
% 5.52/5.84 % abs_1
% 5.52/5.84 thf(fact_5751_abs__1,axiom,
% 5.52/5.84 ( ( abs_abs_rat @ one_one_rat )
% 5.52/5.84 = one_one_rat ) ).
% 5.52/5.84
% 5.52/5.84 % abs_1
% 5.52/5.84 thf(fact_5752_abs__1,axiom,
% 5.52/5.84 ( ( abs_abs_int @ one_one_int )
% 5.52/5.84 = one_one_int ) ).
% 5.52/5.84
% 5.52/5.84 % abs_1
% 5.52/5.84 thf(fact_5753_abs__add__abs,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.52/5.84 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_add_abs
% 5.52/5.84 thf(fact_5754_abs__add__abs,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.52/5.84 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_add_abs
% 5.52/5.84 thf(fact_5755_abs__add__abs,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.52/5.84 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_add_abs
% 5.52/5.84 thf(fact_5756_abs__add__abs,axiom,
% 5.52/5.84 ! [A: int,B: int] :
% 5.52/5.84 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.52/5.84 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_add_abs
% 5.52/5.84 thf(fact_5757_abs__divide,axiom,
% 5.52/5.84 ! [A: complex,B: complex] :
% 5.52/5.84 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.52/5.84 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_divide
% 5.52/5.84 thf(fact_5758_abs__divide,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.52/5.84 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_divide
% 5.52/5.84 thf(fact_5759_abs__divide,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.52/5.84 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_divide
% 5.52/5.84 thf(fact_5760_abs__minus__cancel,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.52/5.84 = ( abs_abs_int @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus_cancel
% 5.52/5.84 thf(fact_5761_abs__minus__cancel,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.52/5.84 = ( abs_abs_real @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus_cancel
% 5.52/5.84 thf(fact_5762_abs__minus__cancel,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.84 = ( abs_abs_Code_integer @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus_cancel
% 5.52/5.84 thf(fact_5763_abs__minus__cancel,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.52/5.84 = ( abs_abs_rat @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus_cancel
% 5.52/5.84 thf(fact_5764_abs__minus,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.52/5.84 = ( abs_abs_int @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus
% 5.52/5.84 thf(fact_5765_abs__minus,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.52/5.84 = ( abs_abs_real @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus
% 5.52/5.84 thf(fact_5766_abs__minus,axiom,
% 5.52/5.84 ! [A: complex] :
% 5.52/5.84 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.52/5.84 = ( abs_abs_complex @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus
% 5.52/5.84 thf(fact_5767_abs__minus,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.52/5.84 = ( abs_abs_Code_integer @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus
% 5.52/5.84 thf(fact_5768_abs__minus,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.52/5.84 = ( abs_abs_rat @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus
% 5.52/5.84 thf(fact_5769_dvd__abs__iff,axiom,
% 5.52/5.84 ! [M: real,K: real] :
% 5.52/5.84 ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 5.52/5.84 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % dvd_abs_iff
% 5.52/5.84 thf(fact_5770_dvd__abs__iff,axiom,
% 5.52/5.84 ! [M: int,K: int] :
% 5.52/5.84 ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 5.52/5.84 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % dvd_abs_iff
% 5.52/5.84 thf(fact_5771_dvd__abs__iff,axiom,
% 5.52/5.84 ! [M: code_integer,K: code_integer] :
% 5.52/5.84 ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 5.52/5.84 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % dvd_abs_iff
% 5.52/5.84 thf(fact_5772_dvd__abs__iff,axiom,
% 5.52/5.84 ! [M: rat,K: rat] :
% 5.52/5.84 ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 5.52/5.84 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % dvd_abs_iff
% 5.52/5.84 thf(fact_5773_abs__dvd__iff,axiom,
% 5.52/5.84 ! [M: real,K: real] :
% 5.52/5.84 ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 5.52/5.84 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_dvd_iff
% 5.52/5.84 thf(fact_5774_abs__dvd__iff,axiom,
% 5.52/5.84 ! [M: int,K: int] :
% 5.52/5.84 ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 5.52/5.84 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_dvd_iff
% 5.52/5.84 thf(fact_5775_abs__dvd__iff,axiom,
% 5.52/5.84 ! [M: code_integer,K: code_integer] :
% 5.52/5.84 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 5.52/5.84 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_dvd_iff
% 5.52/5.84 thf(fact_5776_abs__dvd__iff,axiom,
% 5.52/5.84 ! [M: rat,K: rat] :
% 5.52/5.84 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 5.52/5.84 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_dvd_iff
% 5.52/5.84 thf(fact_5777_abs__bool__eq,axiom,
% 5.52/5.84 ! [P: $o] :
% 5.52/5.84 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.52/5.84 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_bool_eq
% 5.52/5.84 thf(fact_5778_abs__bool__eq,axiom,
% 5.52/5.84 ! [P: $o] :
% 5.52/5.84 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.52/5.84 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_bool_eq
% 5.52/5.84 thf(fact_5779_abs__bool__eq,axiom,
% 5.52/5.84 ! [P: $o] :
% 5.52/5.84 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.52/5.84 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_bool_eq
% 5.52/5.84 thf(fact_5780_abs__bool__eq,axiom,
% 5.52/5.84 ! [P: $o] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 5.52/5.84 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_bool_eq
% 5.52/5.84 thf(fact_5781_tanh__real__less__iff,axiom,
% 5.52/5.84 ! [X2: real,Y2: real] :
% 5.52/5.84 ( ( ord_less_real @ ( tanh_real @ X2 ) @ ( tanh_real @ Y2 ) )
% 5.52/5.84 = ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % tanh_real_less_iff
% 5.52/5.84 thf(fact_5782_abs__of__nonneg,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.52/5.84 => ( ( abs_abs_Code_integer @ A )
% 5.52/5.84 = A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_nonneg
% 5.52/5.84 thf(fact_5783_abs__of__nonneg,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.84 => ( ( abs_abs_real @ A )
% 5.52/5.84 = A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_nonneg
% 5.52/5.84 thf(fact_5784_abs__of__nonneg,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.84 => ( ( abs_abs_rat @ A )
% 5.52/5.84 = A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_nonneg
% 5.52/5.84 thf(fact_5785_abs__of__nonneg,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.84 => ( ( abs_abs_int @ A )
% 5.52/5.84 = A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_nonneg
% 5.52/5.84 thf(fact_5786_abs__le__self__iff,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.52/5.84 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_self_iff
% 5.52/5.84 thf(fact_5787_abs__le__self__iff,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.52/5.84 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_self_iff
% 5.52/5.84 thf(fact_5788_abs__le__self__iff,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.52/5.84 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_self_iff
% 5.52/5.84 thf(fact_5789_abs__le__self__iff,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.52/5.84 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_self_iff
% 5.52/5.84 thf(fact_5790_abs__le__zero__iff,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.52/5.84 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_zero_iff
% 5.52/5.84 thf(fact_5791_abs__le__zero__iff,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.52/5.84 = ( A = zero_zero_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_zero_iff
% 5.52/5.84 thf(fact_5792_abs__le__zero__iff,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.52/5.84 = ( A = zero_zero_rat ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_zero_iff
% 5.52/5.84 thf(fact_5793_abs__le__zero__iff,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.52/5.84 = ( A = zero_zero_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_zero_iff
% 5.52/5.84 thf(fact_5794_zero__less__abs__iff,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.52/5.84 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_less_abs_iff
% 5.52/5.84 thf(fact_5795_zero__less__abs__iff,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.52/5.84 = ( A != zero_zero_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_less_abs_iff
% 5.52/5.84 thf(fact_5796_zero__less__abs__iff,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.52/5.84 = ( A != zero_zero_rat ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_less_abs_iff
% 5.52/5.84 thf(fact_5797_zero__less__abs__iff,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.52/5.84 = ( A != zero_zero_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_less_abs_iff
% 5.52/5.84 thf(fact_5798_abs__neg__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.84 = ( numeral_numeral_int @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_neg_numeral
% 5.52/5.84 thf(fact_5799_abs__neg__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.84 = ( numeral_numeral_real @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_neg_numeral
% 5.52/5.84 thf(fact_5800_abs__neg__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.52/5.84 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_neg_numeral
% 5.52/5.84 thf(fact_5801_abs__neg__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.52/5.84 = ( numeral_numeral_rat @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_neg_numeral
% 5.52/5.84 thf(fact_5802_abs__neg__one,axiom,
% 5.52/5.84 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.84 = one_one_int ) ).
% 5.52/5.84
% 5.52/5.84 % abs_neg_one
% 5.52/5.84 thf(fact_5803_abs__neg__one,axiom,
% 5.52/5.84 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.84 = one_one_real ) ).
% 5.52/5.84
% 5.52/5.84 % abs_neg_one
% 5.52/5.84 thf(fact_5804_abs__neg__one,axiom,
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.84 = one_one_Code_integer ) ).
% 5.52/5.84
% 5.52/5.84 % abs_neg_one
% 5.52/5.84 thf(fact_5805_abs__neg__one,axiom,
% 5.52/5.84 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.84 = one_one_rat ) ).
% 5.52/5.84
% 5.52/5.84 % abs_neg_one
% 5.52/5.84 thf(fact_5806_abs__power__minus,axiom,
% 5.52/5.84 ! [A: int,N: nat] :
% 5.52/5.84 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.52/5.84 = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_power_minus
% 5.52/5.84 thf(fact_5807_abs__power__minus,axiom,
% 5.52/5.84 ! [A: real,N: nat] :
% 5.52/5.84 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.52/5.84 = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_power_minus
% 5.52/5.84 thf(fact_5808_abs__power__minus,axiom,
% 5.52/5.84 ! [A: code_integer,N: nat] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.52/5.84 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_power_minus
% 5.52/5.84 thf(fact_5809_abs__power__minus,axiom,
% 5.52/5.84 ! [A: rat,N: nat] :
% 5.52/5.84 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.52/5.84 = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_power_minus
% 5.52/5.84 thf(fact_5810_tanh__real__pos__iff,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X2 ) )
% 5.52/5.84 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % tanh_real_pos_iff
% 5.52/5.84 thf(fact_5811_tanh__real__neg__iff,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ ( tanh_real @ X2 ) @ zero_zero_real )
% 5.52/5.84 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % tanh_real_neg_iff
% 5.52/5.84 thf(fact_5812_divide__le__0__abs__iff,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.52/5.84 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.84 | ( B = zero_zero_real ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % divide_le_0_abs_iff
% 5.52/5.84 thf(fact_5813_divide__le__0__abs__iff,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.52/5.84 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.84 | ( B = zero_zero_rat ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % divide_le_0_abs_iff
% 5.52/5.84 thf(fact_5814_zero__le__divide__abs__iff,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.52/5.84 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.84 | ( B = zero_zero_real ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_le_divide_abs_iff
% 5.52/5.84 thf(fact_5815_zero__le__divide__abs__iff,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.52/5.84 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.84 | ( B = zero_zero_rat ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_le_divide_abs_iff
% 5.52/5.84 thf(fact_5816_abs__of__nonpos,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.84 => ( ( abs_abs_real @ A )
% 5.52/5.84 = ( uminus_uminus_real @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_nonpos
% 5.52/5.84 thf(fact_5817_abs__of__nonpos,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.52/5.84 => ( ( abs_abs_Code_integer @ A )
% 5.52/5.84 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_nonpos
% 5.52/5.84 thf(fact_5818_abs__of__nonpos,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.52/5.84 => ( ( abs_abs_rat @ A )
% 5.52/5.84 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_nonpos
% 5.52/5.84 thf(fact_5819_abs__of__nonpos,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.52/5.84 => ( ( abs_abs_int @ A )
% 5.52/5.84 = ( uminus_uminus_int @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_nonpos
% 5.52/5.84 thf(fact_5820_artanh__minus__real,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.52/5.84 => ( ( artanh_real @ ( uminus_uminus_real @ X2 ) )
% 5.52/5.84 = ( uminus_uminus_real @ ( artanh_real @ X2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % artanh_minus_real
% 5.52/5.84 thf(fact_5821_zero__less__power__abs__iff,axiom,
% 5.52/5.84 ! [A: code_integer,N: nat] :
% 5.52/5.84 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 5.52/5.84 = ( ( A != zero_z3403309356797280102nteger )
% 5.52/5.84 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_less_power_abs_iff
% 5.52/5.84 thf(fact_5822_zero__less__power__abs__iff,axiom,
% 5.52/5.84 ! [A: real,N: nat] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.52/5.84 = ( ( A != zero_zero_real )
% 5.52/5.84 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_less_power_abs_iff
% 5.52/5.84 thf(fact_5823_zero__less__power__abs__iff,axiom,
% 5.52/5.84 ! [A: rat,N: nat] :
% 5.52/5.84 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 5.52/5.84 = ( ( A != zero_zero_rat )
% 5.52/5.84 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_less_power_abs_iff
% 5.52/5.84 thf(fact_5824_zero__less__power__abs__iff,axiom,
% 5.52/5.84 ! [A: int,N: nat] :
% 5.52/5.84 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 5.52/5.84 = ( ( A != zero_zero_int )
% 5.52/5.84 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_less_power_abs_iff
% 5.52/5.84 thf(fact_5825_power2__abs,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.84 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power2_abs
% 5.52/5.84 thf(fact_5826_power2__abs,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.84 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power2_abs
% 5.52/5.84 thf(fact_5827_power2__abs,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.84 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power2_abs
% 5.52/5.84 thf(fact_5828_power2__abs,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.84 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power2_abs
% 5.52/5.84 thf(fact_5829_abs__power2,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.84 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_power2
% 5.52/5.84 thf(fact_5830_abs__power2,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.84 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_power2
% 5.52/5.84 thf(fact_5831_abs__power2,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.84 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_power2
% 5.52/5.84 thf(fact_5832_abs__power2,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.84 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_power2
% 5.52/5.84 thf(fact_5833_power__even__abs__numeral,axiom,
% 5.52/5.84 ! [W: num,A: code_integer] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.84 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.84 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_even_abs_numeral
% 5.52/5.84 thf(fact_5834_power__even__abs__numeral,axiom,
% 5.52/5.84 ! [W: num,A: rat] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.84 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.84 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_even_abs_numeral
% 5.52/5.84 thf(fact_5835_power__even__abs__numeral,axiom,
% 5.52/5.84 ! [W: num,A: real] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.84 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.84 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_even_abs_numeral
% 5.52/5.84 thf(fact_5836_power__even__abs__numeral,axiom,
% 5.52/5.84 ! [W: num,A: int] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.84 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.52/5.84 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_even_abs_numeral
% 5.52/5.84 thf(fact_5837_abs__ge__self,axiom,
% 5.52/5.84 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ge_self
% 5.52/5.84 thf(fact_5838_abs__ge__self,axiom,
% 5.52/5.84 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ge_self
% 5.52/5.84 thf(fact_5839_abs__ge__self,axiom,
% 5.52/5.84 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ge_self
% 5.52/5.84 thf(fact_5840_abs__ge__self,axiom,
% 5.52/5.84 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ge_self
% 5.52/5.84 thf(fact_5841_abs__le__D1,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.52/5.84 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_D1
% 5.52/5.84 thf(fact_5842_abs__le__D1,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.52/5.84 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_D1
% 5.52/5.84 thf(fact_5843_abs__le__D1,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.52/5.84 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_D1
% 5.52/5.84 thf(fact_5844_abs__le__D1,axiom,
% 5.52/5.84 ! [A: int,B: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.52/5.84 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_D1
% 5.52/5.84 thf(fact_5845_abs__eq__0__iff,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( ( abs_abs_Code_integer @ A )
% 5.52/5.84 = zero_z3403309356797280102nteger )
% 5.52/5.84 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_0_iff
% 5.52/5.84 thf(fact_5846_abs__eq__0__iff,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( ( abs_abs_real @ A )
% 5.52/5.84 = zero_zero_real )
% 5.52/5.84 = ( A = zero_zero_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_0_iff
% 5.52/5.84 thf(fact_5847_abs__eq__0__iff,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( ( abs_abs_rat @ A )
% 5.52/5.84 = zero_zero_rat )
% 5.52/5.84 = ( A = zero_zero_rat ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_0_iff
% 5.52/5.84 thf(fact_5848_abs__eq__0__iff,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( ( abs_abs_int @ A )
% 5.52/5.84 = zero_zero_int )
% 5.52/5.84 = ( A = zero_zero_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_0_iff
% 5.52/5.84 thf(fact_5849_abs__mult,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.52/5.84 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult
% 5.52/5.84 thf(fact_5850_abs__mult,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.52/5.84 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult
% 5.52/5.84 thf(fact_5851_abs__mult,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.52/5.84 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult
% 5.52/5.84 thf(fact_5852_abs__mult,axiom,
% 5.52/5.84 ! [A: int,B: int] :
% 5.52/5.84 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.52/5.84 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult
% 5.52/5.84 thf(fact_5853_abs__one,axiom,
% 5.52/5.84 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.52/5.84 = one_one_Code_integer ) ).
% 5.52/5.84
% 5.52/5.84 % abs_one
% 5.52/5.84 thf(fact_5854_abs__one,axiom,
% 5.52/5.84 ( ( abs_abs_real @ one_one_real )
% 5.52/5.84 = one_one_real ) ).
% 5.52/5.84
% 5.52/5.84 % abs_one
% 5.52/5.84 thf(fact_5855_abs__one,axiom,
% 5.52/5.84 ( ( abs_abs_rat @ one_one_rat )
% 5.52/5.84 = one_one_rat ) ).
% 5.52/5.84
% 5.52/5.84 % abs_one
% 5.52/5.84 thf(fact_5856_abs__one,axiom,
% 5.52/5.84 ( ( abs_abs_int @ one_one_int )
% 5.52/5.84 = one_one_int ) ).
% 5.52/5.84
% 5.52/5.84 % abs_one
% 5.52/5.84 thf(fact_5857_abs__minus__commute,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.52/5.84 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus_commute
% 5.52/5.84 thf(fact_5858_abs__minus__commute,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.52/5.84 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus_commute
% 5.52/5.84 thf(fact_5859_abs__minus__commute,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.52/5.84 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus_commute
% 5.52/5.84 thf(fact_5860_abs__minus__commute,axiom,
% 5.52/5.84 ! [A: int,B: int] :
% 5.52/5.84 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.52/5.84 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus_commute
% 5.52/5.84 thf(fact_5861_abs__eq__iff,axiom,
% 5.52/5.84 ! [X2: int,Y2: int] :
% 5.52/5.84 ( ( ( abs_abs_int @ X2 )
% 5.52/5.84 = ( abs_abs_int @ Y2 ) )
% 5.52/5.84 = ( ( X2 = Y2 )
% 5.52/5.84 | ( X2
% 5.52/5.84 = ( uminus_uminus_int @ Y2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_iff
% 5.52/5.84 thf(fact_5862_abs__eq__iff,axiom,
% 5.52/5.84 ! [X2: real,Y2: real] :
% 5.52/5.84 ( ( ( abs_abs_real @ X2 )
% 5.52/5.84 = ( abs_abs_real @ Y2 ) )
% 5.52/5.84 = ( ( X2 = Y2 )
% 5.52/5.84 | ( X2
% 5.52/5.84 = ( uminus_uminus_real @ Y2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_iff
% 5.52/5.84 thf(fact_5863_abs__eq__iff,axiom,
% 5.52/5.84 ! [X2: code_integer,Y2: code_integer] :
% 5.52/5.84 ( ( ( abs_abs_Code_integer @ X2 )
% 5.52/5.84 = ( abs_abs_Code_integer @ Y2 ) )
% 5.52/5.84 = ( ( X2 = Y2 )
% 5.52/5.84 | ( X2
% 5.52/5.84 = ( uminus1351360451143612070nteger @ Y2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_iff
% 5.52/5.84 thf(fact_5864_abs__eq__iff,axiom,
% 5.52/5.84 ! [X2: rat,Y2: rat] :
% 5.52/5.84 ( ( ( abs_abs_rat @ X2 )
% 5.52/5.84 = ( abs_abs_rat @ Y2 ) )
% 5.52/5.84 = ( ( X2 = Y2 )
% 5.52/5.84 | ( X2
% 5.52/5.84 = ( uminus_uminus_rat @ Y2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_iff
% 5.52/5.84 thf(fact_5865_power__abs,axiom,
% 5.52/5.84 ! [A: code_integer,N: nat] :
% 5.52/5.84 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.52/5.84 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_abs
% 5.52/5.84 thf(fact_5866_power__abs,axiom,
% 5.52/5.84 ! [A: rat,N: nat] :
% 5.52/5.84 ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 5.52/5.84 = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_abs
% 5.52/5.84 thf(fact_5867_power__abs,axiom,
% 5.52/5.84 ! [A: real,N: nat] :
% 5.52/5.84 ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 5.52/5.84 = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_abs
% 5.52/5.84 thf(fact_5868_power__abs,axiom,
% 5.52/5.84 ! [A: int,N: nat] :
% 5.52/5.84 ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 5.52/5.84 = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_abs
% 5.52/5.84 thf(fact_5869_dvd__if__abs__eq,axiom,
% 5.52/5.84 ! [L: real,K: real] :
% 5.52/5.84 ( ( ( abs_abs_real @ L )
% 5.52/5.84 = ( abs_abs_real @ K ) )
% 5.52/5.84 => ( dvd_dvd_real @ L @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % dvd_if_abs_eq
% 5.52/5.84 thf(fact_5870_dvd__if__abs__eq,axiom,
% 5.52/5.84 ! [L: int,K: int] :
% 5.52/5.84 ( ( ( abs_abs_int @ L )
% 5.52/5.84 = ( abs_abs_int @ K ) )
% 5.52/5.84 => ( dvd_dvd_int @ L @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % dvd_if_abs_eq
% 5.52/5.84 thf(fact_5871_dvd__if__abs__eq,axiom,
% 5.52/5.84 ! [L: code_integer,K: code_integer] :
% 5.52/5.84 ( ( ( abs_abs_Code_integer @ L )
% 5.52/5.84 = ( abs_abs_Code_integer @ K ) )
% 5.52/5.84 => ( dvd_dvd_Code_integer @ L @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % dvd_if_abs_eq
% 5.52/5.84 thf(fact_5872_dvd__if__abs__eq,axiom,
% 5.52/5.84 ! [L: rat,K: rat] :
% 5.52/5.84 ( ( ( abs_abs_rat @ L )
% 5.52/5.84 = ( abs_abs_rat @ K ) )
% 5.52/5.84 => ( dvd_dvd_rat @ L @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % dvd_if_abs_eq
% 5.52/5.84 thf(fact_5873_abs__ge__zero,axiom,
% 5.52/5.84 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ge_zero
% 5.52/5.84 thf(fact_5874_abs__ge__zero,axiom,
% 5.52/5.84 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ge_zero
% 5.52/5.84 thf(fact_5875_abs__ge__zero,axiom,
% 5.52/5.84 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ge_zero
% 5.52/5.84 thf(fact_5876_abs__ge__zero,axiom,
% 5.52/5.84 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ge_zero
% 5.52/5.84 thf(fact_5877_abs__of__pos,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.52/5.84 => ( ( abs_abs_Code_integer @ A )
% 5.52/5.84 = A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_pos
% 5.52/5.84 thf(fact_5878_abs__of__pos,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.84 => ( ( abs_abs_real @ A )
% 5.52/5.84 = A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_pos
% 5.52/5.84 thf(fact_5879_abs__of__pos,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.52/5.84 => ( ( abs_abs_rat @ A )
% 5.52/5.84 = A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_pos
% 5.52/5.84 thf(fact_5880_abs__of__pos,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.84 => ( ( abs_abs_int @ A )
% 5.52/5.84 = A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_pos
% 5.52/5.84 thf(fact_5881_abs__not__less__zero,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.52/5.84
% 5.52/5.84 % abs_not_less_zero
% 5.52/5.84 thf(fact_5882_abs__not__less__zero,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.52/5.84
% 5.52/5.84 % abs_not_less_zero
% 5.52/5.84 thf(fact_5883_abs__not__less__zero,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.52/5.84
% 5.52/5.84 % abs_not_less_zero
% 5.52/5.84 thf(fact_5884_abs__not__less__zero,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.52/5.84
% 5.52/5.84 % abs_not_less_zero
% 5.52/5.84 thf(fact_5885_abs__triangle__ineq,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq
% 5.52/5.84 thf(fact_5886_abs__triangle__ineq,axiom,
% 5.52/5.84 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq
% 5.52/5.84 thf(fact_5887_abs__triangle__ineq,axiom,
% 5.52/5.84 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq
% 5.52/5.84 thf(fact_5888_abs__triangle__ineq,axiom,
% 5.52/5.84 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq
% 5.52/5.84 thf(fact_5889_abs__mult__less,axiom,
% 5.52/5.84 ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 5.52/5.84 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.52/5.84 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D2 )
% 5.52/5.84 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult_less
% 5.52/5.84 thf(fact_5890_abs__mult__less,axiom,
% 5.52/5.84 ! [A: real,C: real,B: real,D2: real] :
% 5.52/5.84 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.52/5.84 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D2 )
% 5.52/5.84 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult_less
% 5.52/5.84 thf(fact_5891_abs__mult__less,axiom,
% 5.52/5.84 ! [A: rat,C: rat,B: rat,D2: rat] :
% 5.52/5.84 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.52/5.84 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D2 )
% 5.52/5.84 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult_less
% 5.52/5.84 thf(fact_5892_abs__mult__less,axiom,
% 5.52/5.84 ! [A: int,C: int,B: int,D2: int] :
% 5.52/5.84 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.52/5.84 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D2 )
% 5.52/5.84 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult_less
% 5.52/5.84 thf(fact_5893_abs__triangle__ineq2,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq2
% 5.52/5.84 thf(fact_5894_abs__triangle__ineq2,axiom,
% 5.52/5.84 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq2
% 5.52/5.84 thf(fact_5895_abs__triangle__ineq2,axiom,
% 5.52/5.84 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq2
% 5.52/5.84 thf(fact_5896_abs__triangle__ineq2,axiom,
% 5.52/5.84 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq2
% 5.52/5.84 thf(fact_5897_abs__triangle__ineq3,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq3
% 5.52/5.84 thf(fact_5898_abs__triangle__ineq3,axiom,
% 5.52/5.84 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq3
% 5.52/5.84 thf(fact_5899_abs__triangle__ineq3,axiom,
% 5.52/5.84 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq3
% 5.52/5.84 thf(fact_5900_abs__triangle__ineq3,axiom,
% 5.52/5.84 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq3
% 5.52/5.84 thf(fact_5901_abs__triangle__ineq2__sym,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq2_sym
% 5.52/5.84 thf(fact_5902_abs__triangle__ineq2__sym,axiom,
% 5.52/5.84 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq2_sym
% 5.52/5.84 thf(fact_5903_abs__triangle__ineq2__sym,axiom,
% 5.52/5.84 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq2_sym
% 5.52/5.84 thf(fact_5904_abs__triangle__ineq2__sym,axiom,
% 5.52/5.84 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq2_sym
% 5.52/5.84 thf(fact_5905_nonzero__abs__divide,axiom,
% 5.52/5.84 ! [B: real,A: real] :
% 5.52/5.84 ( ( B != zero_zero_real )
% 5.52/5.84 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.52/5.84 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % nonzero_abs_divide
% 5.52/5.84 thf(fact_5906_nonzero__abs__divide,axiom,
% 5.52/5.84 ! [B: rat,A: rat] :
% 5.52/5.84 ( ( B != zero_zero_rat )
% 5.52/5.84 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.52/5.84 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % nonzero_abs_divide
% 5.52/5.84 thf(fact_5907_abs__leI,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ A @ B )
% 5.52/5.84 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.52/5.84 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_leI
% 5.52/5.84 thf(fact_5908_abs__leI,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.52/5.84 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.52/5.84 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_leI
% 5.52/5.84 thf(fact_5909_abs__leI,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.84 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.52/5.84 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_leI
% 5.52/5.84 thf(fact_5910_abs__leI,axiom,
% 5.52/5.84 ! [A: int,B: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ A @ B )
% 5.52/5.84 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.52/5.84 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_leI
% 5.52/5.84 thf(fact_5911_abs__le__D2,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.52/5.84 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_D2
% 5.52/5.84 thf(fact_5912_abs__le__D2,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.52/5.84 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_D2
% 5.52/5.84 thf(fact_5913_abs__le__D2,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.52/5.84 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_D2
% 5.52/5.84 thf(fact_5914_abs__le__D2,axiom,
% 5.52/5.84 ! [A: int,B: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.52/5.84 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_D2
% 5.52/5.84 thf(fact_5915_abs__le__iff,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.52/5.84 = ( ( ord_less_eq_real @ A @ B )
% 5.52/5.84 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_iff
% 5.52/5.84 thf(fact_5916_abs__le__iff,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.52/5.84 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.52/5.84 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_iff
% 5.52/5.84 thf(fact_5917_abs__le__iff,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.52/5.84 = ( ( ord_less_eq_rat @ A @ B )
% 5.52/5.84 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_iff
% 5.52/5.84 thf(fact_5918_abs__le__iff,axiom,
% 5.52/5.84 ! [A: int,B: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.52/5.84 = ( ( ord_less_eq_int @ A @ B )
% 5.52/5.84 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_iff
% 5.52/5.84 thf(fact_5919_abs__ge__minus__self,axiom,
% 5.52/5.84 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ge_minus_self
% 5.52/5.84 thf(fact_5920_abs__ge__minus__self,axiom,
% 5.52/5.84 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ge_minus_self
% 5.52/5.84 thf(fact_5921_abs__ge__minus__self,axiom,
% 5.52/5.84 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ge_minus_self
% 5.52/5.84 thf(fact_5922_abs__ge__minus__self,axiom,
% 5.52/5.84 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ge_minus_self
% 5.52/5.84 thf(fact_5923_abs__less__iff,axiom,
% 5.52/5.84 ! [A: int,B: int] :
% 5.52/5.84 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.52/5.84 = ( ( ord_less_int @ A @ B )
% 5.52/5.84 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_less_iff
% 5.52/5.84 thf(fact_5924_abs__less__iff,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.52/5.84 = ( ( ord_less_real @ A @ B )
% 5.52/5.84 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_less_iff
% 5.52/5.84 thf(fact_5925_abs__less__iff,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] :
% 5.52/5.84 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.52/5.84 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.52/5.84 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_less_iff
% 5.52/5.84 thf(fact_5926_abs__less__iff,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.52/5.84 = ( ( ord_less_rat @ A @ B )
% 5.52/5.84 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_less_iff
% 5.52/5.84 thf(fact_5927_tanh__real__lt__1,axiom,
% 5.52/5.84 ! [X2: real] : ( ord_less_real @ ( tanh_real @ X2 ) @ one_one_real ) ).
% 5.52/5.84
% 5.52/5.84 % tanh_real_lt_1
% 5.52/5.84 thf(fact_5928_dense__eq0__I,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ! [E2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.52/5.84 => ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ E2 ) )
% 5.52/5.84 => ( X2 = zero_zero_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % dense_eq0_I
% 5.52/5.84 thf(fact_5929_dense__eq0__I,axiom,
% 5.52/5.84 ! [X2: rat] :
% 5.52/5.84 ( ! [E2: rat] :
% 5.52/5.84 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ E2 ) )
% 5.52/5.84 => ( X2 = zero_zero_rat ) ) ).
% 5.52/5.84
% 5.52/5.84 % dense_eq0_I
% 5.52/5.84 thf(fact_5930_abs__eq__mult,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] :
% 5.52/5.84 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.52/5.84 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.52/5.84 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.52/5.84 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.52/5.84 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.52/5.84 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_mult
% 5.52/5.84 thf(fact_5931_abs__eq__mult,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.84 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.52/5.84 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.84 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.52/5.84 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.52/5.84 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_mult
% 5.52/5.84 thf(fact_5932_abs__eq__mult,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.84 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.52/5.84 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.84 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.52/5.84 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.52/5.84 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_mult
% 5.52/5.84 thf(fact_5933_abs__eq__mult,axiom,
% 5.52/5.84 ! [A: int,B: int] :
% 5.52/5.84 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.84 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.52/5.84 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.84 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.52/5.84 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.52/5.84 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_mult
% 5.52/5.84 thf(fact_5934_abs__mult__pos,axiom,
% 5.52/5.84 ! [X2: code_integer,Y2: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.52/5.84 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y2 ) @ X2 )
% 5.52/5.84 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y2 @ X2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult_pos
% 5.52/5.84 thf(fact_5935_abs__mult__pos,axiom,
% 5.52/5.84 ! [X2: real,Y2: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ( times_times_real @ ( abs_abs_real @ Y2 ) @ X2 )
% 5.52/5.84 = ( abs_abs_real @ ( times_times_real @ Y2 @ X2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult_pos
% 5.52/5.84 thf(fact_5936_abs__mult__pos,axiom,
% 5.52/5.84 ! [X2: rat,Y2: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.84 => ( ( times_times_rat @ ( abs_abs_rat @ Y2 ) @ X2 )
% 5.52/5.84 = ( abs_abs_rat @ ( times_times_rat @ Y2 @ X2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult_pos
% 5.52/5.84 thf(fact_5937_abs__mult__pos,axiom,
% 5.52/5.84 ! [X2: int,Y2: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.84 => ( ( times_times_int @ ( abs_abs_int @ Y2 ) @ X2 )
% 5.52/5.84 = ( abs_abs_int @ ( times_times_int @ Y2 @ X2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mult_pos
% 5.52/5.84 thf(fact_5938_eq__abs__iff_H,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( A
% 5.52/5.84 = ( abs_abs_real @ B ) )
% 5.52/5.84 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.84 & ( ( B = A )
% 5.52/5.84 | ( B
% 5.52/5.84 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % eq_abs_iff'
% 5.52/5.84 thf(fact_5939_eq__abs__iff_H,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] :
% 5.52/5.84 ( ( A
% 5.52/5.84 = ( abs_abs_Code_integer @ B ) )
% 5.52/5.84 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.52/5.84 & ( ( B = A )
% 5.52/5.84 | ( B
% 5.52/5.84 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % eq_abs_iff'
% 5.52/5.84 thf(fact_5940_eq__abs__iff_H,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( A
% 5.52/5.84 = ( abs_abs_rat @ B ) )
% 5.52/5.84 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.84 & ( ( B = A )
% 5.52/5.84 | ( B
% 5.52/5.84 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % eq_abs_iff'
% 5.52/5.84 thf(fact_5941_eq__abs__iff_H,axiom,
% 5.52/5.84 ! [A: int,B: int] :
% 5.52/5.84 ( ( A
% 5.52/5.84 = ( abs_abs_int @ B ) )
% 5.52/5.84 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.52/5.84 & ( ( B = A )
% 5.52/5.84 | ( B
% 5.52/5.84 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % eq_abs_iff'
% 5.52/5.84 thf(fact_5942_abs__eq__iff_H,axiom,
% 5.52/5.84 ! [A: real,B: real] :
% 5.52/5.84 ( ( ( abs_abs_real @ A )
% 5.52/5.84 = B )
% 5.52/5.84 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.84 & ( ( A = B )
% 5.52/5.84 | ( A
% 5.52/5.84 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_iff'
% 5.52/5.84 thf(fact_5943_abs__eq__iff_H,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] :
% 5.52/5.84 ( ( ( abs_abs_Code_integer @ A )
% 5.52/5.84 = B )
% 5.52/5.84 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.52/5.84 & ( ( A = B )
% 5.52/5.84 | ( A
% 5.52/5.84 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_iff'
% 5.52/5.84 thf(fact_5944_abs__eq__iff_H,axiom,
% 5.52/5.84 ! [A: rat,B: rat] :
% 5.52/5.84 ( ( ( abs_abs_rat @ A )
% 5.52/5.84 = B )
% 5.52/5.84 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.84 & ( ( A = B )
% 5.52/5.84 | ( A
% 5.52/5.84 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_iff'
% 5.52/5.84 thf(fact_5945_abs__eq__iff_H,axiom,
% 5.52/5.84 ! [A: int,B: int] :
% 5.52/5.84 ( ( ( abs_abs_int @ A )
% 5.52/5.84 = B )
% 5.52/5.84 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.84 & ( ( A = B )
% 5.52/5.84 | ( A
% 5.52/5.84 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_eq_iff'
% 5.52/5.84 thf(fact_5946_abs__minus__le__zero,axiom,
% 5.52/5.84 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus_le_zero
% 5.52/5.84 thf(fact_5947_abs__minus__le__zero,axiom,
% 5.52/5.84 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus_le_zero
% 5.52/5.84 thf(fact_5948_abs__minus__le__zero,axiom,
% 5.52/5.84 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus_le_zero
% 5.52/5.84 thf(fact_5949_abs__minus__le__zero,axiom,
% 5.52/5.84 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.52/5.84
% 5.52/5.84 % abs_minus_le_zero
% 5.52/5.84 thf(fact_5950_abs__div__pos,axiom,
% 5.52/5.84 ! [Y2: real,X2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.84 => ( ( divide_divide_real @ ( abs_abs_real @ X2 ) @ Y2 )
% 5.52/5.84 = ( abs_abs_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_div_pos
% 5.52/5.84 thf(fact_5951_abs__div__pos,axiom,
% 5.52/5.84 ! [Y2: rat,X2: rat] :
% 5.52/5.84 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.52/5.84 => ( ( divide_divide_rat @ ( abs_abs_rat @ X2 ) @ Y2 )
% 5.52/5.84 = ( abs_abs_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_div_pos
% 5.52/5.84 thf(fact_5952_zero__le__power__abs,axiom,
% 5.52/5.84 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_le_power_abs
% 5.52/5.84 thf(fact_5953_zero__le__power__abs,axiom,
% 5.52/5.84 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_le_power_abs
% 5.52/5.84 thf(fact_5954_zero__le__power__abs,axiom,
% 5.52/5.84 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_le_power_abs
% 5.52/5.84 thf(fact_5955_zero__le__power__abs,axiom,
% 5.52/5.84 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_le_power_abs
% 5.52/5.84 thf(fact_5956_abs__if__raw,axiom,
% 5.52/5.84 ( abs_abs_int
% 5.52/5.84 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_if_raw
% 5.52/5.84 thf(fact_5957_abs__if__raw,axiom,
% 5.52/5.84 ( abs_abs_real
% 5.52/5.84 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_if_raw
% 5.52/5.84 thf(fact_5958_abs__if__raw,axiom,
% 5.52/5.84 ( abs_abs_Code_integer
% 5.52/5.84 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_if_raw
% 5.52/5.84 thf(fact_5959_abs__if__raw,axiom,
% 5.52/5.84 ( abs_abs_rat
% 5.52/5.84 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_if_raw
% 5.52/5.84 thf(fact_5960_abs__if,axiom,
% 5.52/5.84 ( abs_abs_int
% 5.52/5.84 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_if
% 5.52/5.84 thf(fact_5961_abs__if,axiom,
% 5.52/5.84 ( abs_abs_real
% 5.52/5.84 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_if
% 5.52/5.84 thf(fact_5962_abs__if,axiom,
% 5.52/5.84 ( abs_abs_Code_integer
% 5.52/5.84 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_if
% 5.52/5.84 thf(fact_5963_abs__if,axiom,
% 5.52/5.84 ( abs_abs_rat
% 5.52/5.84 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_if
% 5.52/5.84 thf(fact_5964_abs__of__neg,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( ord_less_int @ A @ zero_zero_int )
% 5.52/5.84 => ( ( abs_abs_int @ A )
% 5.52/5.84 = ( uminus_uminus_int @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_neg
% 5.52/5.84 thf(fact_5965_abs__of__neg,axiom,
% 5.52/5.84 ! [A: real] :
% 5.52/5.84 ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.84 => ( ( abs_abs_real @ A )
% 5.52/5.84 = ( uminus_uminus_real @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_neg
% 5.52/5.84 thf(fact_5966_abs__of__neg,axiom,
% 5.52/5.84 ! [A: code_integer] :
% 5.52/5.84 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.52/5.84 => ( ( abs_abs_Code_integer @ A )
% 5.52/5.84 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_neg
% 5.52/5.84 thf(fact_5967_abs__of__neg,axiom,
% 5.52/5.84 ! [A: rat] :
% 5.52/5.84 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.52/5.84 => ( ( abs_abs_rat @ A )
% 5.52/5.84 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_of_neg
% 5.52/5.84 thf(fact_5968_abs__diff__le__iff,axiom,
% 5.52/5.84 ! [X2: code_integer,A: code_integer,R: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R )
% 5.52/5.84 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X2 )
% 5.52/5.84 & ( ord_le3102999989581377725nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_diff_le_iff
% 5.52/5.84 thf(fact_5969_abs__diff__le__iff,axiom,
% 5.52/5.84 ! [X2: real,A: real,R: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A ) ) @ R )
% 5.52/5.84 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R ) @ X2 )
% 5.52/5.84 & ( ord_less_eq_real @ X2 @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_diff_le_iff
% 5.52/5.84 thf(fact_5970_abs__diff__le__iff,axiom,
% 5.52/5.84 ! [X2: rat,A: rat,R: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R )
% 5.52/5.84 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R ) @ X2 )
% 5.52/5.84 & ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_diff_le_iff
% 5.52/5.84 thf(fact_5971_abs__diff__le__iff,axiom,
% 5.52/5.84 ! [X2: int,A: int,R: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R )
% 5.52/5.84 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R ) @ X2 )
% 5.52/5.84 & ( ord_less_eq_int @ X2 @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_diff_le_iff
% 5.52/5.84 thf(fact_5972_abs__diff__triangle__ineq,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D2 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_diff_triangle_ineq
% 5.52/5.84 thf(fact_5973_abs__diff__triangle__ineq,axiom,
% 5.52/5.84 ! [A: real,B: real,C: real,D2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D2 ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_diff_triangle_ineq
% 5.52/5.84 thf(fact_5974_abs__diff__triangle__ineq,axiom,
% 5.52/5.84 ! [A: rat,B: rat,C: rat,D2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D2 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_diff_triangle_ineq
% 5.52/5.84 thf(fact_5975_abs__diff__triangle__ineq,axiom,
% 5.52/5.84 ! [A: int,B: int,C: int,D2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D2 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_diff_triangle_ineq
% 5.52/5.84 thf(fact_5976_abs__triangle__ineq4,axiom,
% 5.52/5.84 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq4
% 5.52/5.84 thf(fact_5977_abs__triangle__ineq4,axiom,
% 5.52/5.84 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq4
% 5.52/5.84 thf(fact_5978_abs__triangle__ineq4,axiom,
% 5.52/5.84 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq4
% 5.52/5.84 thf(fact_5979_abs__triangle__ineq4,axiom,
% 5.52/5.84 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_triangle_ineq4
% 5.52/5.84 thf(fact_5980_abs__diff__less__iff,axiom,
% 5.52/5.84 ! [X2: code_integer,A: code_integer,R: code_integer] :
% 5.52/5.84 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R )
% 5.52/5.84 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X2 )
% 5.52/5.84 & ( ord_le6747313008572928689nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_diff_less_iff
% 5.52/5.84 thf(fact_5981_abs__diff__less__iff,axiom,
% 5.52/5.84 ! [X2: real,A: real,R: real] :
% 5.52/5.84 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A ) ) @ R )
% 5.52/5.84 = ( ( ord_less_real @ ( minus_minus_real @ A @ R ) @ X2 )
% 5.52/5.84 & ( ord_less_real @ X2 @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_diff_less_iff
% 5.52/5.84 thf(fact_5982_abs__diff__less__iff,axiom,
% 5.52/5.84 ! [X2: rat,A: rat,R: rat] :
% 5.52/5.84 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R )
% 5.52/5.84 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R ) @ X2 )
% 5.52/5.84 & ( ord_less_rat @ X2 @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_diff_less_iff
% 5.52/5.84 thf(fact_5983_abs__diff__less__iff,axiom,
% 5.52/5.84 ! [X2: int,A: int,R: int] :
% 5.52/5.84 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R )
% 5.52/5.84 = ( ( ord_less_int @ ( minus_minus_int @ A @ R ) @ X2 )
% 5.52/5.84 & ( ord_less_int @ X2 @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_diff_less_iff
% 5.52/5.84 thf(fact_5984_abs__real__def,axiom,
% 5.52/5.84 ( abs_abs_real
% 5.52/5.84 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_real_def
% 5.52/5.84 thf(fact_5985_lemma__interval__lt,axiom,
% 5.52/5.84 ! [A: real,X2: real,B: real] :
% 5.52/5.84 ( ( ord_less_real @ A @ X2 )
% 5.52/5.84 => ( ( ord_less_real @ X2 @ B )
% 5.52/5.84 => ? [D3: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.52/5.84 & ! [Y4: real] :
% 5.52/5.84 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ D3 )
% 5.52/5.84 => ( ( ord_less_real @ A @ Y4 )
% 5.52/5.84 & ( ord_less_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % lemma_interval_lt
% 5.52/5.84 thf(fact_5986_tanh__real__gt__neg1,axiom,
% 5.52/5.84 ! [X2: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % tanh_real_gt_neg1
% 5.52/5.84 thf(fact_5987_abs__add__one__gt__zero,axiom,
% 5.52/5.84 ! [X2: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_add_one_gt_zero
% 5.52/5.84 thf(fact_5988_abs__add__one__gt__zero,axiom,
% 5.52/5.84 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_add_one_gt_zero
% 5.52/5.84 thf(fact_5989_abs__add__one__gt__zero,axiom,
% 5.52/5.84 ! [X2: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_add_one_gt_zero
% 5.52/5.84 thf(fact_5990_abs__add__one__gt__zero,axiom,
% 5.52/5.84 ! [X2: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_add_one_gt_zero
% 5.52/5.84 thf(fact_5991_of__int__leD,axiom,
% 5.52/5.84 ! [N: int,X2: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 5.52/5.84 => ( ( N = zero_zero_int )
% 5.52/5.84 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_leD
% 5.52/5.84 thf(fact_5992_of__int__leD,axiom,
% 5.52/5.84 ! [N: int,X2: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X2 )
% 5.52/5.84 => ( ( N = zero_zero_int )
% 5.52/5.84 | ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_leD
% 5.52/5.84 thf(fact_5993_of__int__leD,axiom,
% 5.52/5.84 ! [N: int,X2: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 5.52/5.84 => ( ( N = zero_zero_int )
% 5.52/5.84 | ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_leD
% 5.52/5.84 thf(fact_5994_of__int__leD,axiom,
% 5.52/5.84 ! [N: int,X2: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 5.52/5.84 => ( ( N = zero_zero_int )
% 5.52/5.84 | ( ord_less_eq_int @ one_one_int @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_leD
% 5.52/5.84 thf(fact_5995_of__int__lessD,axiom,
% 5.52/5.84 ! [N: int,X2: code_integer] :
% 5.52/5.84 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 5.52/5.84 => ( ( N = zero_zero_int )
% 5.52/5.84 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_lessD
% 5.52/5.84 thf(fact_5996_of__int__lessD,axiom,
% 5.52/5.84 ! [N: int,X2: real] :
% 5.52/5.84 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X2 )
% 5.52/5.84 => ( ( N = zero_zero_int )
% 5.52/5.84 | ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_lessD
% 5.52/5.84 thf(fact_5997_of__int__lessD,axiom,
% 5.52/5.84 ! [N: int,X2: rat] :
% 5.52/5.84 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 5.52/5.84 => ( ( N = zero_zero_int )
% 5.52/5.84 | ( ord_less_rat @ one_one_rat @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_lessD
% 5.52/5.84 thf(fact_5998_of__int__lessD,axiom,
% 5.52/5.84 ! [N: int,X2: int] :
% 5.52/5.84 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 5.52/5.84 => ( ( N = zero_zero_int )
% 5.52/5.84 | ( ord_less_int @ one_one_int @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_lessD
% 5.52/5.84 thf(fact_5999_lemma__interval,axiom,
% 5.52/5.84 ! [A: real,X2: real,B: real] :
% 5.52/5.84 ( ( ord_less_real @ A @ X2 )
% 5.52/5.84 => ( ( ord_less_real @ X2 @ B )
% 5.52/5.84 => ? [D3: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.52/5.84 & ! [Y4: real] :
% 5.52/5.84 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ D3 )
% 5.52/5.84 => ( ( ord_less_eq_real @ A @ Y4 )
% 5.52/5.84 & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % lemma_interval
% 5.52/5.84 thf(fact_6000_abs__le__square__iff,axiom,
% 5.52/5.84 ! [X2: code_integer,Y2: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ ( abs_abs_Code_integer @ Y2 ) )
% 5.52/5.84 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_square_iff
% 5.52/5.84 thf(fact_6001_abs__le__square__iff,axiom,
% 5.52/5.84 ! [X2: real,Y2: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ Y2 ) )
% 5.52/5.84 = ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_square_iff
% 5.52/5.84 thf(fact_6002_abs__le__square__iff,axiom,
% 5.52/5.84 ! [X2: rat,Y2: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ ( abs_abs_rat @ Y2 ) )
% 5.52/5.84 = ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_square_iff
% 5.52/5.84 thf(fact_6003_abs__le__square__iff,axiom,
% 5.52/5.84 ! [X2: int,Y2: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ ( abs_abs_int @ Y2 ) )
% 5.52/5.84 = ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_le_square_iff
% 5.52/5.84 thf(fact_6004_abs__square__eq__1,axiom,
% 5.52/5.84 ! [X2: code_integer] :
% 5.52/5.84 ( ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.84 = one_one_Code_integer )
% 5.52/5.84 = ( ( abs_abs_Code_integer @ X2 )
% 5.52/5.84 = one_one_Code_integer ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_square_eq_1
% 5.52/5.84 thf(fact_6005_abs__square__eq__1,axiom,
% 5.52/5.84 ! [X2: rat] :
% 5.52/5.84 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.84 = one_one_rat )
% 5.52/5.84 = ( ( abs_abs_rat @ X2 )
% 5.52/5.84 = one_one_rat ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_square_eq_1
% 5.52/5.84 thf(fact_6006_abs__square__eq__1,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.84 = one_one_real )
% 5.52/5.84 = ( ( abs_abs_real @ X2 )
% 5.52/5.84 = one_one_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_square_eq_1
% 5.52/5.84 thf(fact_6007_abs__square__eq__1,axiom,
% 5.52/5.84 ! [X2: int] :
% 5.52/5.84 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.84 = one_one_int )
% 5.52/5.84 = ( ( abs_abs_int @ X2 )
% 5.52/5.84 = one_one_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_square_eq_1
% 5.52/5.84 thf(fact_6008_power__even__abs,axiom,
% 5.52/5.84 ! [N: nat,A: code_integer] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.84 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 5.52/5.84 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_even_abs
% 5.52/5.84 thf(fact_6009_power__even__abs,axiom,
% 5.52/5.84 ! [N: nat,A: rat] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.84 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 5.52/5.84 = ( power_power_rat @ A @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_even_abs
% 5.52/5.84 thf(fact_6010_power__even__abs,axiom,
% 5.52/5.84 ! [N: nat,A: real] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.84 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 5.52/5.84 = ( power_power_real @ A @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_even_abs
% 5.52/5.84 thf(fact_6011_power__even__abs,axiom,
% 5.52/5.84 ! [N: nat,A: int] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.84 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 5.52/5.84 = ( power_power_int @ A @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_even_abs
% 5.52/5.84 thf(fact_6012_power2__le__iff__abs__le,axiom,
% 5.52/5.84 ! [Y2: code_integer,X2: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y2 )
% 5.52/5.84 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.84 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ Y2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power2_le_iff_abs_le
% 5.52/5.84 thf(fact_6013_power2__le__iff__abs__le,axiom,
% 5.52/5.84 ! [Y2: real,X2: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.84 => ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.84 = ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ Y2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power2_le_iff_abs_le
% 5.52/5.84 thf(fact_6014_power2__le__iff__abs__le,axiom,
% 5.52/5.84 ! [Y2: rat,X2: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.52/5.84 => ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.84 = ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ Y2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power2_le_iff_abs_le
% 5.52/5.84 thf(fact_6015_power2__le__iff__abs__le,axiom,
% 5.52/5.84 ! [Y2: int,X2: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.84 => ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.84 = ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ Y2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power2_le_iff_abs_le
% 5.52/5.84 thf(fact_6016_abs__sqrt__wlog,axiom,
% 5.52/5.84 ! [P: code_integer > code_integer > $o,X2: code_integer] :
% 5.52/5.84 ( ! [X4: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 5.52/5.84 => ( P @ X4 @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.84 => ( P @ ( abs_abs_Code_integer @ X2 ) @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_sqrt_wlog
% 5.52/5.84 thf(fact_6017_abs__sqrt__wlog,axiom,
% 5.52/5.84 ! [P: real > real > $o,X2: real] :
% 5.52/5.84 ( ! [X4: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.52/5.84 => ( P @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.84 => ( P @ ( abs_abs_real @ X2 ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_sqrt_wlog
% 5.52/5.84 thf(fact_6018_abs__sqrt__wlog,axiom,
% 5.52/5.84 ! [P: rat > rat > $o,X2: rat] :
% 5.52/5.84 ( ! [X4: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.52/5.84 => ( P @ X4 @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.84 => ( P @ ( abs_abs_rat @ X2 ) @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_sqrt_wlog
% 5.52/5.84 thf(fact_6019_abs__sqrt__wlog,axiom,
% 5.52/5.84 ! [P: int > int > $o,X2: int] :
% 5.52/5.84 ( ! [X4: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.52/5.84 => ( P @ X4 @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.84 => ( P @ ( abs_abs_int @ X2 ) @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_sqrt_wlog
% 5.52/5.84 thf(fact_6020_abs__square__le__1,axiom,
% 5.52/5.84 ! [X2: code_integer] :
% 5.52/5.84 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.52/5.84 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_square_le_1
% 5.52/5.84 thf(fact_6021_abs__square__le__1,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.52/5.84 = ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_square_le_1
% 5.52/5.84 thf(fact_6022_abs__square__le__1,axiom,
% 5.52/5.84 ! [X2: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.52/5.84 = ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_square_le_1
% 5.52/5.84 thf(fact_6023_abs__square__le__1,axiom,
% 5.52/5.84 ! [X2: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.52/5.84 = ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ one_one_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_square_le_1
% 5.52/5.84 thf(fact_6024_abs__square__less__1,axiom,
% 5.52/5.84 ! [X2: code_integer] :
% 5.52/5.84 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.52/5.84 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_square_less_1
% 5.52/5.84 thf(fact_6025_abs__square__less__1,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.52/5.84 = ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_square_less_1
% 5.52/5.84 thf(fact_6026_abs__square__less__1,axiom,
% 5.52/5.84 ! [X2: rat] :
% 5.52/5.84 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.52/5.84 = ( ord_less_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_square_less_1
% 5.52/5.84 thf(fact_6027_abs__square__less__1,axiom,
% 5.52/5.84 ! [X2: int] :
% 5.52/5.84 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.52/5.84 = ( ord_less_int @ ( abs_abs_int @ X2 ) @ one_one_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_square_less_1
% 5.52/5.84 thf(fact_6028_power__mono__even,axiom,
% 5.52/5.84 ! [N: nat,A: code_integer,B: code_integer] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.84 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.52/5.84 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_mono_even
% 5.52/5.84 thf(fact_6029_power__mono__even,axiom,
% 5.52/5.84 ! [N: nat,A: real,B: real] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.84 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_mono_even
% 5.52/5.84 thf(fact_6030_power__mono__even,axiom,
% 5.52/5.84 ! [N: nat,A: rat,B: rat] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.84 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.52/5.84 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_mono_even
% 5.52/5.84 thf(fact_6031_power__mono__even,axiom,
% 5.52/5.84 ! [N: nat,A: int,B: int] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.84 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.52/5.84 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % power_mono_even
% 5.52/5.84 thf(fact_6032_ex__le__of__int,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ? [Z3: int] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 5.52/5.84
% 5.52/5.84 % ex_le_of_int
% 5.52/5.84 thf(fact_6033_ex__le__of__int,axiom,
% 5.52/5.84 ! [X2: rat] :
% 5.52/5.84 ? [Z3: int] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 5.52/5.84
% 5.52/5.84 % ex_le_of_int
% 5.52/5.84 thf(fact_6034_ex__less__of__int,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ? [Z3: int] : ( ord_less_real @ X2 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 5.52/5.84
% 5.52/5.84 % ex_less_of_int
% 5.52/5.84 thf(fact_6035_ex__less__of__int,axiom,
% 5.52/5.84 ! [X2: rat] :
% 5.52/5.84 ? [Z3: int] : ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 5.52/5.84
% 5.52/5.84 % ex_less_of_int
% 5.52/5.84 thf(fact_6036_ex__of__int__less,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X2 ) ).
% 5.52/5.84
% 5.52/5.84 % ex_of_int_less
% 5.52/5.84 thf(fact_6037_ex__of__int__less,axiom,
% 5.52/5.84 ! [X2: rat] :
% 5.52/5.84 ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X2 ) ).
% 5.52/5.84
% 5.52/5.84 % ex_of_int_less
% 5.52/5.84 thf(fact_6038_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.84 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.52/5.84 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.52/5.84 thf(fact_6039_round__unique,axiom,
% 5.52/5.84 ! [X2: real,Y2: int] :
% 5.52/5.84 ( ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y2 ) )
% 5.52/5.84 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y2 ) @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.52/5.84 => ( ( archim8280529875227126926d_real @ X2 )
% 5.52/5.84 = Y2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % round_unique
% 5.52/5.84 thf(fact_6040_round__unique,axiom,
% 5.52/5.84 ! [X2: rat,Y2: int] :
% 5.52/5.84 ( ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y2 ) )
% 5.52/5.84 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y2 ) @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.84 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.52/5.84 = Y2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % round_unique
% 5.52/5.84 thf(fact_6041_round__unique_H,axiom,
% 5.52/5.84 ! [X2: real,N: int] :
% 5.52/5.84 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.84 => ( ( archim8280529875227126926d_real @ X2 )
% 5.52/5.84 = N ) ) ).
% 5.52/5.84
% 5.52/5.84 % round_unique'
% 5.52/5.84 thf(fact_6042_round__unique_H,axiom,
% 5.52/5.84 ! [X2: rat,N: int] :
% 5.52/5.84 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.52/5.84 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.52/5.84 = N ) ) ).
% 5.52/5.84
% 5.52/5.84 % round_unique'
% 5.52/5.84 thf(fact_6043_of__int__round__abs__le,axiom,
% 5.52/5.84 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) @ X2 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_round_abs_le
% 5.52/5.84 thf(fact_6044_of__int__round__abs__le,axiom,
% 5.52/5.84 ! [X2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) @ X2 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_round_abs_le
% 5.52/5.84 thf(fact_6045_arctan__double,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.52/5.84 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X2 ) )
% 5.52/5.84 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % arctan_double
% 5.52/5.84 thf(fact_6046_of__int__round__gt,axiom,
% 5.52/5.84 ! [X2: real] : ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_round_gt
% 5.52/5.84 thf(fact_6047_of__int__round__gt,axiom,
% 5.52/5.84 ! [X2: rat] : ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_round_gt
% 5.52/5.84 thf(fact_6048_of__int__round__ge,axiom,
% 5.52/5.84 ! [X2: real] : ( ord_less_eq_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_round_ge
% 5.52/5.84 thf(fact_6049_of__int__round__ge,axiom,
% 5.52/5.84 ! [X2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_round_ge
% 5.52/5.84 thf(fact_6050_zabs__less__one__iff,axiom,
% 5.52/5.84 ! [Z: int] :
% 5.52/5.84 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.52/5.84 = ( Z = zero_zero_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % zabs_less_one_iff
% 5.52/5.84 thf(fact_6051_arctan__less__zero__iff,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ ( arctan @ X2 ) @ zero_zero_real )
% 5.52/5.84 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % arctan_less_zero_iff
% 5.52/5.84 thf(fact_6052_zero__less__arctan__iff,axiom,
% 5.52/5.84 ! [X2: real] :
% 5.52/5.84 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X2 ) )
% 5.52/5.84 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % zero_less_arctan_iff
% 5.52/5.84 thf(fact_6053_round__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 5.52/5.84 = ( numeral_numeral_int @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % round_numeral
% 5.52/5.84 thf(fact_6054_round__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 5.52/5.84 = ( numeral_numeral_int @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % round_numeral
% 5.52/5.84 thf(fact_6055_round__1,axiom,
% 5.52/5.84 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.52/5.84 = one_one_int ) ).
% 5.52/5.84
% 5.52/5.84 % round_1
% 5.52/5.84 thf(fact_6056_round__1,axiom,
% 5.52/5.84 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.52/5.84 = one_one_int ) ).
% 5.52/5.84
% 5.52/5.84 % round_1
% 5.52/5.84 thf(fact_6057_round__neg__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.84 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % round_neg_numeral
% 5.52/5.84 thf(fact_6058_round__neg__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.52/5.84 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % round_neg_numeral
% 5.52/5.84 thf(fact_6059_arctan__less__iff,axiom,
% 5.52/5.84 ! [X2: real,Y2: real] :
% 5.52/5.84 ( ( ord_less_real @ ( arctan @ X2 ) @ ( arctan @ Y2 ) )
% 5.52/5.84 = ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % arctan_less_iff
% 5.52/5.84 thf(fact_6060_arctan__monotone,axiom,
% 5.52/5.84 ! [X2: real,Y2: real] :
% 5.52/5.84 ( ( ord_less_real @ X2 @ Y2 )
% 5.52/5.84 => ( ord_less_real @ ( arctan @ X2 ) @ ( arctan @ Y2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % arctan_monotone
% 5.52/5.84 thf(fact_6061_abs__div,axiom,
% 5.52/5.84 ! [Y2: int,X2: int] :
% 5.52/5.84 ( ( dvd_dvd_int @ Y2 @ X2 )
% 5.52/5.84 => ( ( abs_abs_int @ ( divide_divide_int @ X2 @ Y2 ) )
% 5.52/5.84 = ( divide_divide_int @ ( abs_abs_int @ X2 ) @ ( abs_abs_int @ Y2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_div
% 5.52/5.84 thf(fact_6062_round__mono,axiom,
% 5.52/5.84 ! [X2: rat,Y2: rat] :
% 5.52/5.84 ( ( ord_less_eq_rat @ X2 @ Y2 )
% 5.52/5.84 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X2 ) @ ( archim7778729529865785530nd_rat @ Y2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % round_mono
% 5.52/5.84 thf(fact_6063_zabs__def,axiom,
% 5.52/5.84 ( abs_abs_int
% 5.52/5.84 = ( ^ [I4: int] : ( if_int @ ( ord_less_int @ I4 @ zero_zero_int ) @ ( uminus_uminus_int @ I4 ) @ I4 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % zabs_def
% 5.52/5.84 thf(fact_6064_abs__mod__less,axiom,
% 5.52/5.84 ! [L: int,K: int] :
% 5.52/5.84 ( ( L != zero_zero_int )
% 5.52/5.84 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % abs_mod_less
% 5.52/5.84 thf(fact_6065_even__add__abs__iff,axiom,
% 5.52/5.84 ! [K: int,L: int] :
% 5.52/5.84 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 5.52/5.84 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % even_add_abs_iff
% 5.52/5.84 thf(fact_6066_even__abs__add__iff,axiom,
% 5.52/5.84 ! [K: int,L: int] :
% 5.52/5.84 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 5.52/5.84 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % even_abs_add_iff
% 5.52/5.84 thf(fact_6067_round__diff__minimal,axiom,
% 5.52/5.84 ! [Z: real,M: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ M ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % round_diff_minimal
% 5.52/5.84 thf(fact_6068_round__diff__minimal,axiom,
% 5.52/5.84 ! [Z: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % round_diff_minimal
% 5.52/5.84 thf(fact_6069_nat__intermed__int__val,axiom,
% 5.52/5.84 ! [M: nat,N: nat,F: nat > int,K: int] :
% 5.52/5.84 ( ! [I2: nat] :
% 5.52/5.84 ( ( ( ord_less_eq_nat @ M @ I2 )
% 5.52/5.84 & ( ord_less_nat @ I2 @ N ) )
% 5.52/5.84 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.52/5.84 => ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.84 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.52/5.84 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.52/5.84 => ? [I2: nat] :
% 5.52/5.84 ( ( ord_less_eq_nat @ M @ I2 )
% 5.52/5.84 & ( ord_less_eq_nat @ I2 @ N )
% 5.52/5.84 & ( ( F @ I2 )
% 5.52/5.84 = K ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % nat_intermed_int_val
% 5.52/5.84 thf(fact_6070_incr__lemma,axiom,
% 5.52/5.84 ! [D2: int,Z: int,X2: int] :
% 5.52/5.84 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.52/5.84 => ( ord_less_int @ Z @ ( plus_plus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % incr_lemma
% 5.52/5.84 thf(fact_6071_decr__lemma,axiom,
% 5.52/5.84 ! [D2: int,X2: int,Z: int] :
% 5.52/5.84 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.52/5.84 => ( ord_less_int @ ( minus_minus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 5.52/5.84
% 5.52/5.84 % decr_lemma
% 5.52/5.84 thf(fact_6072_nat__ivt__aux,axiom,
% 5.52/5.84 ! [N: nat,F: nat > int,K: int] :
% 5.52/5.84 ( ! [I2: nat] :
% 5.52/5.84 ( ( ord_less_nat @ I2 @ N )
% 5.52/5.84 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.52/5.84 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.52/5.84 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.52/5.84 => ? [I2: nat] :
% 5.52/5.84 ( ( ord_less_eq_nat @ I2 @ N )
% 5.52/5.84 & ( ( F @ I2 )
% 5.52/5.84 = K ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % nat_ivt_aux
% 5.52/5.84 thf(fact_6073_nat0__intermed__int__val,axiom,
% 5.52/5.84 ! [N: nat,F: nat > int,K: int] :
% 5.52/5.84 ( ! [I2: nat] :
% 5.52/5.84 ( ( ord_less_nat @ I2 @ N )
% 5.52/5.84 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.52/5.84 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.52/5.84 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.52/5.84 => ? [I2: nat] :
% 5.52/5.84 ( ( ord_less_eq_nat @ I2 @ N )
% 5.52/5.84 & ( ( F @ I2 )
% 5.52/5.84 = K ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % nat0_intermed_int_val
% 5.52/5.84 thf(fact_6074_arctan__add,axiom,
% 5.52/5.84 ! [X2: real,Y2: real] :
% 5.52/5.84 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.52/5.84 => ( ( ord_less_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.52/5.84 => ( ( plus_plus_real @ ( arctan @ X2 ) @ ( arctan @ Y2 ) )
% 5.52/5.84 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % arctan_add
% 5.52/5.84 thf(fact_6075_of__int__round__le,axiom,
% 5.52/5.84 ! [X2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_round_le
% 5.52/5.84 thf(fact_6076_of__int__round__le,axiom,
% 5.52/5.84 ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_round_le
% 5.52/5.84 thf(fact_6077_add__scale__eq__noteq,axiom,
% 5.52/5.84 ! [R: complex,A: complex,B: complex,C: complex,D2: complex] :
% 5.52/5.84 ( ( R != zero_zero_complex )
% 5.52/5.84 => ( ( ( A = B )
% 5.52/5.84 & ( C != D2 ) )
% 5.52/5.84 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R @ C ) )
% 5.52/5.84 != ( plus_plus_complex @ B @ ( times_times_complex @ R @ D2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % add_scale_eq_noteq
% 5.52/5.84 thf(fact_6078_add__scale__eq__noteq,axiom,
% 5.52/5.84 ! [R: real,A: real,B: real,C: real,D2: real] :
% 5.52/5.84 ( ( R != zero_zero_real )
% 5.52/5.84 => ( ( ( A = B )
% 5.52/5.84 & ( C != D2 ) )
% 5.52/5.84 => ( ( plus_plus_real @ A @ ( times_times_real @ R @ C ) )
% 5.52/5.84 != ( plus_plus_real @ B @ ( times_times_real @ R @ D2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % add_scale_eq_noteq
% 5.52/5.84 thf(fact_6079_add__scale__eq__noteq,axiom,
% 5.52/5.84 ! [R: rat,A: rat,B: rat,C: rat,D2: rat] :
% 5.52/5.84 ( ( R != zero_zero_rat )
% 5.52/5.84 => ( ( ( A = B )
% 5.52/5.84 & ( C != D2 ) )
% 5.52/5.84 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R @ C ) )
% 5.52/5.84 != ( plus_plus_rat @ B @ ( times_times_rat @ R @ D2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % add_scale_eq_noteq
% 5.52/5.84 thf(fact_6080_add__scale__eq__noteq,axiom,
% 5.52/5.84 ! [R: nat,A: nat,B: nat,C: nat,D2: nat] :
% 5.52/5.84 ( ( R != zero_zero_nat )
% 5.52/5.84 => ( ( ( A = B )
% 5.52/5.84 & ( C != D2 ) )
% 5.52/5.84 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 5.52/5.84 != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % add_scale_eq_noteq
% 5.52/5.84 thf(fact_6081_add__scale__eq__noteq,axiom,
% 5.52/5.84 ! [R: int,A: int,B: int,C: int,D2: int] :
% 5.52/5.84 ( ( R != zero_zero_int )
% 5.52/5.84 => ( ( ( A = B )
% 5.52/5.84 & ( C != D2 ) )
% 5.52/5.84 => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 5.52/5.84 != ( plus_plus_int @ B @ ( times_times_int @ R @ D2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % add_scale_eq_noteq
% 5.52/5.84 thf(fact_6082_Sum__Icc__int,axiom,
% 5.52/5.84 ! [M: int,N: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ M @ N )
% 5.52/5.84 => ( ( groups4538972089207619220nt_int
% 5.52/5.84 @ ^ [X: int] : X
% 5.52/5.84 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 5.52/5.84 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % Sum_Icc_int
% 5.52/5.84 thf(fact_6083_even__set__encode__iff,axiom,
% 5.52/5.84 ! [A2: set_nat] :
% 5.52/5.84 ( ( finite_finite_nat @ A2 )
% 5.52/5.84 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.52/5.84 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % even_set_encode_iff
% 5.52/5.84 thf(fact_6084_mask__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 5.52/5.84 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % mask_numeral
% 5.52/5.84 thf(fact_6085_mask__numeral,axiom,
% 5.52/5.84 ! [N: num] :
% 5.52/5.84 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 5.52/5.84 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % mask_numeral
% 5.52/5.84 thf(fact_6086_num_Osize__gen_I3_J,axiom,
% 5.52/5.84 ! [X32: num] :
% 5.52/5.84 ( ( size_num @ ( bit1 @ X32 ) )
% 5.52/5.84 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % num.size_gen(3)
% 5.52/5.84 thf(fact_6087_take__bit__rec,axiom,
% 5.52/5.84 ( bit_se2923211474154528505it_int
% 5.52/5.84 = ( ^ [N3: nat,A4: int] : ( if_int @ ( N3 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_rec
% 5.52/5.84 thf(fact_6088_take__bit__rec,axiom,
% 5.52/5.84 ( bit_se2925701944663578781it_nat
% 5.52/5.84 = ( ^ [N3: nat,A4: nat] : ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_rec
% 5.52/5.84 thf(fact_6089_mask__nat__positive__iff,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.52/5.84 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % mask_nat_positive_iff
% 5.52/5.84 thf(fact_6090_take__bit__of__0,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 5.52/5.84 = zero_zero_int ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_0
% 5.52/5.84 thf(fact_6091_take__bit__of__0,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 5.52/5.84 = zero_zero_nat ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_0
% 5.52/5.84 thf(fact_6092_concat__bit__of__zero__2,axiom,
% 5.52/5.84 ! [N: nat,K: int] :
% 5.52/5.84 ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % concat_bit_of_zero_2
% 5.52/5.84 thf(fact_6093_take__bit__0,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 5.52/5.84 = zero_zero_int ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_0
% 5.52/5.84 thf(fact_6094_take__bit__0,axiom,
% 5.52/5.84 ! [A: nat] :
% 5.52/5.84 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 5.52/5.84 = zero_zero_nat ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_0
% 5.52/5.84 thf(fact_6095_take__bit__Suc__1,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 5.52/5.84 = one_one_int ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_Suc_1
% 5.52/5.84 thf(fact_6096_take__bit__Suc__1,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 5.52/5.84 = one_one_nat ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_Suc_1
% 5.52/5.84 thf(fact_6097_take__bit__numeral__1,axiom,
% 5.52/5.84 ! [L: num] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 5.52/5.84 = one_one_int ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_numeral_1
% 5.52/5.84 thf(fact_6098_take__bit__numeral__1,axiom,
% 5.52/5.84 ! [L: num] :
% 5.52/5.84 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 5.52/5.84 = one_one_nat ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_numeral_1
% 5.52/5.84 thf(fact_6099_mask__eq__0__iff,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( ( bit_se2002935070580805687sk_nat @ N )
% 5.52/5.84 = zero_zero_nat )
% 5.52/5.84 = ( N = zero_zero_nat ) ) ).
% 5.52/5.84
% 5.52/5.84 % mask_eq_0_iff
% 5.52/5.84 thf(fact_6100_mask__eq__0__iff,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( ( bit_se2000444600071755411sk_int @ N )
% 5.52/5.84 = zero_zero_int )
% 5.52/5.84 = ( N = zero_zero_nat ) ) ).
% 5.52/5.84
% 5.52/5.84 % mask_eq_0_iff
% 5.52/5.84 thf(fact_6101_mask__0,axiom,
% 5.52/5.84 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 5.52/5.84 = zero_zero_nat ) ).
% 5.52/5.84
% 5.52/5.84 % mask_0
% 5.52/5.84 thf(fact_6102_mask__0,axiom,
% 5.52/5.84 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 5.52/5.84 = zero_zero_int ) ).
% 5.52/5.84
% 5.52/5.84 % mask_0
% 5.52/5.84 thf(fact_6103_sum__abs,axiom,
% 5.52/5.84 ! [F: int > int,A2: set_int] :
% 5.52/5.84 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.52/5.84 @ ( groups4538972089207619220nt_int
% 5.52/5.84 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_abs
% 5.52/5.84 thf(fact_6104_sum__abs,axiom,
% 5.52/5.84 ! [F: nat > real,A2: set_nat] :
% 5.52/5.84 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.52/5.84 @ ( groups6591440286371151544t_real
% 5.52/5.84 @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_abs
% 5.52/5.84 thf(fact_6105_take__bit__of__1__eq__0__iff,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.52/5.84 = zero_zero_int )
% 5.52/5.84 = ( N = zero_zero_nat ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_1_eq_0_iff
% 5.52/5.84 thf(fact_6106_take__bit__of__1__eq__0__iff,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.52/5.84 = zero_zero_nat )
% 5.52/5.84 = ( N = zero_zero_nat ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_1_eq_0_iff
% 5.52/5.84 thf(fact_6107_mask__Suc__0,axiom,
% 5.52/5.84 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.52/5.84 = one_one_nat ) ).
% 5.52/5.84
% 5.52/5.84 % mask_Suc_0
% 5.52/5.84 thf(fact_6108_mask__Suc__0,axiom,
% 5.52/5.84 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.52/5.84 = one_one_int ) ).
% 5.52/5.84
% 5.52/5.84 % mask_Suc_0
% 5.52/5.84 thf(fact_6109_take__bit__minus__one__eq__mask,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.84 = ( bit_se2119862282449309892nteger @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_minus_one_eq_mask
% 5.52/5.84 thf(fact_6110_take__bit__minus__one__eq__mask,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.84 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_minus_one_eq_mask
% 5.52/5.84 thf(fact_6111_take__bit__of__Suc__0,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.52/5.84 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_Suc_0
% 5.52/5.84 thf(fact_6112_sum__abs__ge__zero,axiom,
% 5.52/5.84 ! [F: int > int,A2: set_int] :
% 5.52/5.84 ( ord_less_eq_int @ zero_zero_int
% 5.52/5.84 @ ( groups4538972089207619220nt_int
% 5.52/5.84 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_abs_ge_zero
% 5.52/5.84 thf(fact_6113_sum__abs__ge__zero,axiom,
% 5.52/5.84 ! [F: nat > real,A2: set_nat] :
% 5.52/5.84 ( ord_less_eq_real @ zero_zero_real
% 5.52/5.84 @ ( groups6591440286371151544t_real
% 5.52/5.84 @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_abs_ge_zero
% 5.52/5.84 thf(fact_6114_take__bit__of__1,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 5.52/5.84 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_1
% 5.52/5.84 thf(fact_6115_take__bit__of__1,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.52/5.84 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_1
% 5.52/5.84 thf(fact_6116_take__bit__of__1,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.52/5.84 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_1
% 5.52/5.84 thf(fact_6117_even__take__bit__eq,axiom,
% 5.52/5.84 ! [N: nat,A: code_integer] :
% 5.52/5.84 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 5.52/5.84 = ( ( N = zero_zero_nat )
% 5.52/5.84 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % even_take_bit_eq
% 5.52/5.84 thf(fact_6118_even__take__bit__eq,axiom,
% 5.52/5.84 ! [N: nat,A: int] :
% 5.52/5.84 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.52/5.84 = ( ( N = zero_zero_nat )
% 5.52/5.84 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % even_take_bit_eq
% 5.52/5.84 thf(fact_6119_even__take__bit__eq,axiom,
% 5.52/5.84 ! [N: nat,A: nat] :
% 5.52/5.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.52/5.84 = ( ( N = zero_zero_nat )
% 5.52/5.84 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % even_take_bit_eq
% 5.52/5.84 thf(fact_6120_take__bit__Suc__0,axiom,
% 5.52/5.84 ! [A: int] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.52/5.84 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_Suc_0
% 5.52/5.84 thf(fact_6121_take__bit__Suc__0,axiom,
% 5.52/5.84 ! [A: nat] :
% 5.52/5.84 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.52/5.84 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_Suc_0
% 5.52/5.84 thf(fact_6122_take__bit__of__exp,axiom,
% 5.52/5.84 ! [M: nat,N: nat] :
% 5.52/5.84 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.84 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_exp
% 5.52/5.84 thf(fact_6123_take__bit__of__exp,axiom,
% 5.52/5.84 ! [M: nat,N: nat] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.84 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_exp
% 5.52/5.84 thf(fact_6124_take__bit__of__exp,axiom,
% 5.52/5.84 ! [M: nat,N: nat] :
% 5.52/5.84 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.84 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_exp
% 5.52/5.84 thf(fact_6125_take__bit__of__2,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.84 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_2
% 5.52/5.84 thf(fact_6126_take__bit__of__2,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.84 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_2
% 5.52/5.84 thf(fact_6127_take__bit__of__2,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.84 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_2
% 5.52/5.84 thf(fact_6128_take__bit__of__int,axiom,
% 5.52/5.84 ! [N: nat,K: int] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 5.52/5.84 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_of_int
% 5.52/5.84 thf(fact_6129_of__int__mask__eq,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.52/5.84 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % of_int_mask_eq
% 5.52/5.84 thf(fact_6130_take__bit__add,axiom,
% 5.52/5.84 ! [N: nat,A: int,B: int] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_add
% 5.52/5.84 thf(fact_6131_take__bit__add,axiom,
% 5.52/5.84 ! [N: nat,A: nat,B: nat] :
% 5.52/5.84 ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 5.52/5.84 = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_add
% 5.52/5.84 thf(fact_6132_take__bit__tightened,axiom,
% 5.52/5.84 ! [N: nat,A: int,B: int,M: nat] :
% 5.52/5.84 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.52/5.84 => ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.84 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_tightened
% 5.52/5.84 thf(fact_6133_take__bit__tightened,axiom,
% 5.52/5.84 ! [N: nat,A: nat,B: nat,M: nat] :
% 5.52/5.84 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.52/5.84 = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 5.52/5.84 => ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.84 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.52/5.84 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_tightened
% 5.52/5.84 thf(fact_6134_take__bit__tightened__less__eq__nat,axiom,
% 5.52/5.84 ! [M: nat,N: nat,Q2: nat] :
% 5.52/5.84 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.84 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_tightened_less_eq_nat
% 5.52/5.84 thf(fact_6135_take__bit__nat__less__eq__self,axiom,
% 5.52/5.84 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_nat_less_eq_self
% 5.52/5.84 thf(fact_6136_take__bit__minus,axiom,
% 5.52/5.84 ! [N: nat,K: int] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_minus
% 5.52/5.84 thf(fact_6137_take__bit__mult,axiom,
% 5.52/5.84 ! [N: nat,K: int,L: int] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_mult
% 5.52/5.84 thf(fact_6138_take__bit__diff,axiom,
% 5.52/5.84 ! [N: nat,K: int,L: int] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_diff
% 5.52/5.84 thf(fact_6139_concat__bit__take__bit__eq,axiom,
% 5.52/5.84 ! [N: nat,B: int] :
% 5.52/5.84 ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.52/5.84 = ( bit_concat_bit @ N @ B ) ) ).
% 5.52/5.84
% 5.52/5.84 % concat_bit_take_bit_eq
% 5.52/5.84 thf(fact_6140_concat__bit__eq__iff,axiom,
% 5.52/5.84 ! [N: nat,K: int,L: int,R: int,S: int] :
% 5.52/5.84 ( ( ( bit_concat_bit @ N @ K @ L )
% 5.52/5.84 = ( bit_concat_bit @ N @ R @ S ) )
% 5.52/5.84 = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ N @ R ) )
% 5.52/5.84 & ( L = S ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % concat_bit_eq_iff
% 5.52/5.84 thf(fact_6141_less__eq__mask,axiom,
% 5.52/5.84 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % less_eq_mask
% 5.52/5.84 thf(fact_6142_sum__mono,axiom,
% 5.52/5.84 ! [K5: set_real,F: real > rat,G: real > rat] :
% 5.52/5.84 ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ K5 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono
% 5.52/5.84 thf(fact_6143_sum__mono,axiom,
% 5.52/5.84 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 5.52/5.84 ( ! [I2: nat] :
% 5.52/5.84 ( ( member_nat @ I2 @ K5 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono
% 5.52/5.84 thf(fact_6144_sum__mono,axiom,
% 5.52/5.84 ! [K5: set_int,F: int > rat,G: int > rat] :
% 5.52/5.84 ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ K5 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono
% 5.52/5.84 thf(fact_6145_sum__mono,axiom,
% 5.52/5.84 ! [K5: set_real,F: real > nat,G: real > nat] :
% 5.52/5.84 ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ K5 )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono
% 5.52/5.84 thf(fact_6146_sum__mono,axiom,
% 5.52/5.84 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.52/5.84 ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ K5 )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono
% 5.52/5.84 thf(fact_6147_sum__mono,axiom,
% 5.52/5.84 ! [K5: set_real,F: real > int,G: real > int] :
% 5.52/5.84 ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ K5 )
% 5.52/5.84 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono
% 5.52/5.84 thf(fact_6148_sum__mono,axiom,
% 5.52/5.84 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.52/5.84 ( ! [I2: nat] :
% 5.52/5.84 ( ( member_nat @ I2 @ K5 )
% 5.52/5.84 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono
% 5.52/5.84 thf(fact_6149_sum__mono,axiom,
% 5.52/5.84 ! [K5: set_int,F: int > int,G: int > int] :
% 5.52/5.84 ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ K5 )
% 5.52/5.84 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F @ K5 ) @ ( groups4538972089207619220nt_int @ G @ K5 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono
% 5.52/5.84 thf(fact_6150_sum__mono,axiom,
% 5.52/5.84 ! [K5: set_nat,F: nat > nat,G: nat > nat] :
% 5.52/5.84 ( ! [I2: nat] :
% 5.52/5.84 ( ( member_nat @ I2 @ K5 )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ K5 ) @ ( groups3542108847815614940at_nat @ G @ K5 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono
% 5.52/5.84 thf(fact_6151_sum__mono,axiom,
% 5.52/5.84 ! [K5: set_nat,F: nat > real,G: nat > real] :
% 5.52/5.84 ( ! [I2: nat] :
% 5.52/5.84 ( ( member_nat @ I2 @ K5 )
% 5.52/5.84 => ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ K5 ) @ ( groups6591440286371151544t_real @ G @ K5 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono
% 5.52/5.84 thf(fact_6152_sum__distrib__left,axiom,
% 5.52/5.84 ! [R: int,F: int > int,A2: set_int] :
% 5.52/5.84 ( ( times_times_int @ R @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.52/5.84 = ( groups4538972089207619220nt_int
% 5.52/5.84 @ ^ [N3: int] : ( times_times_int @ R @ ( F @ N3 ) )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_distrib_left
% 5.52/5.84 thf(fact_6153_sum__distrib__left,axiom,
% 5.52/5.84 ! [R: complex,F: complex > complex,A2: set_complex] :
% 5.52/5.84 ( ( times_times_complex @ R @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.52/5.84 = ( groups7754918857620584856omplex
% 5.52/5.84 @ ^ [N3: complex] : ( times_times_complex @ R @ ( F @ N3 ) )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_distrib_left
% 5.52/5.84 thf(fact_6154_sum__distrib__left,axiom,
% 5.52/5.84 ! [R: nat,F: nat > nat,A2: set_nat] :
% 5.52/5.84 ( ( times_times_nat @ R @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.52/5.84 = ( groups3542108847815614940at_nat
% 5.52/5.84 @ ^ [N3: nat] : ( times_times_nat @ R @ ( F @ N3 ) )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_distrib_left
% 5.52/5.84 thf(fact_6155_sum__distrib__left,axiom,
% 5.52/5.84 ! [R: real,F: nat > real,A2: set_nat] :
% 5.52/5.84 ( ( times_times_real @ R @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.52/5.84 = ( groups6591440286371151544t_real
% 5.52/5.84 @ ^ [N3: nat] : ( times_times_real @ R @ ( F @ N3 ) )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_distrib_left
% 5.52/5.84 thf(fact_6156_sum__distrib__right,axiom,
% 5.52/5.84 ! [F: int > int,A2: set_int,R: int] :
% 5.52/5.84 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R )
% 5.52/5.84 = ( groups4538972089207619220nt_int
% 5.52/5.84 @ ^ [N3: int] : ( times_times_int @ ( F @ N3 ) @ R )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_distrib_right
% 5.52/5.84 thf(fact_6157_sum__distrib__right,axiom,
% 5.52/5.84 ! [F: complex > complex,A2: set_complex,R: complex] :
% 5.52/5.84 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 5.52/5.84 = ( groups7754918857620584856omplex
% 5.52/5.84 @ ^ [N3: complex] : ( times_times_complex @ ( F @ N3 ) @ R )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_distrib_right
% 5.52/5.84 thf(fact_6158_sum__distrib__right,axiom,
% 5.52/5.84 ! [F: nat > nat,A2: set_nat,R: nat] :
% 5.52/5.84 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R )
% 5.52/5.84 = ( groups3542108847815614940at_nat
% 5.52/5.84 @ ^ [N3: nat] : ( times_times_nat @ ( F @ N3 ) @ R )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_distrib_right
% 5.52/5.84 thf(fact_6159_sum__distrib__right,axiom,
% 5.52/5.84 ! [F: nat > real,A2: set_nat,R: real] :
% 5.52/5.84 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 5.52/5.84 = ( groups6591440286371151544t_real
% 5.52/5.84 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ R )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_distrib_right
% 5.52/5.84 thf(fact_6160_sum__product,axiom,
% 5.52/5.84 ! [F: int > int,A2: set_int,G: int > int,B4: set_int] :
% 5.52/5.84 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B4 ) )
% 5.52/5.84 = ( groups4538972089207619220nt_int
% 5.52/5.84 @ ^ [I4: int] :
% 5.52/5.84 ( groups4538972089207619220nt_int
% 5.52/5.84 @ ^ [J3: int] : ( times_times_int @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.52/5.84 @ B4 )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_product
% 5.52/5.84 thf(fact_6161_sum__product,axiom,
% 5.52/5.84 ! [F: complex > complex,A2: set_complex,G: complex > complex,B4: set_complex] :
% 5.52/5.84 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B4 ) )
% 5.52/5.84 = ( groups7754918857620584856omplex
% 5.52/5.84 @ ^ [I4: complex] :
% 5.52/5.84 ( groups7754918857620584856omplex
% 5.52/5.84 @ ^ [J3: complex] : ( times_times_complex @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.52/5.84 @ B4 )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_product
% 5.52/5.84 thf(fact_6162_sum__product,axiom,
% 5.52/5.84 ! [F: nat > nat,A2: set_nat,G: nat > nat,B4: set_nat] :
% 5.52/5.84 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B4 ) )
% 5.52/5.84 = ( groups3542108847815614940at_nat
% 5.52/5.84 @ ^ [I4: nat] :
% 5.52/5.84 ( groups3542108847815614940at_nat
% 5.52/5.84 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.52/5.84 @ B4 )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_product
% 5.52/5.84 thf(fact_6163_sum__product,axiom,
% 5.52/5.84 ! [F: nat > real,A2: set_nat,G: nat > real,B4: set_nat] :
% 5.52/5.84 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B4 ) )
% 5.52/5.84 = ( groups6591440286371151544t_real
% 5.52/5.84 @ ^ [I4: nat] :
% 5.52/5.84 ( groups6591440286371151544t_real
% 5.52/5.84 @ ^ [J3: nat] : ( times_times_real @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.52/5.84 @ B4 )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_product
% 5.52/5.84 thf(fact_6164_sum_Odistrib,axiom,
% 5.52/5.84 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.52/5.84 ( ( groups4538972089207619220nt_int
% 5.52/5.84 @ ^ [X: int] : ( plus_plus_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.52/5.84 @ A2 )
% 5.52/5.84 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.distrib
% 5.52/5.84 thf(fact_6165_sum_Odistrib,axiom,
% 5.52/5.84 ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 5.52/5.84 ( ( groups7754918857620584856omplex
% 5.52/5.84 @ ^ [X: complex] : ( plus_plus_complex @ ( G @ X ) @ ( H2 @ X ) )
% 5.52/5.84 @ A2 )
% 5.52/5.84 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.distrib
% 5.52/5.84 thf(fact_6166_sum_Odistrib,axiom,
% 5.52/5.84 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.52/5.84 ( ( groups3542108847815614940at_nat
% 5.52/5.84 @ ^ [X: nat] : ( plus_plus_nat @ ( G @ X ) @ ( H2 @ X ) )
% 5.52/5.84 @ A2 )
% 5.52/5.84 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.distrib
% 5.52/5.84 thf(fact_6167_sum_Odistrib,axiom,
% 5.52/5.84 ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 5.52/5.84 ( ( groups6591440286371151544t_real
% 5.52/5.84 @ ^ [X: nat] : ( plus_plus_real @ ( G @ X ) @ ( H2 @ X ) )
% 5.52/5.84 @ A2 )
% 5.52/5.84 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.distrib
% 5.52/5.84 thf(fact_6168_sum__divide__distrib,axiom,
% 5.52/5.84 ! [F: complex > complex,A2: set_complex,R: complex] :
% 5.52/5.84 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 5.52/5.84 = ( groups7754918857620584856omplex
% 5.52/5.84 @ ^ [N3: complex] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ R )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_divide_distrib
% 5.52/5.84 thf(fact_6169_sum__divide__distrib,axiom,
% 5.52/5.84 ! [F: nat > real,A2: set_nat,R: real] :
% 5.52/5.84 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 5.52/5.84 = ( groups6591440286371151544t_real
% 5.52/5.84 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ R )
% 5.52/5.84 @ A2 ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_divide_distrib
% 5.52/5.84 thf(fact_6170_mod__sum__eq,axiom,
% 5.52/5.84 ! [F: int > int,A: int,A2: set_int] :
% 5.52/5.84 ( ( modulo_modulo_int
% 5.52/5.84 @ ( groups4538972089207619220nt_int
% 5.52/5.84 @ ^ [I4: int] : ( modulo_modulo_int @ ( F @ I4 ) @ A )
% 5.52/5.84 @ A2 )
% 5.52/5.84 @ A )
% 5.52/5.84 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % mod_sum_eq
% 5.52/5.84 thf(fact_6171_mod__sum__eq,axiom,
% 5.52/5.84 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.52/5.84 ( ( modulo_modulo_nat
% 5.52/5.84 @ ( groups3542108847815614940at_nat
% 5.52/5.84 @ ^ [I4: nat] : ( modulo_modulo_nat @ ( F @ I4 ) @ A )
% 5.52/5.84 @ A2 )
% 5.52/5.84 @ A )
% 5.52/5.84 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % mod_sum_eq
% 5.52/5.84 thf(fact_6172_take__bit__eq__mask__iff,axiom,
% 5.52/5.84 ! [N: nat,K: int] :
% 5.52/5.84 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.52/5.84 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.52/5.84 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.52/5.84 = zero_zero_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_eq_mask_iff
% 5.52/5.84 thf(fact_6173_sum__nonpos,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > real] :
% 5.52/5.84 ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonpos
% 5.52/5.84 thf(fact_6174_sum__nonpos,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > real] :
% 5.52/5.84 ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonpos
% 5.52/5.84 thf(fact_6175_sum__nonpos,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > rat] :
% 5.52/5.84 ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 5.52/5.84 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonpos
% 5.52/5.84 thf(fact_6176_sum__nonpos,axiom,
% 5.52/5.84 ! [A2: set_nat,F: nat > rat] :
% 5.52/5.84 ( ! [X4: nat] :
% 5.52/5.84 ( ( member_nat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 5.52/5.84 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonpos
% 5.52/5.84 thf(fact_6177_sum__nonpos,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > rat] :
% 5.52/5.84 ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 5.52/5.84 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonpos
% 5.52/5.84 thf(fact_6178_sum__nonpos,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > nat] :
% 5.52/5.84 ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 5.52/5.84 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonpos
% 5.52/5.84 thf(fact_6179_sum__nonpos,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > nat] :
% 5.52/5.84 ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 5.52/5.84 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonpos
% 5.52/5.84 thf(fact_6180_sum__nonpos,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > int] :
% 5.52/5.84 ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_int @ ( F @ X4 ) @ zero_zero_int ) )
% 5.52/5.84 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ zero_zero_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonpos
% 5.52/5.84 thf(fact_6181_sum__nonpos,axiom,
% 5.52/5.84 ! [A2: set_nat,F: nat > int] :
% 5.52/5.84 ( ! [X4: nat] :
% 5.52/5.84 ( ( member_nat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_int @ ( F @ X4 ) @ zero_zero_int ) )
% 5.52/5.84 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ zero_zero_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonpos
% 5.52/5.84 thf(fact_6182_sum__nonpos,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > int] :
% 5.52/5.84 ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_int @ ( F @ X4 ) @ zero_zero_int ) )
% 5.52/5.84 => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ zero_zero_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonpos
% 5.52/5.84 thf(fact_6183_sum__nonneg,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > real] :
% 5.52/5.84 ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg
% 5.52/5.84 thf(fact_6184_sum__nonneg,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > real] :
% 5.52/5.84 ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg
% 5.52/5.84 thf(fact_6185_sum__nonneg,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > rat] :
% 5.52/5.84 ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg
% 5.52/5.84 thf(fact_6186_sum__nonneg,axiom,
% 5.52/5.84 ! [A2: set_nat,F: nat > rat] :
% 5.52/5.84 ( ! [X4: nat] :
% 5.52/5.84 ( ( member_nat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg
% 5.52/5.84 thf(fact_6187_sum__nonneg,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > rat] :
% 5.52/5.84 ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg
% 5.52/5.84 thf(fact_6188_sum__nonneg,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > nat] :
% 5.52/5.84 ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg
% 5.52/5.84 thf(fact_6189_sum__nonneg,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > nat] :
% 5.52/5.84 ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg
% 5.52/5.84 thf(fact_6190_sum__nonneg,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > int] :
% 5.52/5.84 ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_eq_int @ zero_zero_int @ ( groups1932886352136224148al_int @ F @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg
% 5.52/5.84 thf(fact_6191_sum__nonneg,axiom,
% 5.52/5.84 ! [A2: set_nat,F: nat > int] :
% 5.52/5.84 ( ! [X4: nat] :
% 5.52/5.84 ( ( member_nat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_eq_int @ zero_zero_int @ ( groups3539618377306564664at_int @ F @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg
% 5.52/5.84 thf(fact_6192_sum__nonneg,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > int] :
% 5.52/5.84 ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_eq_int @ zero_zero_int @ ( groups4538972089207619220nt_int @ F @ A2 ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg
% 5.52/5.84 thf(fact_6193_sum__mono__inv,axiom,
% 5.52/5.84 ! [F: real > rat,I5: set_real,G: real > rat,I: real] :
% 5.52/5.84 ( ( ( groups1300246762558778688al_rat @ F @ I5 )
% 5.52/5.84 = ( groups1300246762558778688al_rat @ G @ I5 ) )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ( member_real @ I @ I5 )
% 5.52/5.84 => ( ( finite_finite_real @ I5 )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = ( G @ I ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono_inv
% 5.52/5.84 thf(fact_6194_sum__mono__inv,axiom,
% 5.52/5.84 ! [F: nat > rat,I5: set_nat,G: nat > rat,I: nat] :
% 5.52/5.84 ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 5.52/5.84 = ( groups2906978787729119204at_rat @ G @ I5 ) )
% 5.52/5.84 => ( ! [I2: nat] :
% 5.52/5.84 ( ( member_nat @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ( member_nat @ I @ I5 )
% 5.52/5.84 => ( ( finite_finite_nat @ I5 )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = ( G @ I ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono_inv
% 5.52/5.84 thf(fact_6195_sum__mono__inv,axiom,
% 5.52/5.84 ! [F: int > rat,I5: set_int,G: int > rat,I: int] :
% 5.52/5.84 ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 5.52/5.84 = ( groups3906332499630173760nt_rat @ G @ I5 ) )
% 5.52/5.84 => ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ( member_int @ I @ I5 )
% 5.52/5.84 => ( ( finite_finite_int @ I5 )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = ( G @ I ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono_inv
% 5.52/5.84 thf(fact_6196_sum__mono__inv,axiom,
% 5.52/5.84 ! [F: complex > rat,I5: set_complex,G: complex > rat,I: complex] :
% 5.52/5.84 ( ( ( groups5058264527183730370ex_rat @ F @ I5 )
% 5.52/5.84 = ( groups5058264527183730370ex_rat @ G @ I5 ) )
% 5.52/5.84 => ( ! [I2: complex] :
% 5.52/5.84 ( ( member_complex @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ( member_complex @ I @ I5 )
% 5.52/5.84 => ( ( finite3207457112153483333omplex @ I5 )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = ( G @ I ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono_inv
% 5.52/5.84 thf(fact_6197_sum__mono__inv,axiom,
% 5.52/5.84 ! [F: extended_enat > rat,I5: set_Extended_enat,G: extended_enat > rat,I: extended_enat] :
% 5.52/5.84 ( ( ( groups1392844769737527556at_rat @ F @ I5 )
% 5.52/5.84 = ( groups1392844769737527556at_rat @ G @ I5 ) )
% 5.52/5.84 => ( ! [I2: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ( member_Extended_enat @ I @ I5 )
% 5.52/5.84 => ( ( finite4001608067531595151d_enat @ I5 )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = ( G @ I ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono_inv
% 5.52/5.84 thf(fact_6198_sum__mono__inv,axiom,
% 5.52/5.84 ! [F: real > nat,I5: set_real,G: real > nat,I: real] :
% 5.52/5.84 ( ( ( groups1935376822645274424al_nat @ F @ I5 )
% 5.52/5.84 = ( groups1935376822645274424al_nat @ G @ I5 ) )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ( member_real @ I @ I5 )
% 5.52/5.84 => ( ( finite_finite_real @ I5 )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = ( G @ I ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono_inv
% 5.52/5.84 thf(fact_6199_sum__mono__inv,axiom,
% 5.52/5.84 ! [F: int > nat,I5: set_int,G: int > nat,I: int] :
% 5.52/5.84 ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 5.52/5.84 = ( groups4541462559716669496nt_nat @ G @ I5 ) )
% 5.52/5.84 => ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ( member_int @ I @ I5 )
% 5.52/5.84 => ( ( finite_finite_int @ I5 )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = ( G @ I ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono_inv
% 5.52/5.84 thf(fact_6200_sum__mono__inv,axiom,
% 5.52/5.84 ! [F: complex > nat,I5: set_complex,G: complex > nat,I: complex] :
% 5.52/5.84 ( ( ( groups5693394587270226106ex_nat @ F @ I5 )
% 5.52/5.84 = ( groups5693394587270226106ex_nat @ G @ I5 ) )
% 5.52/5.84 => ( ! [I2: complex] :
% 5.52/5.84 ( ( member_complex @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ( member_complex @ I @ I5 )
% 5.52/5.84 => ( ( finite3207457112153483333omplex @ I5 )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = ( G @ I ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono_inv
% 5.52/5.84 thf(fact_6201_sum__mono__inv,axiom,
% 5.52/5.84 ! [F: extended_enat > nat,I5: set_Extended_enat,G: extended_enat > nat,I: extended_enat] :
% 5.52/5.84 ( ( ( groups2027974829824023292at_nat @ F @ I5 )
% 5.52/5.84 = ( groups2027974829824023292at_nat @ G @ I5 ) )
% 5.52/5.84 => ( ! [I2: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ( member_Extended_enat @ I @ I5 )
% 5.52/5.84 => ( ( finite4001608067531595151d_enat @ I5 )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = ( G @ I ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono_inv
% 5.52/5.84 thf(fact_6202_sum__mono__inv,axiom,
% 5.52/5.84 ! [F: real > int,I5: set_real,G: real > int,I: real] :
% 5.52/5.84 ( ( ( groups1932886352136224148al_int @ F @ I5 )
% 5.52/5.84 = ( groups1932886352136224148al_int @ G @ I5 ) )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.52/5.84 => ( ( member_real @ I @ I5 )
% 5.52/5.84 => ( ( finite_finite_real @ I5 )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = ( G @ I ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono_inv
% 5.52/5.84 thf(fact_6203_take__bit__tightened__less__eq__int,axiom,
% 5.52/5.84 ! [M: nat,N: nat,K: int] :
% 5.52/5.84 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.84 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_tightened_less_eq_int
% 5.52/5.84 thf(fact_6204_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.52/5.84 ! [N: nat,A: int,B: int] :
% 5.52/5.84 ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.52/5.84 = ( bit_ri631733984087533419it_int @ N @ B ) )
% 5.52/5.84 = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % signed_take_bit_eq_iff_take_bit_eq
% 5.52/5.84 thf(fact_6205_take__bit__int__less__eq__self__iff,axiom,
% 5.52/5.84 ! [N: nat,K: int] :
% 5.52/5.84 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.52/5.84 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_int_less_eq_self_iff
% 5.52/5.84 thf(fact_6206_take__bit__nonnegative,axiom,
% 5.52/5.84 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_nonnegative
% 5.52/5.84 thf(fact_6207_not__take__bit__negative,axiom,
% 5.52/5.84 ! [N: nat,K: int] :
% 5.52/5.84 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 5.52/5.84
% 5.52/5.84 % not_take_bit_negative
% 5.52/5.84 thf(fact_6208_take__bit__int__greater__self__iff,axiom,
% 5.52/5.84 ! [K: int,N: nat] :
% 5.52/5.84 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.52/5.84 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_int_greater_self_iff
% 5.52/5.84 thf(fact_6209_signed__take__bit__take__bit,axiom,
% 5.52/5.84 ! [M: nat,N: nat,A: int] :
% 5.52/5.84 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.52/5.84 = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % signed_take_bit_take_bit
% 5.52/5.84 thf(fact_6210_take__bit__unset__bit__eq,axiom,
% 5.52/5.84 ! [N: nat,M: nat,A: int] :
% 5.52/5.84 ( ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.84 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.52/5.84 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.52/5.84 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.52/5.84 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_unset_bit_eq
% 5.52/5.84 thf(fact_6211_take__bit__unset__bit__eq,axiom,
% 5.52/5.84 ! [N: nat,M: nat,A: nat] :
% 5.52/5.84 ( ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.84 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.52/5.84 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.52/5.84 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.52/5.84 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.52/5.84 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_unset_bit_eq
% 5.52/5.84 thf(fact_6212_take__bit__set__bit__eq,axiom,
% 5.52/5.84 ! [N: nat,M: nat,A: int] :
% 5.52/5.84 ( ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.84 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.52/5.84 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.52/5.84 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.52/5.84 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_set_bit_eq
% 5.52/5.84 thf(fact_6213_take__bit__set__bit__eq,axiom,
% 5.52/5.84 ! [N: nat,M: nat,A: nat] :
% 5.52/5.84 ( ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.84 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.52/5.84 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.52/5.84 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.52/5.84 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.52/5.84 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_set_bit_eq
% 5.52/5.84 thf(fact_6214_take__bit__flip__bit__eq,axiom,
% 5.52/5.84 ! [N: nat,M: nat,A: int] :
% 5.52/5.84 ( ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.84 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.52/5.84 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.52/5.84 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.52/5.84 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_flip_bit_eq
% 5.52/5.84 thf(fact_6215_take__bit__flip__bit__eq,axiom,
% 5.52/5.84 ! [N: nat,M: nat,A: nat] :
% 5.52/5.84 ( ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.84 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.52/5.84 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.52/5.84 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.52/5.84 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.52/5.84 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_flip_bit_eq
% 5.52/5.84 thf(fact_6216_mask__nonnegative__int,axiom,
% 5.52/5.84 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % mask_nonnegative_int
% 5.52/5.84 thf(fact_6217_not__mask__negative__int,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 5.52/5.84
% 5.52/5.84 % not_mask_negative_int
% 5.52/5.84 thf(fact_6218_sum__le__included,axiom,
% 5.52/5.84 ! [S: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 5.52/5.84 ( ( finite_finite_int @ S )
% 5.52/5.84 => ( ( finite_finite_int @ T )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ T )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ S )
% 5.52/5.84 => ? [Xa: int] :
% 5.52/5.84 ( ( member_int @ Xa @ T )
% 5.52/5.84 & ( ( I @ Xa )
% 5.52/5.84 = X4 )
% 5.52/5.84 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_le_included
% 5.52/5.84 thf(fact_6219_sum__le__included,axiom,
% 5.52/5.84 ! [S: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 5.52/5.84 ( ( finite_finite_int @ S )
% 5.52/5.84 => ( ( finite3207457112153483333omplex @ T )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ T )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ S )
% 5.52/5.84 => ? [Xa: complex] :
% 5.52/5.84 ( ( member_complex @ Xa @ T )
% 5.52/5.84 & ( ( I @ Xa )
% 5.52/5.84 = X4 )
% 5.52/5.84 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_le_included
% 5.52/5.84 thf(fact_6220_sum__le__included,axiom,
% 5.52/5.84 ! [S: set_int,T: set_Extended_enat,G: extended_enat > real,I: extended_enat > int,F: int > real] :
% 5.52/5.84 ( ( finite_finite_int @ S )
% 5.52/5.84 => ( ( finite4001608067531595151d_enat @ T )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ T )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ S )
% 5.52/5.84 => ? [Xa: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ Xa @ T )
% 5.52/5.84 & ( ( I @ Xa )
% 5.52/5.84 = X4 )
% 5.52/5.84 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups4148127829035722712t_real @ G @ T ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_le_included
% 5.52/5.84 thf(fact_6221_sum__le__included,axiom,
% 5.52/5.84 ! [S: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ S )
% 5.52/5.84 => ( ( finite_finite_int @ T )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ T )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ S )
% 5.52/5.84 => ? [Xa: int] :
% 5.52/5.84 ( ( member_int @ Xa @ T )
% 5.52/5.84 & ( ( I @ Xa )
% 5.52/5.84 = X4 )
% 5.52/5.84 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_le_included
% 5.52/5.84 thf(fact_6222_sum__le__included,axiom,
% 5.52/5.84 ! [S: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ S )
% 5.52/5.84 => ( ( finite3207457112153483333omplex @ T )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ T )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ S )
% 5.52/5.84 => ? [Xa: complex] :
% 5.52/5.84 ( ( member_complex @ Xa @ T )
% 5.52/5.84 & ( ( I @ Xa )
% 5.52/5.84 = X4 )
% 5.52/5.84 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_le_included
% 5.52/5.84 thf(fact_6223_sum__le__included,axiom,
% 5.52/5.84 ! [S: set_complex,T: set_Extended_enat,G: extended_enat > real,I: extended_enat > complex,F: complex > real] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ S )
% 5.52/5.84 => ( ( finite4001608067531595151d_enat @ T )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ T )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ S )
% 5.52/5.84 => ? [Xa: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ Xa @ T )
% 5.52/5.84 & ( ( I @ Xa )
% 5.52/5.84 = X4 )
% 5.52/5.84 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups4148127829035722712t_real @ G @ T ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_le_included
% 5.52/5.84 thf(fact_6224_sum__le__included,axiom,
% 5.52/5.84 ! [S: set_Extended_enat,T: set_int,G: int > real,I: int > extended_enat,F: extended_enat > real] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ S )
% 5.52/5.84 => ( ( finite_finite_int @ T )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ T )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ S )
% 5.52/5.84 => ? [Xa: int] :
% 5.52/5.84 ( ( member_int @ Xa @ T )
% 5.52/5.84 & ( ( I @ Xa )
% 5.52/5.84 = X4 )
% 5.52/5.84 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_le_included
% 5.52/5.84 thf(fact_6225_sum__le__included,axiom,
% 5.52/5.84 ! [S: set_Extended_enat,T: set_complex,G: complex > real,I: complex > extended_enat,F: extended_enat > real] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ S )
% 5.52/5.84 => ( ( finite3207457112153483333omplex @ T )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ T )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ S )
% 5.52/5.84 => ? [Xa: complex] :
% 5.52/5.84 ( ( member_complex @ Xa @ T )
% 5.52/5.84 & ( ( I @ Xa )
% 5.52/5.84 = X4 )
% 5.52/5.84 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_le_included
% 5.52/5.84 thf(fact_6226_sum__le__included,axiom,
% 5.52/5.84 ! [S: set_Extended_enat,T: set_Extended_enat,G: extended_enat > real,I: extended_enat > extended_enat,F: extended_enat > real] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ S )
% 5.52/5.84 => ( ( finite4001608067531595151d_enat @ T )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ T )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ S )
% 5.52/5.84 => ? [Xa: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ Xa @ T )
% 5.52/5.84 & ( ( I @ Xa )
% 5.52/5.84 = X4 )
% 5.52/5.84 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S ) @ ( groups4148127829035722712t_real @ G @ T ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_le_included
% 5.52/5.84 thf(fact_6227_sum__le__included,axiom,
% 5.52/5.84 ! [S: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 5.52/5.84 ( ( finite_finite_nat @ S )
% 5.52/5.84 => ( ( finite_finite_nat @ T )
% 5.52/5.84 => ( ! [X4: nat] :
% 5.52/5.84 ( ( member_nat @ X4 @ T )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ! [X4: nat] :
% 5.52/5.84 ( ( member_nat @ X4 @ S )
% 5.52/5.84 => ? [Xa: nat] :
% 5.52/5.84 ( ( member_nat @ Xa @ T )
% 5.52/5.84 & ( ( I @ Xa )
% 5.52/5.84 = X4 )
% 5.52/5.84 & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.52/5.84 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_le_included
% 5.52/5.84 thf(fact_6228_sum__nonneg__eq__0__iff,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > real] :
% 5.52/5.84 ( ( finite_finite_real @ A2 )
% 5.52/5.84 => ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 5.52/5.84 = zero_zero_real )
% 5.52/5.84 = ( ! [X: real] :
% 5.52/5.84 ( ( member_real @ X @ A2 )
% 5.52/5.84 => ( ( F @ X )
% 5.52/5.84 = zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_eq_0_iff
% 5.52/5.84 thf(fact_6229_sum__nonneg__eq__0__iff,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > real] :
% 5.52/5.84 ( ( finite_finite_int @ A2 )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 5.52/5.84 = zero_zero_real )
% 5.52/5.84 = ( ! [X: int] :
% 5.52/5.84 ( ( member_int @ X @ A2 )
% 5.52/5.84 => ( ( F @ X )
% 5.52/5.84 = zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_eq_0_iff
% 5.52/5.84 thf(fact_6230_sum__nonneg__eq__0__iff,axiom,
% 5.52/5.84 ! [A2: set_complex,F: complex > real] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 5.52/5.84 = zero_zero_real )
% 5.52/5.84 = ( ! [X: complex] :
% 5.52/5.84 ( ( member_complex @ X @ A2 )
% 5.52/5.84 => ( ( F @ X )
% 5.52/5.84 = zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_eq_0_iff
% 5.52/5.84 thf(fact_6231_sum__nonneg__eq__0__iff,axiom,
% 5.52/5.84 ! [A2: set_Extended_enat,F: extended_enat > real] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ( ( groups4148127829035722712t_real @ F @ A2 )
% 5.52/5.84 = zero_zero_real )
% 5.52/5.84 = ( ! [X: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X @ A2 )
% 5.52/5.84 => ( ( F @ X )
% 5.52/5.84 = zero_zero_real ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_eq_0_iff
% 5.52/5.84 thf(fact_6232_sum__nonneg__eq__0__iff,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > rat] :
% 5.52/5.84 ( ( finite_finite_real @ A2 )
% 5.52/5.84 => ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 5.52/5.84 = zero_zero_rat )
% 5.52/5.84 = ( ! [X: real] :
% 5.52/5.84 ( ( member_real @ X @ A2 )
% 5.52/5.84 => ( ( F @ X )
% 5.52/5.84 = zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_eq_0_iff
% 5.52/5.84 thf(fact_6233_sum__nonneg__eq__0__iff,axiom,
% 5.52/5.84 ! [A2: set_nat,F: nat > rat] :
% 5.52/5.84 ( ( finite_finite_nat @ A2 )
% 5.52/5.84 => ( ! [X4: nat] :
% 5.52/5.84 ( ( member_nat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 5.52/5.84 = zero_zero_rat )
% 5.52/5.84 = ( ! [X: nat] :
% 5.52/5.84 ( ( member_nat @ X @ A2 )
% 5.52/5.84 => ( ( F @ X )
% 5.52/5.84 = zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_eq_0_iff
% 5.52/5.84 thf(fact_6234_sum__nonneg__eq__0__iff,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > rat] :
% 5.52/5.84 ( ( finite_finite_int @ A2 )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 5.52/5.84 = zero_zero_rat )
% 5.52/5.84 = ( ! [X: int] :
% 5.52/5.84 ( ( member_int @ X @ A2 )
% 5.52/5.84 => ( ( F @ X )
% 5.52/5.84 = zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_eq_0_iff
% 5.52/5.84 thf(fact_6235_sum__nonneg__eq__0__iff,axiom,
% 5.52/5.84 ! [A2: set_complex,F: complex > rat] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 5.52/5.84 = zero_zero_rat )
% 5.52/5.84 = ( ! [X: complex] :
% 5.52/5.84 ( ( member_complex @ X @ A2 )
% 5.52/5.84 => ( ( F @ X )
% 5.52/5.84 = zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_eq_0_iff
% 5.52/5.84 thf(fact_6236_sum__nonneg__eq__0__iff,axiom,
% 5.52/5.84 ! [A2: set_Extended_enat,F: extended_enat > rat] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ( ( groups1392844769737527556at_rat @ F @ A2 )
% 5.52/5.84 = zero_zero_rat )
% 5.52/5.84 = ( ! [X: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X @ A2 )
% 5.52/5.84 => ( ( F @ X )
% 5.52/5.84 = zero_zero_rat ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_eq_0_iff
% 5.52/5.84 thf(fact_6237_sum__nonneg__eq__0__iff,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > nat] :
% 5.52/5.84 ( ( finite_finite_real @ A2 )
% 5.52/5.84 => ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 5.52/5.84 = zero_zero_nat )
% 5.52/5.84 = ( ! [X: real] :
% 5.52/5.84 ( ( member_real @ X @ A2 )
% 5.52/5.84 => ( ( F @ X )
% 5.52/5.84 = zero_zero_nat ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_eq_0_iff
% 5.52/5.84 thf(fact_6238_sum__strict__mono__ex1,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > real,G: int > real] :
% 5.52/5.84 ( ( finite_finite_int @ A2 )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ? [X6: int] :
% 5.52/5.84 ( ( member_int @ X6 @ A2 )
% 5.52/5.84 & ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.52/5.84 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono_ex1
% 5.52/5.84 thf(fact_6239_sum__strict__mono__ex1,axiom,
% 5.52/5.84 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ? [X6: complex] :
% 5.52/5.84 ( ( member_complex @ X6 @ A2 )
% 5.52/5.84 & ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.52/5.84 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono_ex1
% 5.52/5.84 thf(fact_6240_sum__strict__mono__ex1,axiom,
% 5.52/5.84 ! [A2: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ? [X6: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X6 @ A2 )
% 5.52/5.84 & ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.52/5.84 => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A2 ) @ ( groups4148127829035722712t_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono_ex1
% 5.52/5.84 thf(fact_6241_sum__strict__mono__ex1,axiom,
% 5.52/5.84 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.52/5.84 ( ( finite_finite_nat @ A2 )
% 5.52/5.84 => ( ! [X4: nat] :
% 5.52/5.84 ( ( member_nat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ? [X6: nat] :
% 5.52/5.84 ( ( member_nat @ X6 @ A2 )
% 5.52/5.84 & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono_ex1
% 5.52/5.84 thf(fact_6242_sum__strict__mono__ex1,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.52/5.84 ( ( finite_finite_int @ A2 )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ? [X6: int] :
% 5.52/5.84 ( ( member_int @ X6 @ A2 )
% 5.52/5.84 & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono_ex1
% 5.52/5.84 thf(fact_6243_sum__strict__mono__ex1,axiom,
% 5.52/5.84 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ? [X6: complex] :
% 5.52/5.84 ( ( member_complex @ X6 @ A2 )
% 5.52/5.84 & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono_ex1
% 5.52/5.84 thf(fact_6244_sum__strict__mono__ex1,axiom,
% 5.52/5.84 ! [A2: set_Extended_enat,F: extended_enat > rat,G: extended_enat > rat] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ? [X6: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X6 @ A2 )
% 5.52/5.84 & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A2 ) @ ( groups1392844769737527556at_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono_ex1
% 5.52/5.84 thf(fact_6245_sum__strict__mono__ex1,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.52/5.84 ( ( finite_finite_int @ A2 )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ? [X6: int] :
% 5.52/5.84 ( ( member_int @ X6 @ A2 )
% 5.52/5.84 & ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.52/5.84 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono_ex1
% 5.52/5.84 thf(fact_6246_sum__strict__mono__ex1,axiom,
% 5.52/5.84 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ? [X6: complex] :
% 5.52/5.84 ( ( member_complex @ X6 @ A2 )
% 5.52/5.84 & ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.52/5.84 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono_ex1
% 5.52/5.84 thf(fact_6247_sum__strict__mono__ex1,axiom,
% 5.52/5.84 ! [A2: set_Extended_enat,F: extended_enat > nat,G: extended_enat > nat] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ? [X6: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X6 @ A2 )
% 5.52/5.84 & ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.52/5.84 => ( ord_less_nat @ ( groups2027974829824023292at_nat @ F @ A2 ) @ ( groups2027974829824023292at_nat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono_ex1
% 5.52/5.84 thf(fact_6248_sum_Orelated,axiom,
% 5.52/5.84 ! [R2: complex > complex > $o,S3: set_nat,H2: nat > complex,G: nat > complex] :
% 5.52/5.84 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 5.52/5.84 => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 5.52/5.84 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.84 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.84 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X22 @ Y23 ) ) )
% 5.52/5.84 => ( ( finite_finite_nat @ S3 )
% 5.52/5.84 => ( ! [X4: nat] :
% 5.52/5.84 ( ( member_nat @ X4 @ S3 )
% 5.52/5.84 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( R2 @ ( groups2073611262835488442omplex @ H2 @ S3 ) @ ( groups2073611262835488442omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.related
% 5.52/5.84 thf(fact_6249_sum_Orelated,axiom,
% 5.52/5.84 ! [R2: complex > complex > $o,S3: set_int,H2: int > complex,G: int > complex] :
% 5.52/5.84 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 5.52/5.84 => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 5.52/5.84 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.84 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.84 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X22 @ Y23 ) ) )
% 5.52/5.84 => ( ( finite_finite_int @ S3 )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ S3 )
% 5.52/5.84 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( R2 @ ( groups3049146728041665814omplex @ H2 @ S3 ) @ ( groups3049146728041665814omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.related
% 5.52/5.84 thf(fact_6250_sum_Orelated,axiom,
% 5.52/5.84 ! [R2: complex > complex > $o,S3: set_Extended_enat,H2: extended_enat > complex,G: extended_enat > complex] :
% 5.52/5.84 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 5.52/5.84 => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 5.52/5.84 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.84 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.84 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X22 @ Y23 ) ) )
% 5.52/5.84 => ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ S3 )
% 5.52/5.84 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( R2 @ ( groups6818542070133387226omplex @ H2 @ S3 ) @ ( groups6818542070133387226omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.related
% 5.52/5.84 thf(fact_6251_sum_Orelated,axiom,
% 5.52/5.84 ! [R2: real > real > $o,S3: set_int,H2: int > real,G: int > real] :
% 5.52/5.84 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 5.52/5.84 => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 5.52/5.84 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.84 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.84 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X22 @ Y23 ) ) )
% 5.52/5.84 => ( ( finite_finite_int @ S3 )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ S3 )
% 5.52/5.84 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( R2 @ ( groups8778361861064173332t_real @ H2 @ S3 ) @ ( groups8778361861064173332t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.related
% 5.52/5.84 thf(fact_6252_sum_Orelated,axiom,
% 5.52/5.84 ! [R2: real > real > $o,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.52/5.84 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 5.52/5.84 => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 5.52/5.84 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.84 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.84 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X22 @ Y23 ) ) )
% 5.52/5.84 => ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ S3 )
% 5.52/5.84 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( R2 @ ( groups5808333547571424918x_real @ H2 @ S3 ) @ ( groups5808333547571424918x_real @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.related
% 5.52/5.84 thf(fact_6253_sum_Orelated,axiom,
% 5.52/5.84 ! [R2: real > real > $o,S3: set_Extended_enat,H2: extended_enat > real,G: extended_enat > real] :
% 5.52/5.84 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 5.52/5.84 => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 5.52/5.84 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.84 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.84 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X22 @ Y23 ) ) )
% 5.52/5.84 => ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ S3 )
% 5.52/5.84 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( R2 @ ( groups4148127829035722712t_real @ H2 @ S3 ) @ ( groups4148127829035722712t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.related
% 5.52/5.84 thf(fact_6254_sum_Orelated,axiom,
% 5.52/5.84 ! [R2: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 5.52/5.84 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 5.52/5.84 => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 5.52/5.84 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.84 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.84 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X22 @ Y23 ) ) )
% 5.52/5.84 => ( ( finite_finite_nat @ S3 )
% 5.52/5.84 => ( ! [X4: nat] :
% 5.52/5.84 ( ( member_nat @ X4 @ S3 )
% 5.52/5.84 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( R2 @ ( groups2906978787729119204at_rat @ H2 @ S3 ) @ ( groups2906978787729119204at_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.related
% 5.52/5.84 thf(fact_6255_sum_Orelated,axiom,
% 5.52/5.84 ! [R2: rat > rat > $o,S3: set_int,H2: int > rat,G: int > rat] :
% 5.52/5.84 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 5.52/5.84 => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 5.52/5.84 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.84 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.84 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X22 @ Y23 ) ) )
% 5.52/5.84 => ( ( finite_finite_int @ S3 )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ S3 )
% 5.52/5.84 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( R2 @ ( groups3906332499630173760nt_rat @ H2 @ S3 ) @ ( groups3906332499630173760nt_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.related
% 5.52/5.84 thf(fact_6256_sum_Orelated,axiom,
% 5.52/5.84 ! [R2: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.52/5.84 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 5.52/5.84 => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 5.52/5.84 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.84 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.84 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X22 @ Y23 ) ) )
% 5.52/5.84 => ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ S3 )
% 5.52/5.84 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( R2 @ ( groups5058264527183730370ex_rat @ H2 @ S3 ) @ ( groups5058264527183730370ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.related
% 5.52/5.84 thf(fact_6257_sum_Orelated,axiom,
% 5.52/5.84 ! [R2: rat > rat > $o,S3: set_Extended_enat,H2: extended_enat > rat,G: extended_enat > rat] :
% 5.52/5.84 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 5.52/5.84 => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 5.52/5.84 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.84 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.84 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X22 @ Y23 ) ) )
% 5.52/5.84 => ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ S3 )
% 5.52/5.84 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( R2 @ ( groups1392844769737527556at_rat @ H2 @ S3 ) @ ( groups1392844769737527556at_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.related
% 5.52/5.84 thf(fact_6258_sum__strict__mono,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > real,G: real > real] :
% 5.52/5.84 ( ( finite_finite_real @ A2 )
% 5.52/5.84 => ( ( A2 != bot_bot_set_real )
% 5.52/5.84 => ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono
% 5.52/5.84 thf(fact_6259_sum__strict__mono,axiom,
% 5.52/5.84 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.84 => ( ( A2 != bot_bot_set_complex )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono
% 5.52/5.84 thf(fact_6260_sum__strict__mono,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > real,G: int > real] :
% 5.52/5.84 ( ( finite_finite_int @ A2 )
% 5.52/5.84 => ( ( A2 != bot_bot_set_int )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono
% 5.52/5.84 thf(fact_6261_sum__strict__mono,axiom,
% 5.52/5.84 ! [A2: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.84 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A2 ) @ ( groups4148127829035722712t_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono
% 5.52/5.84 thf(fact_6262_sum__strict__mono,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.52/5.84 ( ( finite_finite_real @ A2 )
% 5.52/5.84 => ( ( A2 != bot_bot_set_real )
% 5.52/5.84 => ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono
% 5.52/5.84 thf(fact_6263_sum__strict__mono,axiom,
% 5.52/5.84 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.84 => ( ( A2 != bot_bot_set_complex )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono
% 5.52/5.84 thf(fact_6264_sum__strict__mono,axiom,
% 5.52/5.84 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.52/5.84 ( ( finite_finite_nat @ A2 )
% 5.52/5.84 => ( ( A2 != bot_bot_set_nat )
% 5.52/5.84 => ( ! [X4: nat] :
% 5.52/5.84 ( ( member_nat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono
% 5.52/5.84 thf(fact_6265_sum__strict__mono,axiom,
% 5.52/5.84 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.52/5.84 ( ( finite_finite_int @ A2 )
% 5.52/5.84 => ( ( A2 != bot_bot_set_int )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono
% 5.52/5.84 thf(fact_6266_sum__strict__mono,axiom,
% 5.52/5.84 ! [A2: set_Extended_enat,F: extended_enat > rat,G: extended_enat > rat] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.84 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A2 ) @ ( groups1392844769737527556at_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono
% 5.52/5.84 thf(fact_6267_sum__strict__mono,axiom,
% 5.52/5.84 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.52/5.84 ( ( finite_finite_real @ A2 )
% 5.52/5.84 => ( ( A2 != bot_bot_set_real )
% 5.52/5.84 => ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ A2 )
% 5.52/5.84 => ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.84 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono
% 5.52/5.84 thf(fact_6268_take__bit__signed__take__bit,axiom,
% 5.52/5.84 ! [M: nat,N: nat,A: int] :
% 5.52/5.84 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.84 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 5.52/5.84 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_signed_take_bit
% 5.52/5.84 thf(fact_6269_take__bit__decr__eq,axiom,
% 5.52/5.84 ! [N: nat,K: int] :
% 5.52/5.84 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.52/5.84 != zero_zero_int )
% 5.52/5.84 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 5.52/5.84 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_decr_eq
% 5.52/5.84 thf(fact_6270_sum__nonneg__0,axiom,
% 5.52/5.84 ! [S: set_real,F: real > real,I: real] :
% 5.52/5.84 ( ( finite_finite_real @ S )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 5.52/5.84 = zero_zero_real )
% 5.52/5.84 => ( ( member_real @ I @ S )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = zero_zero_real ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_0
% 5.52/5.84 thf(fact_6271_sum__nonneg__0,axiom,
% 5.52/5.84 ! [S: set_int,F: int > real,I: int] :
% 5.52/5.84 ( ( finite_finite_int @ S )
% 5.52/5.84 => ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 5.52/5.84 = zero_zero_real )
% 5.52/5.84 => ( ( member_int @ I @ S )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = zero_zero_real ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_0
% 5.52/5.84 thf(fact_6272_sum__nonneg__0,axiom,
% 5.52/5.84 ! [S: set_complex,F: complex > real,I: complex] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ S )
% 5.52/5.84 => ( ! [I2: complex] :
% 5.52/5.84 ( ( member_complex @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 5.52/5.84 = zero_zero_real )
% 5.52/5.84 => ( ( member_complex @ I @ S )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = zero_zero_real ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_0
% 5.52/5.84 thf(fact_6273_sum__nonneg__0,axiom,
% 5.52/5.84 ! [S: set_Extended_enat,F: extended_enat > real,I: extended_enat] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ S )
% 5.52/5.84 => ( ! [I2: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups4148127829035722712t_real @ F @ S )
% 5.52/5.84 = zero_zero_real )
% 5.52/5.84 => ( ( member_Extended_enat @ I @ S )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = zero_zero_real ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_0
% 5.52/5.84 thf(fact_6274_sum__nonneg__0,axiom,
% 5.52/5.84 ! [S: set_real,F: real > rat,I: real] :
% 5.52/5.84 ( ( finite_finite_real @ S )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 5.52/5.84 = zero_zero_rat )
% 5.52/5.84 => ( ( member_real @ I @ S )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = zero_zero_rat ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_0
% 5.52/5.84 thf(fact_6275_sum__nonneg__0,axiom,
% 5.52/5.84 ! [S: set_nat,F: nat > rat,I: nat] :
% 5.52/5.84 ( ( finite_finite_nat @ S )
% 5.52/5.84 => ( ! [I2: nat] :
% 5.52/5.84 ( ( member_nat @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 5.52/5.84 = zero_zero_rat )
% 5.52/5.84 => ( ( member_nat @ I @ S )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = zero_zero_rat ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_0
% 5.52/5.84 thf(fact_6276_sum__nonneg__0,axiom,
% 5.52/5.84 ! [S: set_int,F: int > rat,I: int] :
% 5.52/5.84 ( ( finite_finite_int @ S )
% 5.52/5.84 => ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 5.52/5.84 = zero_zero_rat )
% 5.52/5.84 => ( ( member_int @ I @ S )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = zero_zero_rat ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_0
% 5.52/5.84 thf(fact_6277_sum__nonneg__0,axiom,
% 5.52/5.84 ! [S: set_complex,F: complex > rat,I: complex] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ S )
% 5.52/5.84 => ( ! [I2: complex] :
% 5.52/5.84 ( ( member_complex @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 5.52/5.84 = zero_zero_rat )
% 5.52/5.84 => ( ( member_complex @ I @ S )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = zero_zero_rat ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_0
% 5.52/5.84 thf(fact_6278_sum__nonneg__0,axiom,
% 5.52/5.84 ! [S: set_Extended_enat,F: extended_enat > rat,I: extended_enat] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ S )
% 5.52/5.84 => ( ! [I2: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups1392844769737527556at_rat @ F @ S )
% 5.52/5.84 = zero_zero_rat )
% 5.52/5.84 => ( ( member_Extended_enat @ I @ S )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = zero_zero_rat ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_0
% 5.52/5.84 thf(fact_6279_sum__nonneg__0,axiom,
% 5.52/5.84 ! [S: set_real,F: real > nat,I: real] :
% 5.52/5.84 ( ( finite_finite_real @ S )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 5.52/5.84 = zero_zero_nat )
% 5.52/5.84 => ( ( member_real @ I @ S )
% 5.52/5.84 => ( ( F @ I )
% 5.52/5.84 = zero_zero_nat ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_0
% 5.52/5.84 thf(fact_6280_sum__nonneg__leq__bound,axiom,
% 5.52/5.84 ! [S: set_real,F: real > real,B4: real,I: real] :
% 5.52/5.84 ( ( finite_finite_real @ S )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 5.52/5.84 = B4 )
% 5.52/5.84 => ( ( member_real @ I @ S )
% 5.52/5.84 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_leq_bound
% 5.52/5.84 thf(fact_6281_sum__nonneg__leq__bound,axiom,
% 5.52/5.84 ! [S: set_int,F: int > real,B4: real,I: int] :
% 5.52/5.84 ( ( finite_finite_int @ S )
% 5.52/5.84 => ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 5.52/5.84 = B4 )
% 5.52/5.84 => ( ( member_int @ I @ S )
% 5.52/5.84 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_leq_bound
% 5.52/5.84 thf(fact_6282_sum__nonneg__leq__bound,axiom,
% 5.52/5.84 ! [S: set_complex,F: complex > real,B4: real,I: complex] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ S )
% 5.52/5.84 => ( ! [I2: complex] :
% 5.52/5.84 ( ( member_complex @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 5.52/5.84 = B4 )
% 5.52/5.84 => ( ( member_complex @ I @ S )
% 5.52/5.84 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_leq_bound
% 5.52/5.84 thf(fact_6283_sum__nonneg__leq__bound,axiom,
% 5.52/5.84 ! [S: set_Extended_enat,F: extended_enat > real,B4: real,I: extended_enat] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ S )
% 5.52/5.84 => ( ! [I2: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups4148127829035722712t_real @ F @ S )
% 5.52/5.84 = B4 )
% 5.52/5.84 => ( ( member_Extended_enat @ I @ S )
% 5.52/5.84 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_leq_bound
% 5.52/5.84 thf(fact_6284_sum__nonneg__leq__bound,axiom,
% 5.52/5.84 ! [S: set_real,F: real > rat,B4: rat,I: real] :
% 5.52/5.84 ( ( finite_finite_real @ S )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 5.52/5.84 = B4 )
% 5.52/5.84 => ( ( member_real @ I @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_leq_bound
% 5.52/5.84 thf(fact_6285_sum__nonneg__leq__bound,axiom,
% 5.52/5.84 ! [S: set_nat,F: nat > rat,B4: rat,I: nat] :
% 5.52/5.84 ( ( finite_finite_nat @ S )
% 5.52/5.84 => ( ! [I2: nat] :
% 5.52/5.84 ( ( member_nat @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 5.52/5.84 = B4 )
% 5.52/5.84 => ( ( member_nat @ I @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_leq_bound
% 5.52/5.84 thf(fact_6286_sum__nonneg__leq__bound,axiom,
% 5.52/5.84 ! [S: set_int,F: int > rat,B4: rat,I: int] :
% 5.52/5.84 ( ( finite_finite_int @ S )
% 5.52/5.84 => ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 5.52/5.84 = B4 )
% 5.52/5.84 => ( ( member_int @ I @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_leq_bound
% 5.52/5.84 thf(fact_6287_sum__nonneg__leq__bound,axiom,
% 5.52/5.84 ! [S: set_complex,F: complex > rat,B4: rat,I: complex] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ S )
% 5.52/5.84 => ( ! [I2: complex] :
% 5.52/5.84 ( ( member_complex @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 5.52/5.84 = B4 )
% 5.52/5.84 => ( ( member_complex @ I @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_leq_bound
% 5.52/5.84 thf(fact_6288_sum__nonneg__leq__bound,axiom,
% 5.52/5.84 ! [S: set_Extended_enat,F: extended_enat > rat,B4: rat,I: extended_enat] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ S )
% 5.52/5.84 => ( ! [I2: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups1392844769737527556at_rat @ F @ S )
% 5.52/5.84 = B4 )
% 5.52/5.84 => ( ( member_Extended_enat @ I @ S )
% 5.52/5.84 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_leq_bound
% 5.52/5.84 thf(fact_6289_sum__nonneg__leq__bound,axiom,
% 5.52/5.84 ! [S: set_real,F: real > nat,B4: nat,I: real] :
% 5.52/5.84 ( ( finite_finite_real @ S )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ S )
% 5.52/5.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 5.52/5.84 = B4 )
% 5.52/5.84 => ( ( member_real @ I @ S )
% 5.52/5.84 => ( ord_less_eq_nat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_nonneg_leq_bound
% 5.52/5.84 thf(fact_6290_less__mask,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.52/5.84 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % less_mask
% 5.52/5.84 thf(fact_6291_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.52/5.84 ! [N: nat,K: int] :
% 5.52/5.84 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.52/5.84 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.52/5.84 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_eq_mask_iff_exp_dvd
% 5.52/5.84 thf(fact_6292_sum__pos2,axiom,
% 5.52/5.84 ! [I5: set_real,I: real,F: real > real] :
% 5.52/5.84 ( ( finite_finite_real @ I5 )
% 5.52/5.84 => ( ( member_real @ I @ I5 )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos2
% 5.52/5.84 thf(fact_6293_sum__pos2,axiom,
% 5.52/5.84 ! [I5: set_int,I: int,F: int > real] :
% 5.52/5.84 ( ( finite_finite_int @ I5 )
% 5.52/5.84 => ( ( member_int @ I @ I5 )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.52/5.84 => ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos2
% 5.52/5.84 thf(fact_6294_sum__pos2,axiom,
% 5.52/5.84 ! [I5: set_complex,I: complex,F: complex > real] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ I5 )
% 5.52/5.84 => ( ( member_complex @ I @ I5 )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.52/5.84 => ( ! [I2: complex] :
% 5.52/5.84 ( ( member_complex @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos2
% 5.52/5.84 thf(fact_6295_sum__pos2,axiom,
% 5.52/5.84 ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > real] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ I5 )
% 5.52/5.84 => ( ( member_Extended_enat @ I @ I5 )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.52/5.84 => ( ! [I2: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( groups4148127829035722712t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos2
% 5.52/5.84 thf(fact_6296_sum__pos2,axiom,
% 5.52/5.84 ! [I5: set_real,I: real,F: real > rat] :
% 5.52/5.84 ( ( finite_finite_real @ I5 )
% 5.52/5.84 => ( ( member_real @ I @ I5 )
% 5.52/5.84 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos2
% 5.52/5.84 thf(fact_6297_sum__pos2,axiom,
% 5.52/5.84 ! [I5: set_nat,I: nat,F: nat > rat] :
% 5.52/5.84 ( ( finite_finite_nat @ I5 )
% 5.52/5.84 => ( ( member_nat @ I @ I5 )
% 5.52/5.84 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.52/5.84 => ( ! [I2: nat] :
% 5.52/5.84 ( ( member_nat @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos2
% 5.52/5.84 thf(fact_6298_sum__pos2,axiom,
% 5.52/5.84 ! [I5: set_int,I: int,F: int > rat] :
% 5.52/5.84 ( ( finite_finite_int @ I5 )
% 5.52/5.84 => ( ( member_int @ I @ I5 )
% 5.52/5.84 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.52/5.84 => ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos2
% 5.52/5.84 thf(fact_6299_sum__pos2,axiom,
% 5.52/5.84 ! [I5: set_complex,I: complex,F: complex > rat] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ I5 )
% 5.52/5.84 => ( ( member_complex @ I @ I5 )
% 5.52/5.84 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.52/5.84 => ( ! [I2: complex] :
% 5.52/5.84 ( ( member_complex @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos2
% 5.52/5.84 thf(fact_6300_sum__pos2,axiom,
% 5.52/5.84 ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > rat] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ I5 )
% 5.52/5.84 => ( ( member_Extended_enat @ I @ I5 )
% 5.52/5.84 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.52/5.84 => ( ! [I2: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( groups1392844769737527556at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos2
% 5.52/5.84 thf(fact_6301_sum__pos2,axiom,
% 5.52/5.84 ! [I5: set_real,I: real,F: real > nat] :
% 5.52/5.84 ( ( finite_finite_real @ I5 )
% 5.52/5.84 => ( ( member_real @ I @ I5 )
% 5.52/5.84 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos2
% 5.52/5.84 thf(fact_6302_sum__pos,axiom,
% 5.52/5.84 ! [I5: set_real,F: real > real] :
% 5.52/5.84 ( ( finite_finite_real @ I5 )
% 5.52/5.84 => ( ( I5 != bot_bot_set_real )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos
% 5.52/5.84 thf(fact_6303_sum__pos,axiom,
% 5.52/5.84 ! [I5: set_complex,F: complex > real] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ I5 )
% 5.52/5.84 => ( ( I5 != bot_bot_set_complex )
% 5.52/5.84 => ( ! [I2: complex] :
% 5.52/5.84 ( ( member_complex @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos
% 5.52/5.84 thf(fact_6304_sum__pos,axiom,
% 5.52/5.84 ! [I5: set_int,F: int > real] :
% 5.52/5.84 ( ( finite_finite_int @ I5 )
% 5.52/5.84 => ( ( I5 != bot_bot_set_int )
% 5.52/5.84 => ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos
% 5.52/5.84 thf(fact_6305_sum__pos,axiom,
% 5.52/5.84 ! [I5: set_Extended_enat,F: extended_enat > real] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ I5 )
% 5.52/5.84 => ( ( I5 != bot_bo7653980558646680370d_enat )
% 5.52/5.84 => ( ! [I2: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_real @ zero_zero_real @ ( groups4148127829035722712t_real @ F @ I5 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos
% 5.52/5.84 thf(fact_6306_sum__pos,axiom,
% 5.52/5.84 ! [I5: set_real,F: real > rat] :
% 5.52/5.84 ( ( finite_finite_real @ I5 )
% 5.52/5.84 => ( ( I5 != bot_bot_set_real )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos
% 5.52/5.84 thf(fact_6307_sum__pos,axiom,
% 5.52/5.84 ! [I5: set_complex,F: complex > rat] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ I5 )
% 5.52/5.84 => ( ( I5 != bot_bot_set_complex )
% 5.52/5.84 => ( ! [I2: complex] :
% 5.52/5.84 ( ( member_complex @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos
% 5.52/5.84 thf(fact_6308_sum__pos,axiom,
% 5.52/5.84 ! [I5: set_nat,F: nat > rat] :
% 5.52/5.84 ( ( finite_finite_nat @ I5 )
% 5.52/5.84 => ( ( I5 != bot_bot_set_nat )
% 5.52/5.84 => ( ! [I2: nat] :
% 5.52/5.84 ( ( member_nat @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos
% 5.52/5.84 thf(fact_6309_sum__pos,axiom,
% 5.52/5.84 ! [I5: set_int,F: int > rat] :
% 5.52/5.84 ( ( finite_finite_int @ I5 )
% 5.52/5.84 => ( ( I5 != bot_bot_set_int )
% 5.52/5.84 => ( ! [I2: int] :
% 5.52/5.84 ( ( member_int @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos
% 5.52/5.84 thf(fact_6310_sum__pos,axiom,
% 5.52/5.84 ! [I5: set_Extended_enat,F: extended_enat > rat] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ I5 )
% 5.52/5.84 => ( ( I5 != bot_bo7653980558646680370d_enat )
% 5.52/5.84 => ( ! [I2: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_rat @ zero_zero_rat @ ( groups1392844769737527556at_rat @ F @ I5 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos
% 5.52/5.84 thf(fact_6311_sum__pos,axiom,
% 5.52/5.84 ! [I5: set_real,F: real > nat] :
% 5.52/5.84 ( ( finite_finite_real @ I5 )
% 5.52/5.84 => ( ( I5 != bot_bot_set_real )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ I5 )
% 5.52/5.84 => ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.52/5.84 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_pos
% 5.52/5.84 thf(fact_6312_sum_Osubset__diff,axiom,
% 5.52/5.84 ! [B4: set_int,A2: set_int,G: int > real] :
% 5.52/5.84 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.52/5.84 => ( ( finite_finite_int @ A2 )
% 5.52/5.84 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.52/5.84 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups8778361861064173332t_real @ G @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.subset_diff
% 5.52/5.84 thf(fact_6313_sum_Osubset__diff,axiom,
% 5.52/5.84 ! [B4: set_complex,A2: set_complex,G: complex > real] :
% 5.52/5.84 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.52/5.84 => ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.84 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.52/5.84 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups5808333547571424918x_real @ G @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.subset_diff
% 5.52/5.84 thf(fact_6314_sum_Osubset__diff,axiom,
% 5.52/5.84 ! [B4: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > real] :
% 5.52/5.84 ( ( ord_le7203529160286727270d_enat @ B4 @ A2 )
% 5.52/5.84 => ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.84 => ( ( groups4148127829035722712t_real @ G @ A2 )
% 5.52/5.84 = ( plus_plus_real @ ( groups4148127829035722712t_real @ G @ ( minus_925952699566721837d_enat @ A2 @ B4 ) ) @ ( groups4148127829035722712t_real @ G @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.subset_diff
% 5.52/5.84 thf(fact_6315_sum_Osubset__diff,axiom,
% 5.52/5.84 ! [B4: set_int,A2: set_int,G: int > rat] :
% 5.52/5.84 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.52/5.84 => ( ( finite_finite_int @ A2 )
% 5.52/5.84 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.52/5.84 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups3906332499630173760nt_rat @ G @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.subset_diff
% 5.52/5.84 thf(fact_6316_sum_Osubset__diff,axiom,
% 5.52/5.84 ! [B4: set_complex,A2: set_complex,G: complex > rat] :
% 5.52/5.84 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.52/5.84 => ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.84 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.52/5.84 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups5058264527183730370ex_rat @ G @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.subset_diff
% 5.52/5.84 thf(fact_6317_sum_Osubset__diff,axiom,
% 5.52/5.84 ! [B4: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > rat] :
% 5.52/5.84 ( ( ord_le7203529160286727270d_enat @ B4 @ A2 )
% 5.52/5.84 => ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.84 => ( ( groups1392844769737527556at_rat @ G @ A2 )
% 5.52/5.84 = ( plus_plus_rat @ ( groups1392844769737527556at_rat @ G @ ( minus_925952699566721837d_enat @ A2 @ B4 ) ) @ ( groups1392844769737527556at_rat @ G @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.subset_diff
% 5.52/5.84 thf(fact_6318_sum_Osubset__diff,axiom,
% 5.52/5.84 ! [B4: set_int,A2: set_int,G: int > nat] :
% 5.52/5.84 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.52/5.84 => ( ( finite_finite_int @ A2 )
% 5.52/5.84 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.52/5.84 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups4541462559716669496nt_nat @ G @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.subset_diff
% 5.52/5.84 thf(fact_6319_sum_Osubset__diff,axiom,
% 5.52/5.84 ! [B4: set_complex,A2: set_complex,G: complex > nat] :
% 5.52/5.84 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.52/5.84 => ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.84 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.52/5.84 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups5693394587270226106ex_nat @ G @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.subset_diff
% 5.52/5.84 thf(fact_6320_sum_Osubset__diff,axiom,
% 5.52/5.84 ! [B4: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > nat] :
% 5.52/5.84 ( ( ord_le7203529160286727270d_enat @ B4 @ A2 )
% 5.52/5.84 => ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.84 => ( ( groups2027974829824023292at_nat @ G @ A2 )
% 5.52/5.84 = ( plus_plus_nat @ ( groups2027974829824023292at_nat @ G @ ( minus_925952699566721837d_enat @ A2 @ B4 ) ) @ ( groups2027974829824023292at_nat @ G @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.subset_diff
% 5.52/5.84 thf(fact_6321_sum_Osubset__diff,axiom,
% 5.52/5.84 ! [B4: set_complex,A2: set_complex,G: complex > int] :
% 5.52/5.84 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.52/5.84 => ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.84 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.52/5.84 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups5690904116761175830ex_int @ G @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum.subset_diff
% 5.52/5.84 thf(fact_6322_take__bit__Suc__bit0,axiom,
% 5.52/5.84 ! [N: nat,K: num] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.52/5.84 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_Suc_bit0
% 5.52/5.84 thf(fact_6323_take__bit__Suc__bit0,axiom,
% 5.52/5.84 ! [N: nat,K: num] :
% 5.52/5.84 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.52/5.84 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_Suc_bit0
% 5.52/5.84 thf(fact_6324_take__bit__eq__mod,axiom,
% 5.52/5.84 ( bit_se2923211474154528505it_int
% 5.52/5.84 = ( ^ [N3: nat,A4: int] : ( modulo_modulo_int @ A4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_eq_mod
% 5.52/5.84 thf(fact_6325_take__bit__eq__mod,axiom,
% 5.52/5.84 ( bit_se2925701944663578781it_nat
% 5.52/5.84 = ( ^ [N3: nat,A4: nat] : ( modulo_modulo_nat @ A4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_eq_mod
% 5.52/5.84 thf(fact_6326_sum__mono2,axiom,
% 5.52/5.84 ! [B4: set_real,A2: set_real,F: real > real] :
% 5.52/5.84 ( ( finite_finite_real @ B4 )
% 5.52/5.84 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.52/5.84 => ( ! [B2: real] :
% 5.52/5.84 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B2 ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono2
% 5.52/5.84 thf(fact_6327_sum__mono2,axiom,
% 5.52/5.84 ! [B4: set_int,A2: set_int,F: int > real] :
% 5.52/5.84 ( ( finite_finite_int @ B4 )
% 5.52/5.84 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.52/5.84 => ( ! [B2: int] :
% 5.52/5.84 ( ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A2 ) )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B2 ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono2
% 5.52/5.84 thf(fact_6328_sum__mono2,axiom,
% 5.52/5.84 ! [B4: set_complex,A2: set_complex,F: complex > real] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ B4 )
% 5.52/5.84 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.52/5.84 => ( ! [B2: complex] :
% 5.52/5.84 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B2 ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono2
% 5.52/5.84 thf(fact_6329_sum__mono2,axiom,
% 5.52/5.84 ! [B4: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > real] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ B4 )
% 5.52/5.84 => ( ( ord_le7203529160286727270d_enat @ A2 @ B4 )
% 5.52/5.84 => ( ! [B2: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ B4 @ A2 ) )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B2 ) ) )
% 5.52/5.84 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ A2 ) @ ( groups4148127829035722712t_real @ F @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono2
% 5.52/5.84 thf(fact_6330_sum__mono2,axiom,
% 5.52/5.84 ! [B4: set_real,A2: set_real,F: real > rat] :
% 5.52/5.84 ( ( finite_finite_real @ B4 )
% 5.52/5.84 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.52/5.84 => ( ! [B2: real] :
% 5.52/5.84 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.52/5.84 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono2
% 5.52/5.84 thf(fact_6331_sum__mono2,axiom,
% 5.52/5.84 ! [B4: set_int,A2: set_int,F: int > rat] :
% 5.52/5.84 ( ( finite_finite_int @ B4 )
% 5.52/5.84 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.52/5.84 => ( ! [B2: int] :
% 5.52/5.84 ( ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A2 ) )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.52/5.84 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono2
% 5.52/5.84 thf(fact_6332_sum__mono2,axiom,
% 5.52/5.84 ! [B4: set_complex,A2: set_complex,F: complex > rat] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ B4 )
% 5.52/5.84 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.52/5.84 => ( ! [B2: complex] :
% 5.52/5.84 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.52/5.84 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono2
% 5.52/5.84 thf(fact_6333_sum__mono2,axiom,
% 5.52/5.84 ! [B4: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > rat] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ B4 )
% 5.52/5.84 => ( ( ord_le7203529160286727270d_enat @ A2 @ B4 )
% 5.52/5.84 => ( ! [B2: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ B4 @ A2 ) )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.52/5.84 => ( ord_less_eq_rat @ ( groups1392844769737527556at_rat @ F @ A2 ) @ ( groups1392844769737527556at_rat @ F @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono2
% 5.52/5.84 thf(fact_6334_sum__mono2,axiom,
% 5.52/5.84 ! [B4: set_real,A2: set_real,F: real > nat] :
% 5.52/5.84 ( ( finite_finite_real @ B4 )
% 5.52/5.84 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.52/5.84 => ( ! [B2: real] :
% 5.52/5.84 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.52/5.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B2 ) ) )
% 5.52/5.84 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono2
% 5.52/5.84 thf(fact_6335_sum__mono2,axiom,
% 5.52/5.84 ! [B4: set_int,A2: set_int,F: int > nat] :
% 5.52/5.84 ( ( finite_finite_int @ B4 )
% 5.52/5.84 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.52/5.84 => ( ! [B2: int] :
% 5.52/5.84 ( ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A2 ) )
% 5.52/5.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B2 ) ) )
% 5.52/5.84 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B4 ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_mono2
% 5.52/5.84 thf(fact_6336_take__bit__nat__eq__self__iff,axiom,
% 5.52/5.84 ! [N: nat,M: nat] :
% 5.52/5.84 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.52/5.84 = M )
% 5.52/5.84 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_nat_eq_self_iff
% 5.52/5.84 thf(fact_6337_take__bit__nat__less__exp,axiom,
% 5.52/5.84 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_nat_less_exp
% 5.52/5.84 thf(fact_6338_take__bit__nat__eq__self,axiom,
% 5.52/5.84 ! [M: nat,N: nat] :
% 5.52/5.84 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.84 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.52/5.84 = M ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_nat_eq_self
% 5.52/5.84 thf(fact_6339_take__bit__nat__def,axiom,
% 5.52/5.84 ( bit_se2925701944663578781it_nat
% 5.52/5.84 = ( ^ [N3: nat,M3: nat] : ( modulo_modulo_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_nat_def
% 5.52/5.84 thf(fact_6340_take__bit__int__less__exp,axiom,
% 5.52/5.84 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_int_less_exp
% 5.52/5.84 thf(fact_6341_take__bit__int__def,axiom,
% 5.52/5.84 ( bit_se2923211474154528505it_int
% 5.52/5.84 = ( ^ [N3: nat,K2: int] : ( modulo_modulo_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_int_def
% 5.52/5.84 thf(fact_6342_num_Osize__gen_I1_J,axiom,
% 5.52/5.84 ( ( size_num @ one )
% 5.52/5.84 = zero_zero_nat ) ).
% 5.52/5.84
% 5.52/5.84 % num.size_gen(1)
% 5.52/5.84 thf(fact_6343_take__bit__eq__0__iff,axiom,
% 5.52/5.84 ! [N: nat,A: code_integer] :
% 5.52/5.84 ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.52/5.84 = zero_z3403309356797280102nteger )
% 5.52/5.84 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_eq_0_iff
% 5.52/5.84 thf(fact_6344_take__bit__eq__0__iff,axiom,
% 5.52/5.84 ! [N: nat,A: int] :
% 5.52/5.84 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.52/5.84 = zero_zero_int )
% 5.52/5.84 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_eq_0_iff
% 5.52/5.84 thf(fact_6345_take__bit__eq__0__iff,axiom,
% 5.52/5.84 ! [N: nat,A: nat] :
% 5.52/5.84 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.52/5.84 = zero_zero_nat )
% 5.52/5.84 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_eq_0_iff
% 5.52/5.84 thf(fact_6346_sum__strict__mono2,axiom,
% 5.52/5.84 ! [B4: set_real,A2: set_real,B: real,F: real > real] :
% 5.52/5.84 ( ( finite_finite_real @ B4 )
% 5.52/5.84 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.52/5.84 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.52/5.84 => ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ B4 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B4 ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono2
% 5.52/5.84 thf(fact_6347_sum__strict__mono2,axiom,
% 5.52/5.84 ! [B4: set_int,A2: set_int,B: int,F: int > real] :
% 5.52/5.84 ( ( finite_finite_int @ B4 )
% 5.52/5.84 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.52/5.84 => ( ( member_int @ B @ ( minus_minus_set_int @ B4 @ A2 ) )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ B4 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B4 ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono2
% 5.52/5.84 thf(fact_6348_sum__strict__mono2,axiom,
% 5.52/5.84 ! [B4: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ B4 )
% 5.52/5.84 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.52/5.84 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ B4 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B4 ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono2
% 5.52/5.84 thf(fact_6349_sum__strict__mono2,axiom,
% 5.52/5.84 ! [B4: set_Extended_enat,A2: set_Extended_enat,B: extended_enat,F: extended_enat > real] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ B4 )
% 5.52/5.84 => ( ( ord_le7203529160286727270d_enat @ A2 @ B4 )
% 5.52/5.84 => ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ B4 @ A2 ) )
% 5.52/5.84 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ B4 )
% 5.52/5.84 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A2 ) @ ( groups4148127829035722712t_real @ F @ B4 ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono2
% 5.52/5.84 thf(fact_6350_sum__strict__mono2,axiom,
% 5.52/5.84 ! [B4: set_real,A2: set_real,B: real,F: real > rat] :
% 5.52/5.84 ( ( finite_finite_real @ B4 )
% 5.52/5.84 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.52/5.84 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.52/5.84 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.52/5.84 => ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ B4 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono2
% 5.52/5.84 thf(fact_6351_sum__strict__mono2,axiom,
% 5.52/5.84 ! [B4: set_int,A2: set_int,B: int,F: int > rat] :
% 5.52/5.84 ( ( finite_finite_int @ B4 )
% 5.52/5.84 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.52/5.84 => ( ( member_int @ B @ ( minus_minus_set_int @ B4 @ A2 ) )
% 5.52/5.84 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ B4 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono2
% 5.52/5.84 thf(fact_6352_sum__strict__mono2,axiom,
% 5.52/5.84 ! [B4: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 5.52/5.84 ( ( finite3207457112153483333omplex @ B4 )
% 5.52/5.84 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.52/5.84 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.52/5.84 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.52/5.84 => ( ! [X4: complex] :
% 5.52/5.84 ( ( member_complex @ X4 @ B4 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono2
% 5.52/5.84 thf(fact_6353_sum__strict__mono2,axiom,
% 5.52/5.84 ! [B4: set_Extended_enat,A2: set_Extended_enat,B: extended_enat,F: extended_enat > rat] :
% 5.52/5.84 ( ( finite4001608067531595151d_enat @ B4 )
% 5.52/5.84 => ( ( ord_le7203529160286727270d_enat @ A2 @ B4 )
% 5.52/5.84 => ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ B4 @ A2 ) )
% 5.52/5.84 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.52/5.84 => ( ! [X4: extended_enat] :
% 5.52/5.84 ( ( member_Extended_enat @ X4 @ B4 )
% 5.52/5.84 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A2 ) @ ( groups1392844769737527556at_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono2
% 5.52/5.84 thf(fact_6354_sum__strict__mono2,axiom,
% 5.52/5.84 ! [B4: set_real,A2: set_real,B: real,F: real > nat] :
% 5.52/5.84 ( ( finite_finite_real @ B4 )
% 5.52/5.84 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.52/5.84 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.52/5.84 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.52/5.84 => ( ! [X4: real] :
% 5.52/5.84 ( ( member_real @ X4 @ B4 )
% 5.52/5.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono2
% 5.52/5.84 thf(fact_6355_sum__strict__mono2,axiom,
% 5.52/5.84 ! [B4: set_int,A2: set_int,B: int,F: int > nat] :
% 5.52/5.84 ( ( finite_finite_int @ B4 )
% 5.52/5.84 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.52/5.84 => ( ( member_int @ B @ ( minus_minus_set_int @ B4 @ A2 ) )
% 5.52/5.84 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.52/5.84 => ( ! [X4: int] :
% 5.52/5.84 ( ( member_int @ X4 @ B4 )
% 5.52/5.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.52/5.84 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % sum_strict_mono2
% 5.52/5.84 thf(fact_6356_take__bit__numeral__bit0,axiom,
% 5.52/5.84 ! [L: num,K: num] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.52/5.84 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_numeral_bit0
% 5.52/5.84 thf(fact_6357_take__bit__numeral__bit0,axiom,
% 5.52/5.84 ! [L: num,K: num] :
% 5.52/5.84 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.52/5.84 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_numeral_bit0
% 5.52/5.84 thf(fact_6358_take__bit__nat__less__self__iff,axiom,
% 5.52/5.84 ! [N: nat,M: nat] :
% 5.52/5.84 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 5.52/5.84 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_nat_less_self_iff
% 5.52/5.84 thf(fact_6359_Suc__mask__eq__exp,axiom,
% 5.52/5.84 ! [N: nat] :
% 5.52/5.84 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.52/5.84 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % Suc_mask_eq_exp
% 5.52/5.84 thf(fact_6360_mask__nat__less__exp,axiom,
% 5.52/5.84 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.84
% 5.52/5.84 % mask_nat_less_exp
% 5.52/5.84 thf(fact_6361_take__bit__Suc__minus__bit0,axiom,
% 5.52/5.84 ! [N: nat,K: num] :
% 5.52/5.84 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.52/5.84 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % take_bit_Suc_minus_bit0
% 5.52/5.84 thf(fact_6362_convex__sum__bound__le,axiom,
% 5.52/5.84 ! [I5: set_real,X2: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.52/5.84 ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ I5 )
% 5.52/5.84 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.52/5.84 => ( ( ( groups7713935264441627589nteger @ X2 @ I5 )
% 5.52/5.84 = one_one_Code_integer )
% 5.52/5.84 => ( ! [I2: real] :
% 5.52/5.84 ( ( member_real @ I2 @ I5 )
% 5.52/5.84 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.52/5.84 => ( ord_le3102999989581377725nteger
% 5.52/5.84 @ ( abs_abs_Code_integer
% 5.52/5.84 @ ( minus_8373710615458151222nteger
% 5.52/5.84 @ ( groups7713935264441627589nteger
% 5.52/5.84 @ ^ [I4: real] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.52/5.84 @ I5 )
% 5.52/5.84 @ B ) )
% 5.52/5.84 @ Delta ) ) ) ) ).
% 5.52/5.84
% 5.52/5.84 % convex_sum_bound_le
% 5.52/5.84 thf(fact_6363_convex__sum__bound__le,axiom,
% 5.52/5.85 ! [I5: set_nat,X2: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.52/5.85 ( ! [I2: nat] :
% 5.52/5.85 ( ( member_nat @ I2 @ I5 )
% 5.52/5.85 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.52/5.85 => ( ( ( groups7501900531339628137nteger @ X2 @ I5 )
% 5.52/5.85 = one_one_Code_integer )
% 5.52/5.85 => ( ! [I2: nat] :
% 5.52/5.85 ( ( member_nat @ I2 @ I5 )
% 5.52/5.85 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.52/5.85 => ( ord_le3102999989581377725nteger
% 5.52/5.85 @ ( abs_abs_Code_integer
% 5.52/5.85 @ ( minus_8373710615458151222nteger
% 5.52/5.85 @ ( groups7501900531339628137nteger
% 5.52/5.85 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 @ B ) )
% 5.52/5.85 @ Delta ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % convex_sum_bound_le
% 5.52/5.85 thf(fact_6364_convex__sum__bound__le,axiom,
% 5.52/5.85 ! [I5: set_int,X2: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.52/5.85 ( ! [I2: int] :
% 5.52/5.85 ( ( member_int @ I2 @ I5 )
% 5.52/5.85 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.52/5.85 => ( ( ( groups7873554091576472773nteger @ X2 @ I5 )
% 5.52/5.85 = one_one_Code_integer )
% 5.52/5.85 => ( ! [I2: int] :
% 5.52/5.85 ( ( member_int @ I2 @ I5 )
% 5.52/5.85 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.52/5.85 => ( ord_le3102999989581377725nteger
% 5.52/5.85 @ ( abs_abs_Code_integer
% 5.52/5.85 @ ( minus_8373710615458151222nteger
% 5.52/5.85 @ ( groups7873554091576472773nteger
% 5.52/5.85 @ ^ [I4: int] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 @ B ) )
% 5.52/5.85 @ Delta ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % convex_sum_bound_le
% 5.52/5.85 thf(fact_6365_convex__sum__bound__le,axiom,
% 5.52/5.85 ! [I5: set_real,X2: real > real,A: real > real,B: real,Delta: real] :
% 5.52/5.85 ( ! [I2: real] :
% 5.52/5.85 ( ( member_real @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_real @ zero_zero_real @ ( X2 @ I2 ) ) )
% 5.52/5.85 => ( ( ( groups8097168146408367636l_real @ X2 @ I5 )
% 5.52/5.85 = one_one_real )
% 5.52/5.85 => ( ! [I2: real] :
% 5.52/5.85 ( ( member_real @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.52/5.85 => ( ord_less_eq_real
% 5.52/5.85 @ ( abs_abs_real
% 5.52/5.85 @ ( minus_minus_real
% 5.52/5.85 @ ( groups8097168146408367636l_real
% 5.52/5.85 @ ^ [I4: real] : ( times_times_real @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 @ B ) )
% 5.52/5.85 @ Delta ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % convex_sum_bound_le
% 5.52/5.85 thf(fact_6366_convex__sum__bound__le,axiom,
% 5.52/5.85 ! [I5: set_int,X2: int > real,A: int > real,B: real,Delta: real] :
% 5.52/5.85 ( ! [I2: int] :
% 5.52/5.85 ( ( member_int @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_real @ zero_zero_real @ ( X2 @ I2 ) ) )
% 5.52/5.85 => ( ( ( groups8778361861064173332t_real @ X2 @ I5 )
% 5.52/5.85 = one_one_real )
% 5.52/5.85 => ( ! [I2: int] :
% 5.52/5.85 ( ( member_int @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.52/5.85 => ( ord_less_eq_real
% 5.52/5.85 @ ( abs_abs_real
% 5.52/5.85 @ ( minus_minus_real
% 5.52/5.85 @ ( groups8778361861064173332t_real
% 5.52/5.85 @ ^ [I4: int] : ( times_times_real @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 @ B ) )
% 5.52/5.85 @ Delta ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % convex_sum_bound_le
% 5.52/5.85 thf(fact_6367_convex__sum__bound__le,axiom,
% 5.52/5.85 ! [I5: set_real,X2: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.52/5.85 ( ! [I2: real] :
% 5.52/5.85 ( ( member_real @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I2 ) ) )
% 5.52/5.85 => ( ( ( groups1300246762558778688al_rat @ X2 @ I5 )
% 5.52/5.85 = one_one_rat )
% 5.52/5.85 => ( ! [I2: real] :
% 5.52/5.85 ( ( member_real @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.52/5.85 => ( ord_less_eq_rat
% 5.52/5.85 @ ( abs_abs_rat
% 5.52/5.85 @ ( minus_minus_rat
% 5.52/5.85 @ ( groups1300246762558778688al_rat
% 5.52/5.85 @ ^ [I4: real] : ( times_times_rat @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 @ B ) )
% 5.52/5.85 @ Delta ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % convex_sum_bound_le
% 5.52/5.85 thf(fact_6368_convex__sum__bound__le,axiom,
% 5.52/5.85 ! [I5: set_nat,X2: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.52/5.85 ( ! [I2: nat] :
% 5.52/5.85 ( ( member_nat @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I2 ) ) )
% 5.52/5.85 => ( ( ( groups2906978787729119204at_rat @ X2 @ I5 )
% 5.52/5.85 = one_one_rat )
% 5.52/5.85 => ( ! [I2: nat] :
% 5.52/5.85 ( ( member_nat @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.52/5.85 => ( ord_less_eq_rat
% 5.52/5.85 @ ( abs_abs_rat
% 5.52/5.85 @ ( minus_minus_rat
% 5.52/5.85 @ ( groups2906978787729119204at_rat
% 5.52/5.85 @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 @ B ) )
% 5.52/5.85 @ Delta ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % convex_sum_bound_le
% 5.52/5.85 thf(fact_6369_convex__sum__bound__le,axiom,
% 5.52/5.85 ! [I5: set_int,X2: int > rat,A: int > rat,B: rat,Delta: rat] :
% 5.52/5.85 ( ! [I2: int] :
% 5.52/5.85 ( ( member_int @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I2 ) ) )
% 5.52/5.85 => ( ( ( groups3906332499630173760nt_rat @ X2 @ I5 )
% 5.52/5.85 = one_one_rat )
% 5.52/5.85 => ( ! [I2: int] :
% 5.52/5.85 ( ( member_int @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.52/5.85 => ( ord_less_eq_rat
% 5.52/5.85 @ ( abs_abs_rat
% 5.52/5.85 @ ( minus_minus_rat
% 5.52/5.85 @ ( groups3906332499630173760nt_rat
% 5.52/5.85 @ ^ [I4: int] : ( times_times_rat @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 @ B ) )
% 5.52/5.85 @ Delta ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % convex_sum_bound_le
% 5.52/5.85 thf(fact_6370_convex__sum__bound__le,axiom,
% 5.52/5.85 ! [I5: set_real,X2: real > int,A: real > int,B: int,Delta: int] :
% 5.52/5.85 ( ! [I2: real] :
% 5.52/5.85 ( ( member_real @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_int @ zero_zero_int @ ( X2 @ I2 ) ) )
% 5.52/5.85 => ( ( ( groups1932886352136224148al_int @ X2 @ I5 )
% 5.52/5.85 = one_one_int )
% 5.52/5.85 => ( ! [I2: real] :
% 5.52/5.85 ( ( member_real @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.52/5.85 => ( ord_less_eq_int
% 5.52/5.85 @ ( abs_abs_int
% 5.52/5.85 @ ( minus_minus_int
% 5.52/5.85 @ ( groups1932886352136224148al_int
% 5.52/5.85 @ ^ [I4: real] : ( times_times_int @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 @ B ) )
% 5.52/5.85 @ Delta ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % convex_sum_bound_le
% 5.52/5.85 thf(fact_6371_convex__sum__bound__le,axiom,
% 5.52/5.85 ! [I5: set_nat,X2: nat > int,A: nat > int,B: int,Delta: int] :
% 5.52/5.85 ( ! [I2: nat] :
% 5.52/5.85 ( ( member_nat @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_int @ zero_zero_int @ ( X2 @ I2 ) ) )
% 5.52/5.85 => ( ( ( groups3539618377306564664at_int @ X2 @ I5 )
% 5.52/5.85 = one_one_int )
% 5.52/5.85 => ( ! [I2: nat] :
% 5.52/5.85 ( ( member_nat @ I2 @ I5 )
% 5.52/5.85 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.52/5.85 => ( ord_less_eq_int
% 5.52/5.85 @ ( abs_abs_int
% 5.52/5.85 @ ( minus_minus_int
% 5.52/5.85 @ ( groups3539618377306564664at_int
% 5.52/5.85 @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 @ B ) )
% 5.52/5.85 @ Delta ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % convex_sum_bound_le
% 5.52/5.85 thf(fact_6372_take__bit__int__greater__eq__self__iff,axiom,
% 5.52/5.85 ! [K: int,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.52/5.85 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_int_greater_eq_self_iff
% 5.52/5.85 thf(fact_6373_take__bit__int__less__self__iff,axiom,
% 5.52/5.85 ! [N: nat,K: int] :
% 5.52/5.85 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.52/5.85 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_int_less_self_iff
% 5.52/5.85 thf(fact_6374_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 5.52/5.85 = ( N = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % semiring_bit_operations_class.even_mask_iff
% 5.52/5.85 thf(fact_6375_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.52/5.85 = ( N = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % semiring_bit_operations_class.even_mask_iff
% 5.52/5.85 thf(fact_6376_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.52/5.85 = ( N = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % semiring_bit_operations_class.even_mask_iff
% 5.52/5.85 thf(fact_6377_add__0__iff,axiom,
% 5.52/5.85 ! [B: complex,A: complex] :
% 5.52/5.85 ( ( B
% 5.52/5.85 = ( plus_plus_complex @ B @ A ) )
% 5.52/5.85 = ( A = zero_zero_complex ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_0_iff
% 5.52/5.85 thf(fact_6378_add__0__iff,axiom,
% 5.52/5.85 ! [B: real,A: real] :
% 5.52/5.85 ( ( B
% 5.52/5.85 = ( plus_plus_real @ B @ A ) )
% 5.52/5.85 = ( A = zero_zero_real ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_0_iff
% 5.52/5.85 thf(fact_6379_add__0__iff,axiom,
% 5.52/5.85 ! [B: rat,A: rat] :
% 5.52/5.85 ( ( B
% 5.52/5.85 = ( plus_plus_rat @ B @ A ) )
% 5.52/5.85 = ( A = zero_zero_rat ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_0_iff
% 5.52/5.85 thf(fact_6380_add__0__iff,axiom,
% 5.52/5.85 ! [B: nat,A: nat] :
% 5.52/5.85 ( ( B
% 5.52/5.85 = ( plus_plus_nat @ B @ A ) )
% 5.52/5.85 = ( A = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_0_iff
% 5.52/5.85 thf(fact_6381_add__0__iff,axiom,
% 5.52/5.85 ! [B: int,A: int] :
% 5.52/5.85 ( ( B
% 5.52/5.85 = ( plus_plus_int @ B @ A ) )
% 5.52/5.85 = ( A = zero_zero_int ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_0_iff
% 5.52/5.85 thf(fact_6382_crossproduct__noteq,axiom,
% 5.52/5.85 ! [A: complex,B: complex,C: complex,D2: complex] :
% 5.52/5.85 ( ( ( A != B )
% 5.52/5.85 & ( C != D2 ) )
% 5.52/5.85 = ( ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D2 ) )
% 5.52/5.85 != ( plus_plus_complex @ ( times_times_complex @ A @ D2 ) @ ( times_times_complex @ B @ C ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % crossproduct_noteq
% 5.52/5.85 thf(fact_6383_crossproduct__noteq,axiom,
% 5.52/5.85 ! [A: real,B: real,C: real,D2: real] :
% 5.52/5.85 ( ( ( A != B )
% 5.52/5.85 & ( C != D2 ) )
% 5.52/5.85 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) )
% 5.52/5.85 != ( plus_plus_real @ ( times_times_real @ A @ D2 ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % crossproduct_noteq
% 5.52/5.85 thf(fact_6384_crossproduct__noteq,axiom,
% 5.52/5.85 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.52/5.85 ( ( ( A != B )
% 5.52/5.85 & ( C != D2 ) )
% 5.52/5.85 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) )
% 5.52/5.85 != ( plus_plus_rat @ ( times_times_rat @ A @ D2 ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % crossproduct_noteq
% 5.52/5.85 thf(fact_6385_crossproduct__noteq,axiom,
% 5.52/5.85 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.52/5.85 ( ( ( A != B )
% 5.52/5.85 & ( C != D2 ) )
% 5.52/5.85 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) )
% 5.52/5.85 != ( plus_plus_nat @ ( times_times_nat @ A @ D2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % crossproduct_noteq
% 5.52/5.85 thf(fact_6386_crossproduct__noteq,axiom,
% 5.52/5.85 ! [A: int,B: int,C: int,D2: int] :
% 5.52/5.85 ( ( ( A != B )
% 5.52/5.85 & ( C != D2 ) )
% 5.52/5.85 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) )
% 5.52/5.85 != ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % crossproduct_noteq
% 5.52/5.85 thf(fact_6387_crossproduct__eq,axiom,
% 5.52/5.85 ! [W: complex,Y2: complex,X2: complex,Z: complex] :
% 5.52/5.85 ( ( ( plus_plus_complex @ ( times_times_complex @ W @ Y2 ) @ ( times_times_complex @ X2 @ Z ) )
% 5.52/5.85 = ( plus_plus_complex @ ( times_times_complex @ W @ Z ) @ ( times_times_complex @ X2 @ Y2 ) ) )
% 5.52/5.85 = ( ( W = X2 )
% 5.52/5.85 | ( Y2 = Z ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % crossproduct_eq
% 5.52/5.85 thf(fact_6388_crossproduct__eq,axiom,
% 5.52/5.85 ! [W: real,Y2: real,X2: real,Z: real] :
% 5.52/5.85 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y2 ) @ ( times_times_real @ X2 @ Z ) )
% 5.52/5.85 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X2 @ Y2 ) ) )
% 5.52/5.85 = ( ( W = X2 )
% 5.52/5.85 | ( Y2 = Z ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % crossproduct_eq
% 5.52/5.85 thf(fact_6389_crossproduct__eq,axiom,
% 5.52/5.85 ! [W: rat,Y2: rat,X2: rat,Z: rat] :
% 5.52/5.85 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y2 ) @ ( times_times_rat @ X2 @ Z ) )
% 5.52/5.85 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X2 @ Y2 ) ) )
% 5.52/5.85 = ( ( W = X2 )
% 5.52/5.85 | ( Y2 = Z ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % crossproduct_eq
% 5.52/5.85 thf(fact_6390_crossproduct__eq,axiom,
% 5.52/5.85 ! [W: nat,Y2: nat,X2: nat,Z: nat] :
% 5.52/5.85 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y2 ) @ ( times_times_nat @ X2 @ Z ) )
% 5.52/5.85 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X2 @ Y2 ) ) )
% 5.52/5.85 = ( ( W = X2 )
% 5.52/5.85 | ( Y2 = Z ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % crossproduct_eq
% 5.52/5.85 thf(fact_6391_crossproduct__eq,axiom,
% 5.52/5.85 ! [W: int,Y2: int,X2: int,Z: int] :
% 5.52/5.85 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y2 ) @ ( times_times_int @ X2 @ Z ) )
% 5.52/5.85 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X2 @ Y2 ) ) )
% 5.52/5.85 = ( ( W = X2 )
% 5.52/5.85 | ( Y2 = Z ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % crossproduct_eq
% 5.52/5.85 thf(fact_6392_take__bit__int__eq__self__iff,axiom,
% 5.52/5.85 ! [N: nat,K: int] :
% 5.52/5.85 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.52/5.85 = K )
% 5.52/5.85 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.85 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_int_eq_self_iff
% 5.52/5.85 thf(fact_6393_take__bit__int__eq__self,axiom,
% 5.52/5.85 ! [K: int,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.85 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.85 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.52/5.85 = K ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_int_eq_self
% 5.52/5.85 thf(fact_6394_mask__nat__def,axiom,
% 5.52/5.85 ( bit_se2002935070580805687sk_nat
% 5.52/5.85 = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mask_nat_def
% 5.52/5.85 thf(fact_6395_mask__half__int,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.85 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mask_half_int
% 5.52/5.85 thf(fact_6396_take__bit__numeral__minus__bit0,axiom,
% 5.52/5.85 ! [L: num,K: num] :
% 5.52/5.85 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.52/5.85 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_numeral_minus_bit0
% 5.52/5.85 thf(fact_6397_take__bit__incr__eq,axiom,
% 5.52/5.85 ! [N: nat,K: int] :
% 5.52/5.85 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.52/5.85 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.52/5.85 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.52/5.85 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_incr_eq
% 5.52/5.85 thf(fact_6398_mask__int__def,axiom,
% 5.52/5.85 ( bit_se2000444600071755411sk_int
% 5.52/5.85 = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mask_int_def
% 5.52/5.85 thf(fact_6399_take__bit__Suc__minus__1__eq,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.85 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_Suc_minus_1_eq
% 5.52/5.85 thf(fact_6400_take__bit__Suc__minus__1__eq,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.85 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_Suc_minus_1_eq
% 5.52/5.85 thf(fact_6401_take__bit__Suc__bit1,axiom,
% 5.52/5.85 ! [N: nat,K: num] :
% 5.52/5.85 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.52/5.85 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_Suc_bit1
% 5.52/5.85 thf(fact_6402_take__bit__Suc__bit1,axiom,
% 5.52/5.85 ! [N: nat,K: num] :
% 5.52/5.85 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.52/5.85 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_Suc_bit1
% 5.52/5.85 thf(fact_6403_take__bit__numeral__minus__1__eq,axiom,
% 5.52/5.85 ! [K: num] :
% 5.52/5.85 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.85 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_numeral_minus_1_eq
% 5.52/5.85 thf(fact_6404_take__bit__numeral__minus__1__eq,axiom,
% 5.52/5.85 ! [K: num] :
% 5.52/5.85 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.85 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_numeral_minus_1_eq
% 5.52/5.85 thf(fact_6405_take__bit__Suc,axiom,
% 5.52/5.85 ! [N: nat,A: int] :
% 5.52/5.85 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.52/5.85 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_Suc
% 5.52/5.85 thf(fact_6406_take__bit__Suc,axiom,
% 5.52/5.85 ! [N: nat,A: nat] :
% 5.52/5.85 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 5.52/5.85 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_Suc
% 5.52/5.85 thf(fact_6407_mask__eq__exp__minus__1,axiom,
% 5.52/5.85 ( bit_se2002935070580805687sk_nat
% 5.52/5.85 = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mask_eq_exp_minus_1
% 5.52/5.85 thf(fact_6408_mask__eq__exp__minus__1,axiom,
% 5.52/5.85 ( bit_se2000444600071755411sk_int
% 5.52/5.85 = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mask_eq_exp_minus_1
% 5.52/5.85 thf(fact_6409_take__bit__int__less__eq,axiom,
% 5.52/5.85 ! [N: nat,K: int] :
% 5.52/5.85 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.52/5.85 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.85 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_int_less_eq
% 5.52/5.85 thf(fact_6410_take__bit__int__greater__eq,axiom,
% 5.52/5.85 ! [K: int,N: nat] :
% 5.52/5.85 ( ( ord_less_int @ K @ zero_zero_int )
% 5.52/5.85 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_int_greater_eq
% 5.52/5.85 thf(fact_6411_signed__take__bit__eq__take__bit__shift,axiom,
% 5.52/5.85 ( bit_ri631733984087533419it_int
% 5.52/5.85 = ( ^ [N3: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % signed_take_bit_eq_take_bit_shift
% 5.52/5.85 thf(fact_6412_stable__imp__take__bit__eq,axiom,
% 5.52/5.85 ! [A: code_integer,N: nat] :
% 5.52/5.85 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.85 = A )
% 5.52/5.85 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.85 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.52/5.85 = zero_z3403309356797280102nteger ) )
% 5.52/5.85 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.85 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.52/5.85 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % stable_imp_take_bit_eq
% 5.52/5.85 thf(fact_6413_stable__imp__take__bit__eq,axiom,
% 5.52/5.85 ! [A: int,N: nat] :
% 5.52/5.85 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.85 = A )
% 5.52/5.85 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.85 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.52/5.85 = zero_zero_int ) )
% 5.52/5.85 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.85 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.52/5.85 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % stable_imp_take_bit_eq
% 5.52/5.85 thf(fact_6414_stable__imp__take__bit__eq,axiom,
% 5.52/5.85 ! [A: nat,N: nat] :
% 5.52/5.85 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.85 = A )
% 5.52/5.85 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.85 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.52/5.85 = zero_zero_nat ) )
% 5.52/5.85 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.85 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.52/5.85 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % stable_imp_take_bit_eq
% 5.52/5.85 thf(fact_6415_take__bit__numeral__bit1,axiom,
% 5.52/5.85 ! [L: num,K: num] :
% 5.52/5.85 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.52/5.85 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_numeral_bit1
% 5.52/5.85 thf(fact_6416_take__bit__numeral__bit1,axiom,
% 5.52/5.85 ! [L: num,K: num] :
% 5.52/5.85 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.52/5.85 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_numeral_bit1
% 5.52/5.85 thf(fact_6417_take__bit__minus__small__eq,axiom,
% 5.52/5.85 ! [K: int,N: nat] :
% 5.52/5.85 ( ( ord_less_int @ zero_zero_int @ K )
% 5.52/5.85 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.85 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.52/5.85 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_minus_small_eq
% 5.52/5.85 thf(fact_6418_num_Osize__gen_I2_J,axiom,
% 5.52/5.85 ! [X23: num] :
% 5.52/5.85 ( ( size_num @ ( bit0 @ X23 ) )
% 5.52/5.85 = ( plus_plus_nat @ ( size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % num.size_gen(2)
% 5.52/5.85 thf(fact_6419_take__bit__numeral__minus__bit1,axiom,
% 5.52/5.85 ! [L: num,K: num] :
% 5.52/5.85 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.52/5.85 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_numeral_minus_bit1
% 5.52/5.85 thf(fact_6420_infinite__int__iff__unbounded,axiom,
% 5.52/5.85 ! [S3: set_int] :
% 5.52/5.85 ( ( ~ ( finite_finite_int @ S3 ) )
% 5.52/5.85 = ( ! [M3: int] :
% 5.52/5.85 ? [N3: int] :
% 5.52/5.85 ( ( ord_less_int @ M3 @ ( abs_abs_int @ N3 ) )
% 5.52/5.85 & ( member_int @ N3 @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % infinite_int_iff_unbounded
% 5.52/5.85 thf(fact_6421_take__bit__Suc__minus__bit1,axiom,
% 5.52/5.85 ! [N: nat,K: num] :
% 5.52/5.85 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.52/5.85 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_Suc_minus_bit1
% 5.52/5.85 thf(fact_6422_tanh__real__altdef,axiom,
% 5.52/5.85 ( tanh_real
% 5.52/5.85 = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % tanh_real_altdef
% 5.52/5.85 thf(fact_6423_and__int__unfold,axiom,
% 5.52/5.85 ( bit_se725231765392027082nd_int
% 5.52/5.85 = ( ^ [K2: int,L2: int] :
% 5.52/5.85 ( if_int
% 5.52/5.85 @ ( ( K2 = zero_zero_int )
% 5.52/5.85 | ( L2 = zero_zero_int ) )
% 5.52/5.85 @ zero_zero_int
% 5.52/5.85 @ ( if_int
% 5.52/5.85 @ ( K2
% 5.52/5.85 = ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.85 @ L2
% 5.52/5.85 @ ( if_int
% 5.52/5.85 @ ( L2
% 5.52/5.85 = ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.85 @ K2
% 5.52/5.85 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_int_unfold
% 5.52/5.85 thf(fact_6424_power__numeral,axiom,
% 5.52/5.85 ! [K: num,L: num] :
% 5.52/5.85 ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.52/5.85 = ( numera6690914467698888265omplex @ ( pow @ K @ L ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % power_numeral
% 5.52/5.85 thf(fact_6425_power__numeral,axiom,
% 5.52/5.85 ! [K: num,L: num] :
% 5.52/5.85 ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.52/5.85 = ( numeral_numeral_real @ ( pow @ K @ L ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % power_numeral
% 5.52/5.85 thf(fact_6426_power__numeral,axiom,
% 5.52/5.85 ! [K: num,L: num] :
% 5.52/5.85 ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.52/5.85 = ( numeral_numeral_rat @ ( pow @ K @ L ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % power_numeral
% 5.52/5.85 thf(fact_6427_power__numeral,axiom,
% 5.52/5.85 ! [K: num,L: num] :
% 5.52/5.85 ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.52/5.85 = ( numeral_numeral_nat @ ( pow @ K @ L ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % power_numeral
% 5.52/5.85 thf(fact_6428_power__numeral,axiom,
% 5.52/5.85 ! [K: num,L: num] :
% 5.52/5.85 ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.52/5.85 = ( numeral_numeral_int @ ( pow @ K @ L ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % power_numeral
% 5.52/5.85 thf(fact_6429_and_Oidem,axiom,
% 5.52/5.85 ! [A: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ A @ A )
% 5.52/5.85 = A ) ).
% 5.52/5.85
% 5.52/5.85 % and.idem
% 5.52/5.85 thf(fact_6430_and_Oidem,axiom,
% 5.52/5.85 ! [A: nat] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ A @ A )
% 5.52/5.85 = A ) ).
% 5.52/5.85
% 5.52/5.85 % and.idem
% 5.52/5.85 thf(fact_6431_and_Oleft__idem,axiom,
% 5.52/5.85 ! [A: int,B: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.52/5.85 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.52/5.85
% 5.52/5.85 % and.left_idem
% 5.52/5.85 thf(fact_6432_and_Oleft__idem,axiom,
% 5.52/5.85 ! [A: nat,B: nat] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.52/5.85 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.52/5.85
% 5.52/5.85 % and.left_idem
% 5.52/5.85 thf(fact_6433_and_Oright__idem,axiom,
% 5.52/5.85 ! [A: int,B: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 5.52/5.85 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.52/5.85
% 5.52/5.85 % and.right_idem
% 5.52/5.85 thf(fact_6434_and_Oright__idem,axiom,
% 5.52/5.85 ! [A: nat,B: nat] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 5.52/5.85 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.52/5.85
% 5.52/5.85 % and.right_idem
% 5.52/5.85 thf(fact_6435_and__zero__eq,axiom,
% 5.52/5.85 ! [A: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.52/5.85 = zero_zero_int ) ).
% 5.52/5.85
% 5.52/5.85 % and_zero_eq
% 5.52/5.85 thf(fact_6436_and__zero__eq,axiom,
% 5.52/5.85 ! [A: nat] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.52/5.85 = zero_zero_nat ) ).
% 5.52/5.85
% 5.52/5.85 % and_zero_eq
% 5.52/5.85 thf(fact_6437_zero__and__eq,axiom,
% 5.52/5.85 ! [A: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.52/5.85 = zero_zero_int ) ).
% 5.52/5.85
% 5.52/5.85 % zero_and_eq
% 5.52/5.85 thf(fact_6438_zero__and__eq,axiom,
% 5.52/5.85 ! [A: nat] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.52/5.85 = zero_zero_nat ) ).
% 5.52/5.85
% 5.52/5.85 % zero_and_eq
% 5.52/5.85 thf(fact_6439_bit_Oconj__zero__left,axiom,
% 5.52/5.85 ! [X2: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X2 )
% 5.52/5.85 = zero_zero_int ) ).
% 5.52/5.85
% 5.52/5.85 % bit.conj_zero_left
% 5.52/5.85 thf(fact_6440_bit_Oconj__zero__right,axiom,
% 5.52/5.85 ! [X2: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ X2 @ zero_zero_int )
% 5.52/5.85 = zero_zero_int ) ).
% 5.52/5.85
% 5.52/5.85 % bit.conj_zero_right
% 5.52/5.85 thf(fact_6441_exp__less__mono,axiom,
% 5.52/5.85 ! [X2: real,Y2: real] :
% 5.52/5.85 ( ( ord_less_real @ X2 @ Y2 )
% 5.52/5.85 => ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_less_mono
% 5.52/5.85 thf(fact_6442_exp__less__cancel__iff,axiom,
% 5.52/5.85 ! [X2: real,Y2: real] :
% 5.52/5.85 ( ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) )
% 5.52/5.85 = ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_less_cancel_iff
% 5.52/5.85 thf(fact_6443_take__bit__and,axiom,
% 5.52/5.85 ! [N: nat,A: int,B: int] :
% 5.52/5.85 ( ( bit_se2923211474154528505it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.52/5.85 = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_and
% 5.52/5.85 thf(fact_6444_take__bit__and,axiom,
% 5.52/5.85 ! [N: nat,A: nat,B: nat] :
% 5.52/5.85 ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.52/5.85 = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_and
% 5.52/5.85 thf(fact_6445_exp__zero,axiom,
% 5.52/5.85 ( ( exp_complex @ zero_zero_complex )
% 5.52/5.85 = one_one_complex ) ).
% 5.52/5.85
% 5.52/5.85 % exp_zero
% 5.52/5.85 thf(fact_6446_exp__zero,axiom,
% 5.52/5.85 ( ( exp_real @ zero_zero_real )
% 5.52/5.85 = one_one_real ) ).
% 5.52/5.85
% 5.52/5.85 % exp_zero
% 5.52/5.85 thf(fact_6447_bit_Oconj__one__right,axiom,
% 5.52/5.85 ! [X2: code_integer] :
% 5.52/5.85 ( ( bit_se3949692690581998587nteger @ X2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.85 = X2 ) ).
% 5.52/5.85
% 5.52/5.85 % bit.conj_one_right
% 5.52/5.85 thf(fact_6448_bit_Oconj__one__right,axiom,
% 5.52/5.85 ! [X2: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ X2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.85 = X2 ) ).
% 5.52/5.85
% 5.52/5.85 % bit.conj_one_right
% 5.52/5.85 thf(fact_6449_and_Oright__neutral,axiom,
% 5.52/5.85 ! [A: code_integer] :
% 5.52/5.85 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.85 = A ) ).
% 5.52/5.85
% 5.52/5.85 % and.right_neutral
% 5.52/5.85 thf(fact_6450_and_Oright__neutral,axiom,
% 5.52/5.85 ! [A: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.85 = A ) ).
% 5.52/5.85
% 5.52/5.85 % and.right_neutral
% 5.52/5.85 thf(fact_6451_and_Oleft__neutral,axiom,
% 5.52/5.85 ! [A: code_integer] :
% 5.52/5.85 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.52/5.85 = A ) ).
% 5.52/5.85
% 5.52/5.85 % and.left_neutral
% 5.52/5.85 thf(fact_6452_and_Oleft__neutral,axiom,
% 5.52/5.85 ! [A: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.52/5.85 = A ) ).
% 5.52/5.85
% 5.52/5.85 % and.left_neutral
% 5.52/5.85 thf(fact_6453_and__nonnegative__int__iff,axiom,
% 5.52/5.85 ! [K: int,L: int] :
% 5.52/5.85 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.52/5.85 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.85 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_nonnegative_int_iff
% 5.52/5.85 thf(fact_6454_and__negative__int__iff,axiom,
% 5.52/5.85 ! [K: int,L: int] :
% 5.52/5.85 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 5.52/5.85 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.52/5.85 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_negative_int_iff
% 5.52/5.85 thf(fact_6455_pred__numeral__inc,axiom,
% 5.52/5.85 ! [K: num] :
% 5.52/5.85 ( ( pred_numeral @ ( inc @ K ) )
% 5.52/5.85 = ( numeral_numeral_nat @ K ) ) ).
% 5.52/5.85
% 5.52/5.85 % pred_numeral_inc
% 5.52/5.85 thf(fact_6456_and__numerals_I8_J,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ one_one_int )
% 5.52/5.85 = one_one_int ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(8)
% 5.52/5.85 thf(fact_6457_and__numerals_I8_J,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ one_one_nat )
% 5.52/5.85 = one_one_nat ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(8)
% 5.52/5.85 thf(fact_6458_and__numerals_I2_J,axiom,
% 5.52/5.85 ! [Y2: num] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 5.52/5.85 = one_one_int ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(2)
% 5.52/5.85 thf(fact_6459_and__numerals_I2_J,axiom,
% 5.52/5.85 ! [Y2: num] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.52/5.85 = one_one_nat ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(2)
% 5.52/5.85 thf(fact_6460_exp__less__one__iff,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ( ( ord_less_real @ ( exp_real @ X2 ) @ one_one_real )
% 5.52/5.85 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_less_one_iff
% 5.52/5.85 thf(fact_6461_one__less__exp__iff,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ( ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) )
% 5.52/5.85 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % one_less_exp_iff
% 5.52/5.85 thf(fact_6462_exp__ln,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( exp_real @ ( ln_ln_real @ X2 ) )
% 5.52/5.85 = X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_ln
% 5.52/5.85 thf(fact_6463_exp__ln__iff,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ( ( ( exp_real @ ( ln_ln_real @ X2 ) )
% 5.52/5.85 = X2 )
% 5.52/5.85 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_ln_iff
% 5.52/5.85 thf(fact_6464_and__numerals_I5_J,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ one_one_int )
% 5.52/5.85 = zero_zero_int ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(5)
% 5.52/5.85 thf(fact_6465_and__numerals_I5_J,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ one_one_nat )
% 5.52/5.85 = zero_zero_nat ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(5)
% 5.52/5.85 thf(fact_6466_and__numerals_I1_J,axiom,
% 5.52/5.85 ! [Y2: num] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 5.52/5.85 = zero_zero_int ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(1)
% 5.52/5.85 thf(fact_6467_and__numerals_I1_J,axiom,
% 5.52/5.85 ! [Y2: num] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.52/5.85 = zero_zero_nat ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(1)
% 5.52/5.85 thf(fact_6468_and__numerals_I3_J,axiom,
% 5.52/5.85 ! [X2: num,Y2: num] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 5.52/5.85 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(3)
% 5.52/5.85 thf(fact_6469_and__numerals_I3_J,axiom,
% 5.52/5.85 ! [X2: num,Y2: num] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.52/5.85 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(3)
% 5.52/5.85 thf(fact_6470_sum_Ocl__ivl__Suc,axiom,
% 5.52/5.85 ! [N: nat,M: nat,G: nat > complex] :
% 5.52/5.85 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.85 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = zero_zero_complex ) )
% 5.52/5.85 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.85 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.cl_ivl_Suc
% 5.52/5.85 thf(fact_6471_sum_Ocl__ivl__Suc,axiom,
% 5.52/5.85 ! [N: nat,M: nat,G: nat > rat] :
% 5.52/5.85 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = zero_zero_rat ) )
% 5.52/5.85 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.cl_ivl_Suc
% 5.52/5.85 thf(fact_6472_sum_Ocl__ivl__Suc,axiom,
% 5.52/5.85 ! [N: nat,M: nat,G: nat > int] :
% 5.52/5.85 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.85 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = zero_zero_int ) )
% 5.52/5.85 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.85 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.cl_ivl_Suc
% 5.52/5.85 thf(fact_6473_sum_Ocl__ivl__Suc,axiom,
% 5.52/5.85 ! [N: nat,M: nat,G: nat > nat] :
% 5.52/5.85 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.85 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = zero_zero_nat ) )
% 5.52/5.85 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.85 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.cl_ivl_Suc
% 5.52/5.85 thf(fact_6474_sum_Ocl__ivl__Suc,axiom,
% 5.52/5.85 ! [N: nat,M: nat,G: nat > real] :
% 5.52/5.85 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.85 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = zero_zero_real ) )
% 5.52/5.85 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.85 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.cl_ivl_Suc
% 5.52/5.85 thf(fact_6475_add__neg__numeral__special_I6_J,axiom,
% 5.52/5.85 ! [M: num] :
% 5.52/5.85 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.85 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_neg_numeral_special(6)
% 5.52/5.85 thf(fact_6476_add__neg__numeral__special_I6_J,axiom,
% 5.52/5.85 ! [M: num] :
% 5.52/5.85 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.85 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_neg_numeral_special(6)
% 5.52/5.85 thf(fact_6477_add__neg__numeral__special_I6_J,axiom,
% 5.52/5.85 ! [M: num] :
% 5.52/5.85 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.85 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_neg_numeral_special(6)
% 5.52/5.85 thf(fact_6478_add__neg__numeral__special_I6_J,axiom,
% 5.52/5.85 ! [M: num] :
% 5.52/5.85 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.85 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_neg_numeral_special(6)
% 5.52/5.85 thf(fact_6479_add__neg__numeral__special_I6_J,axiom,
% 5.52/5.85 ! [M: num] :
% 5.52/5.85 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.85 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_neg_numeral_special(6)
% 5.52/5.85 thf(fact_6480_add__neg__numeral__special_I5_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.85 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_neg_numeral_special(5)
% 5.52/5.85 thf(fact_6481_add__neg__numeral__special_I5_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.85 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_neg_numeral_special(5)
% 5.52/5.85 thf(fact_6482_add__neg__numeral__special_I5_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.52/5.85 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_neg_numeral_special(5)
% 5.52/5.85 thf(fact_6483_add__neg__numeral__special_I5_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.52/5.85 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_neg_numeral_special(5)
% 5.52/5.85 thf(fact_6484_add__neg__numeral__special_I5_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.52/5.85 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_neg_numeral_special(5)
% 5.52/5.85 thf(fact_6485_diff__numeral__special_I6_J,axiom,
% 5.52/5.85 ! [M: num] :
% 5.52/5.85 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.85 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % diff_numeral_special(6)
% 5.52/5.85 thf(fact_6486_diff__numeral__special_I6_J,axiom,
% 5.52/5.85 ! [M: num] :
% 5.52/5.85 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.85 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % diff_numeral_special(6)
% 5.52/5.85 thf(fact_6487_diff__numeral__special_I6_J,axiom,
% 5.52/5.85 ! [M: num] :
% 5.52/5.85 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.52/5.85 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % diff_numeral_special(6)
% 5.52/5.85 thf(fact_6488_diff__numeral__special_I6_J,axiom,
% 5.52/5.85 ! [M: num] :
% 5.52/5.85 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.85 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % diff_numeral_special(6)
% 5.52/5.85 thf(fact_6489_diff__numeral__special_I6_J,axiom,
% 5.52/5.85 ! [M: num] :
% 5.52/5.85 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.52/5.85 = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % diff_numeral_special(6)
% 5.52/5.85 thf(fact_6490_diff__numeral__special_I5_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.85 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % diff_numeral_special(5)
% 5.52/5.85 thf(fact_6491_diff__numeral__special_I5_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 5.52/5.85 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % diff_numeral_special(5)
% 5.52/5.85 thf(fact_6492_diff__numeral__special_I5_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 5.52/5.85 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % diff_numeral_special(5)
% 5.52/5.85 thf(fact_6493_diff__numeral__special_I5_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 5.52/5.85 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % diff_numeral_special(5)
% 5.52/5.85 thf(fact_6494_diff__numeral__special_I5_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 5.52/5.85 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % diff_numeral_special(5)
% 5.52/5.85 thf(fact_6495_and__minus__numerals_I6_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.52/5.85 = one_one_int ) ).
% 5.52/5.85
% 5.52/5.85 % and_minus_numerals(6)
% 5.52/5.85 thf(fact_6496_and__minus__numerals_I2_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.52/5.85 = one_one_int ) ).
% 5.52/5.85
% 5.52/5.85 % and_minus_numerals(2)
% 5.52/5.85 thf(fact_6497_sum__zero__power,axiom,
% 5.52/5.85 ! [A2: set_nat,C: nat > complex] :
% 5.52/5.85 ( ( ( ( finite_finite_nat @ A2 )
% 5.52/5.85 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.52/5.85 => ( ( groups2073611262835488442omplex
% 5.52/5.85 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = ( C @ zero_zero_nat ) ) )
% 5.52/5.85 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.52/5.85 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.52/5.85 => ( ( groups2073611262835488442omplex
% 5.52/5.85 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = zero_zero_complex ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_zero_power
% 5.52/5.85 thf(fact_6498_sum__zero__power,axiom,
% 5.52/5.85 ! [A2: set_nat,C: nat > rat] :
% 5.52/5.85 ( ( ( ( finite_finite_nat @ A2 )
% 5.52/5.85 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat
% 5.52/5.85 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = ( C @ zero_zero_nat ) ) )
% 5.52/5.85 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.52/5.85 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat
% 5.52/5.85 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = zero_zero_rat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_zero_power
% 5.52/5.85 thf(fact_6499_sum__zero__power,axiom,
% 5.52/5.85 ! [A2: set_nat,C: nat > real] :
% 5.52/5.85 ( ( ( ( finite_finite_nat @ A2 )
% 5.52/5.85 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.52/5.85 => ( ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = ( C @ zero_zero_nat ) ) )
% 5.52/5.85 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.52/5.85 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.52/5.85 => ( ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = zero_zero_real ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_zero_power
% 5.52/5.85 thf(fact_6500_and__numerals_I6_J,axiom,
% 5.52/5.85 ! [X2: num,Y2: num] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 5.52/5.85 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(6)
% 5.52/5.85 thf(fact_6501_and__numerals_I6_J,axiom,
% 5.52/5.85 ! [X2: num,Y2: num] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.52/5.85 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(6)
% 5.52/5.85 thf(fact_6502_and__numerals_I4_J,axiom,
% 5.52/5.85 ! [X2: num,Y2: num] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 5.52/5.85 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(4)
% 5.52/5.85 thf(fact_6503_and__numerals_I4_J,axiom,
% 5.52/5.85 ! [X2: num,Y2: num] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.52/5.85 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(4)
% 5.52/5.85 thf(fact_6504_and__minus__numerals_I5_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.52/5.85 = zero_zero_int ) ).
% 5.52/5.85
% 5.52/5.85 % and_minus_numerals(5)
% 5.52/5.85 thf(fact_6505_and__minus__numerals_I1_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.52/5.85 = zero_zero_int ) ).
% 5.52/5.85
% 5.52/5.85 % and_minus_numerals(1)
% 5.52/5.85 thf(fact_6506_sum__zero__power_H,axiom,
% 5.52/5.85 ! [A2: set_nat,C: nat > complex,D2: nat > complex] :
% 5.52/5.85 ( ( ( ( finite_finite_nat @ A2 )
% 5.52/5.85 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.52/5.85 => ( ( groups2073611262835488442omplex
% 5.52/5.85 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D2 @ I4 ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 5.52/5.85 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.52/5.85 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.52/5.85 => ( ( groups2073611262835488442omplex
% 5.52/5.85 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D2 @ I4 ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = zero_zero_complex ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_zero_power'
% 5.52/5.85 thf(fact_6507_sum__zero__power_H,axiom,
% 5.52/5.85 ! [A2: set_nat,C: nat > rat,D2: nat > rat] :
% 5.52/5.85 ( ( ( ( finite_finite_nat @ A2 )
% 5.52/5.85 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat
% 5.52/5.85 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D2 @ I4 ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 5.52/5.85 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.52/5.85 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat
% 5.52/5.85 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D2 @ I4 ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = zero_zero_rat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_zero_power'
% 5.52/5.85 thf(fact_6508_sum__zero__power_H,axiom,
% 5.52/5.85 ! [A2: set_nat,C: nat > real,D2: nat > real] :
% 5.52/5.85 ( ( ( ( finite_finite_nat @ A2 )
% 5.52/5.85 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.52/5.85 => ( ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D2 @ I4 ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 5.52/5.85 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.52/5.85 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.52/5.85 => ( ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D2 @ I4 ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = zero_zero_real ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_zero_power'
% 5.52/5.85 thf(fact_6509_and__numerals_I7_J,axiom,
% 5.52/5.85 ! [X2: num,Y2: num] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 5.52/5.85 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(7)
% 5.52/5.85 thf(fact_6510_and__numerals_I7_J,axiom,
% 5.52/5.85 ! [X2: num,Y2: num] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.52/5.85 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_numerals(7)
% 5.52/5.85 thf(fact_6511_of__int__and__eq,axiom,
% 5.52/5.85 ! [K: int,L: int] :
% 5.52/5.85 ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.52/5.85 = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_int_and_eq
% 5.52/5.85 thf(fact_6512_and_Oassoc,axiom,
% 5.52/5.85 ! [A: int,B: int,C: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 5.52/5.85 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and.assoc
% 5.52/5.85 thf(fact_6513_and_Oassoc,axiom,
% 5.52/5.85 ! [A: nat,B: nat,C: nat] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 5.52/5.85 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and.assoc
% 5.52/5.85 thf(fact_6514_and_Ocommute,axiom,
% 5.52/5.85 ( bit_se725231765392027082nd_int
% 5.52/5.85 = ( ^ [A4: int,B3: int] : ( bit_se725231765392027082nd_int @ B3 @ A4 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and.commute
% 5.52/5.85 thf(fact_6515_and_Ocommute,axiom,
% 5.52/5.85 ( bit_se727722235901077358nd_nat
% 5.52/5.85 = ( ^ [A4: nat,B3: nat] : ( bit_se727722235901077358nd_nat @ B3 @ A4 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and.commute
% 5.52/5.85 thf(fact_6516_and_Oleft__commute,axiom,
% 5.52/5.85 ! [B: int,A: int,C: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 5.52/5.85 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and.left_commute
% 5.52/5.85 thf(fact_6517_and_Oleft__commute,axiom,
% 5.52/5.85 ! [B: nat,A: nat,C: nat] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 5.52/5.85 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and.left_commute
% 5.52/5.85 thf(fact_6518_exp__less__cancel,axiom,
% 5.52/5.85 ! [X2: real,Y2: real] :
% 5.52/5.85 ( ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) )
% 5.52/5.85 => ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_less_cancel
% 5.52/5.85 thf(fact_6519_exp__times__arg__commute,axiom,
% 5.52/5.85 ! [A2: complex] :
% 5.52/5.85 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 5.52/5.85 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_times_arg_commute
% 5.52/5.85 thf(fact_6520_exp__times__arg__commute,axiom,
% 5.52/5.85 ! [A2: real] :
% 5.52/5.85 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 5.52/5.85 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_times_arg_commute
% 5.52/5.85 thf(fact_6521_num__induct,axiom,
% 5.52/5.85 ! [P: num > $o,X2: num] :
% 5.52/5.85 ( ( P @ one )
% 5.52/5.85 => ( ! [X4: num] :
% 5.52/5.85 ( ( P @ X4 )
% 5.52/5.85 => ( P @ ( inc @ X4 ) ) )
% 5.52/5.85 => ( P @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % num_induct
% 5.52/5.85 thf(fact_6522_add__inc,axiom,
% 5.52/5.85 ! [X2: num,Y2: num] :
% 5.52/5.85 ( ( plus_plus_num @ X2 @ ( inc @ Y2 ) )
% 5.52/5.85 = ( inc @ ( plus_plus_num @ X2 @ Y2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_inc
% 5.52/5.85 thf(fact_6523_and__eq__minus__1__iff,axiom,
% 5.52/5.85 ! [A: code_integer,B: code_integer] :
% 5.52/5.85 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 5.52/5.85 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.85 = ( ( A
% 5.52/5.85 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.52/5.85 & ( B
% 5.52/5.85 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_eq_minus_1_iff
% 5.52/5.85 thf(fact_6524_and__eq__minus__1__iff,axiom,
% 5.52/5.85 ! [A: int,B: int] :
% 5.52/5.85 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 5.52/5.85 = ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.85 = ( ( A
% 5.52/5.85 = ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.85 & ( B
% 5.52/5.85 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_eq_minus_1_iff
% 5.52/5.85 thf(fact_6525_not__exp__less__zero,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ~ ( ord_less_real @ ( exp_real @ X2 ) @ zero_zero_real ) ).
% 5.52/5.85
% 5.52/5.85 % not_exp_less_zero
% 5.52/5.85 thf(fact_6526_exp__gt__zero,axiom,
% 5.52/5.85 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_gt_zero
% 5.52/5.85 thf(fact_6527_exp__total,axiom,
% 5.52/5.85 ! [Y2: real] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.85 => ? [X4: real] :
% 5.52/5.85 ( ( exp_real @ X4 )
% 5.52/5.85 = Y2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_total
% 5.52/5.85 thf(fact_6528_AND__lower,axiom,
% 5.52/5.85 ! [X2: int,Y2: int] :
% 5.52/5.85 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.85 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X2 @ Y2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % AND_lower
% 5.52/5.85 thf(fact_6529_AND__upper1,axiom,
% 5.52/5.85 ! [X2: int,Y2: int] :
% 5.52/5.85 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.85 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y2 ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % AND_upper1
% 5.52/5.85 thf(fact_6530_AND__upper2,axiom,
% 5.52/5.85 ! [Y2: int,X2: int] :
% 5.52/5.85 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.85 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y2 ) @ Y2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % AND_upper2
% 5.52/5.85 thf(fact_6531_AND__upper1_H,axiom,
% 5.52/5.85 ! [Y2: int,Z: int,Ya: int] :
% 5.52/5.85 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.85 => ( ( ord_less_eq_int @ Y2 @ Z )
% 5.52/5.85 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y2 @ Ya ) @ Z ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % AND_upper1'
% 5.52/5.85 thf(fact_6532_AND__upper2_H,axiom,
% 5.52/5.85 ! [Y2: int,Z: int,X2: int] :
% 5.52/5.85 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.85 => ( ( ord_less_eq_int @ Y2 @ Z )
% 5.52/5.85 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % AND_upper2'
% 5.52/5.85 thf(fact_6533_mult__exp__exp,axiom,
% 5.52/5.85 ! [X2: complex,Y2: complex] :
% 5.52/5.85 ( ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y2 ) )
% 5.52/5.85 = ( exp_complex @ ( plus_plus_complex @ X2 @ Y2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mult_exp_exp
% 5.52/5.85 thf(fact_6534_mult__exp__exp,axiom,
% 5.52/5.85 ! [X2: real,Y2: real] :
% 5.52/5.85 ( ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) )
% 5.52/5.85 = ( exp_real @ ( plus_plus_real @ X2 @ Y2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mult_exp_exp
% 5.52/5.85 thf(fact_6535_exp__add__commuting,axiom,
% 5.52/5.85 ! [X2: complex,Y2: complex] :
% 5.52/5.85 ( ( ( times_times_complex @ X2 @ Y2 )
% 5.52/5.85 = ( times_times_complex @ Y2 @ X2 ) )
% 5.52/5.85 => ( ( exp_complex @ ( plus_plus_complex @ X2 @ Y2 ) )
% 5.52/5.85 = ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_add_commuting
% 5.52/5.85 thf(fact_6536_exp__add__commuting,axiom,
% 5.52/5.85 ! [X2: real,Y2: real] :
% 5.52/5.85 ( ( ( times_times_real @ X2 @ Y2 )
% 5.52/5.85 = ( times_times_real @ Y2 @ X2 ) )
% 5.52/5.85 => ( ( exp_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.52/5.85 = ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_add_commuting
% 5.52/5.85 thf(fact_6537_exp__diff,axiom,
% 5.52/5.85 ! [X2: complex,Y2: complex] :
% 5.52/5.85 ( ( exp_complex @ ( minus_minus_complex @ X2 @ Y2 ) )
% 5.52/5.85 = ( divide1717551699836669952omplex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_diff
% 5.52/5.85 thf(fact_6538_exp__diff,axiom,
% 5.52/5.85 ! [X2: real,Y2: real] :
% 5.52/5.85 ( ( exp_real @ ( minus_minus_real @ X2 @ Y2 ) )
% 5.52/5.85 = ( divide_divide_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_diff
% 5.52/5.85 thf(fact_6539_take__bit__eq__mask,axiom,
% 5.52/5.85 ( bit_se2923211474154528505it_int
% 5.52/5.85 = ( ^ [N3: nat,A4: int] : ( bit_se725231765392027082nd_int @ A4 @ ( bit_se2000444600071755411sk_int @ N3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_eq_mask
% 5.52/5.85 thf(fact_6540_take__bit__eq__mask,axiom,
% 5.52/5.85 ( bit_se2925701944663578781it_nat
% 5.52/5.85 = ( ^ [N3: nat,A4: nat] : ( bit_se727722235901077358nd_nat @ A4 @ ( bit_se2002935070580805687sk_nat @ N3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_eq_mask
% 5.52/5.85 thf(fact_6541_sum__subtractf__nat,axiom,
% 5.52/5.85 ! [A2: set_option_nat,G: option_nat > nat,F: option_nat > nat] :
% 5.52/5.85 ( ! [X4: option_nat] :
% 5.52/5.85 ( ( member_option_nat @ X4 @ A2 )
% 5.52/5.85 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( groups1921984841883549356at_nat
% 5.52/5.85 @ ^ [X: option_nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = ( minus_minus_nat @ ( groups1921984841883549356at_nat @ F @ A2 ) @ ( groups1921984841883549356at_nat @ G @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_subtractf_nat
% 5.52/5.85 thf(fact_6542_sum__subtractf__nat,axiom,
% 5.52/5.85 ! [A2: set_real,G: real > nat,F: real > nat] :
% 5.52/5.85 ( ! [X4: real] :
% 5.52/5.85 ( ( member_real @ X4 @ A2 )
% 5.52/5.85 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( groups1935376822645274424al_nat
% 5.52/5.85 @ ^ [X: real] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_subtractf_nat
% 5.52/5.85 thf(fact_6543_sum__subtractf__nat,axiom,
% 5.52/5.85 ! [A2: set_set_nat_rat,G: set_nat_rat > nat,F: set_nat_rat > nat] :
% 5.52/5.85 ( ! [X4: set_nat_rat] :
% 5.52/5.85 ( ( member_set_nat_rat @ X4 @ A2 )
% 5.52/5.85 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( groups207172935752626313at_nat
% 5.52/5.85 @ ^ [X: set_nat_rat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = ( minus_minus_nat @ ( groups207172935752626313at_nat @ F @ A2 ) @ ( groups207172935752626313at_nat @ G @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_subtractf_nat
% 5.52/5.85 thf(fact_6544_sum__subtractf__nat,axiom,
% 5.52/5.85 ! [A2: set_int,G: int > nat,F: int > nat] :
% 5.52/5.85 ( ! [X4: int] :
% 5.52/5.85 ( ( member_int @ X4 @ A2 )
% 5.52/5.85 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( groups4541462559716669496nt_nat
% 5.52/5.85 @ ^ [X: int] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_subtractf_nat
% 5.52/5.85 thf(fact_6545_sum__subtractf__nat,axiom,
% 5.52/5.85 ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 5.52/5.85 ( ! [X4: nat] :
% 5.52/5.85 ( ( member_nat @ X4 @ A2 )
% 5.52/5.85 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( groups3542108847815614940at_nat
% 5.52/5.85 @ ^ [X: nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.52/5.85 @ A2 )
% 5.52/5.85 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_subtractf_nat
% 5.52/5.85 thf(fact_6546_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.52/5.85 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.52/5.85 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.52/5.85 = ( groups3542108847815614940at_nat
% 5.52/5.85 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.shift_bounds_cl_nat_ivl
% 5.52/5.85 thf(fact_6547_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.52/5.85 ! [G: nat > real,M: nat,K: nat,N: nat] :
% 5.52/5.85 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.52/5.85 = ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.shift_bounds_cl_nat_ivl
% 5.52/5.85 thf(fact_6548_pow_Osimps_I1_J,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( pow @ X2 @ one )
% 5.52/5.85 = X2 ) ).
% 5.52/5.85
% 5.52/5.85 % pow.simps(1)
% 5.52/5.85 thf(fact_6549_inc_Osimps_I1_J,axiom,
% 5.52/5.85 ( ( inc @ one )
% 5.52/5.85 = ( bit0 @ one ) ) ).
% 5.52/5.85
% 5.52/5.85 % inc.simps(1)
% 5.52/5.85 thf(fact_6550_inc_Osimps_I3_J,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( inc @ ( bit1 @ X2 ) )
% 5.52/5.85 = ( bit0 @ ( inc @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % inc.simps(3)
% 5.52/5.85 thf(fact_6551_inc_Osimps_I2_J,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( inc @ ( bit0 @ X2 ) )
% 5.52/5.85 = ( bit1 @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % inc.simps(2)
% 5.52/5.85 thf(fact_6552_sum__SucD,axiom,
% 5.52/5.85 ! [F: nat > nat,A2: set_nat,N: nat] :
% 5.52/5.85 ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.52/5.85 = ( suc @ N ) )
% 5.52/5.85 => ? [X4: nat] :
% 5.52/5.85 ( ( member_nat @ X4 @ A2 )
% 5.52/5.85 & ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_SucD
% 5.52/5.85 thf(fact_6553_sum__eq__1__iff,axiom,
% 5.52/5.85 ! [A2: set_int,F: int > nat] :
% 5.52/5.85 ( ( finite_finite_int @ A2 )
% 5.52/5.85 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.52/5.85 = one_one_nat )
% 5.52/5.85 = ( ? [X: int] :
% 5.52/5.85 ( ( member_int @ X @ A2 )
% 5.52/5.85 & ( ( F @ X )
% 5.52/5.85 = one_one_nat )
% 5.52/5.85 & ! [Y: int] :
% 5.52/5.85 ( ( member_int @ Y @ A2 )
% 5.52/5.85 => ( ( X != Y )
% 5.52/5.85 => ( ( F @ Y )
% 5.52/5.85 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_eq_1_iff
% 5.52/5.85 thf(fact_6554_sum__eq__1__iff,axiom,
% 5.52/5.85 ! [A2: set_complex,F: complex > nat] :
% 5.52/5.85 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.85 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.52/5.85 = one_one_nat )
% 5.52/5.85 = ( ? [X: complex] :
% 5.52/5.85 ( ( member_complex @ X @ A2 )
% 5.52/5.85 & ( ( F @ X )
% 5.52/5.85 = one_one_nat )
% 5.52/5.85 & ! [Y: complex] :
% 5.52/5.85 ( ( member_complex @ Y @ A2 )
% 5.52/5.85 => ( ( X != Y )
% 5.52/5.85 => ( ( F @ Y )
% 5.52/5.85 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_eq_1_iff
% 5.52/5.85 thf(fact_6555_sum__eq__1__iff,axiom,
% 5.52/5.85 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 5.52/5.85 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.85 => ( ( ( groups2027974829824023292at_nat @ F @ A2 )
% 5.52/5.85 = one_one_nat )
% 5.52/5.85 = ( ? [X: extended_enat] :
% 5.52/5.85 ( ( member_Extended_enat @ X @ A2 )
% 5.52/5.85 & ( ( F @ X )
% 5.52/5.85 = one_one_nat )
% 5.52/5.85 & ! [Y: extended_enat] :
% 5.52/5.85 ( ( member_Extended_enat @ Y @ A2 )
% 5.52/5.85 => ( ( X != Y )
% 5.52/5.85 => ( ( F @ Y )
% 5.52/5.85 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_eq_1_iff
% 5.52/5.85 thf(fact_6556_sum__eq__1__iff,axiom,
% 5.52/5.85 ! [A2: set_nat,F: nat > nat] :
% 5.52/5.85 ( ( finite_finite_nat @ A2 )
% 5.52/5.85 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.52/5.85 = one_one_nat )
% 5.52/5.85 = ( ? [X: nat] :
% 5.52/5.85 ( ( member_nat @ X @ A2 )
% 5.52/5.85 & ( ( F @ X )
% 5.52/5.85 = one_one_nat )
% 5.52/5.85 & ! [Y: nat] :
% 5.52/5.85 ( ( member_nat @ Y @ A2 )
% 5.52/5.85 => ( ( X != Y )
% 5.52/5.85 => ( ( F @ Y )
% 5.52/5.85 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_eq_1_iff
% 5.52/5.85 thf(fact_6557_exp__gt__one,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_gt_one
% 5.52/5.85 thf(fact_6558_add__One,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( plus_plus_num @ X2 @ one )
% 5.52/5.85 = ( inc @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % add_One
% 5.52/5.85 thf(fact_6559_AND__upper2_H_H,axiom,
% 5.52/5.85 ! [Y2: int,Z: int,X2: int] :
% 5.52/5.85 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.85 => ( ( ord_less_int @ Y2 @ Z )
% 5.52/5.85 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % AND_upper2''
% 5.52/5.85 thf(fact_6560_AND__upper1_H_H,axiom,
% 5.52/5.85 ! [Y2: int,Z: int,Ya: int] :
% 5.52/5.85 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.85 => ( ( ord_less_int @ Y2 @ Z )
% 5.52/5.85 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y2 @ Ya ) @ Z ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % AND_upper1''
% 5.52/5.85 thf(fact_6561_and__less__eq,axiom,
% 5.52/5.85 ! [L: int,K: int] :
% 5.52/5.85 ( ( ord_less_int @ L @ zero_zero_int )
% 5.52/5.85 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_less_eq
% 5.52/5.85 thf(fact_6562_inc__BitM__eq,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( inc @ ( bitM @ N ) )
% 5.52/5.85 = ( bit0 @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % inc_BitM_eq
% 5.52/5.85 thf(fact_6563_exp__minus__inverse,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ( ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) )
% 5.52/5.85 = one_one_real ) ).
% 5.52/5.85
% 5.52/5.85 % exp_minus_inverse
% 5.52/5.85 thf(fact_6564_exp__minus__inverse,axiom,
% 5.52/5.85 ! [X2: complex] :
% 5.52/5.85 ( ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) )
% 5.52/5.85 = one_one_complex ) ).
% 5.52/5.85
% 5.52/5.85 % exp_minus_inverse
% 5.52/5.85 thf(fact_6565_BitM__inc__eq,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( bitM @ ( inc @ N ) )
% 5.52/5.85 = ( bit1 @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % BitM_inc_eq
% 5.52/5.85 thf(fact_6566_mult__inc,axiom,
% 5.52/5.85 ! [X2: num,Y2: num] :
% 5.52/5.85 ( ( times_times_num @ X2 @ ( inc @ Y2 ) )
% 5.52/5.85 = ( plus_plus_num @ ( times_times_num @ X2 @ Y2 ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % mult_inc
% 5.52/5.85 thf(fact_6567_sum__power__add,axiom,
% 5.52/5.85 ! [X2: complex,M: nat,I5: set_nat] :
% 5.52/5.85 ( ( groups2073611262835488442omplex
% 5.52/5.85 @ ^ [I4: nat] : ( power_power_complex @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 = ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ I5 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_power_add
% 5.52/5.85 thf(fact_6568_sum__power__add,axiom,
% 5.52/5.85 ! [X2: rat,M: nat,I5: set_nat] :
% 5.52/5.85 ( ( groups2906978787729119204at_rat
% 5.52/5.85 @ ^ [I4: nat] : ( power_power_rat @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 = ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ I5 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_power_add
% 5.52/5.85 thf(fact_6569_sum__power__add,axiom,
% 5.52/5.85 ! [X2: int,M: nat,I5: set_nat] :
% 5.52/5.85 ( ( groups3539618377306564664at_int
% 5.52/5.85 @ ^ [I4: nat] : ( power_power_int @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 = ( times_times_int @ ( power_power_int @ X2 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ I5 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_power_add
% 5.52/5.85 thf(fact_6570_sum__power__add,axiom,
% 5.52/5.85 ! [X2: real,M: nat,I5: set_nat] :
% 5.52/5.85 ( ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [I4: nat] : ( power_power_real @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.52/5.85 @ I5 )
% 5.52/5.85 = ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ I5 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_power_add
% 5.52/5.85 thf(fact_6571_sum_OatLeastAtMost__rev,axiom,
% 5.52/5.85 ! [G: nat > nat,N: nat,M: nat] :
% 5.52/5.85 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.52/5.85 = ( groups3542108847815614940at_nat
% 5.52/5.85 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.atLeastAtMost_rev
% 5.52/5.85 thf(fact_6572_sum_OatLeastAtMost__rev,axiom,
% 5.52/5.85 ! [G: nat > real,N: nat,M: nat] :
% 5.52/5.85 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.52/5.85 = ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.atLeastAtMost_rev
% 5.52/5.85 thf(fact_6573_sum__roots__unity,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( ord_less_nat @ one_one_nat @ N )
% 5.52/5.85 => ( ( groups7754918857620584856omplex
% 5.52/5.85 @ ^ [X: complex] : X
% 5.52/5.85 @ ( collect_complex
% 5.52/5.85 @ ^ [Z2: complex] :
% 5.52/5.85 ( ( power_power_complex @ Z2 @ N )
% 5.52/5.85 = one_one_complex ) ) )
% 5.52/5.85 = zero_zero_complex ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_roots_unity
% 5.52/5.85 thf(fact_6574_sum__nth__roots,axiom,
% 5.52/5.85 ! [N: nat,C: complex] :
% 5.52/5.85 ( ( ord_less_nat @ one_one_nat @ N )
% 5.52/5.85 => ( ( groups7754918857620584856omplex
% 5.52/5.85 @ ^ [X: complex] : X
% 5.52/5.85 @ ( collect_complex
% 5.52/5.85 @ ^ [Z2: complex] :
% 5.52/5.85 ( ( power_power_complex @ Z2 @ N )
% 5.52/5.85 = C ) ) )
% 5.52/5.85 = zero_zero_complex ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_nth_roots
% 5.52/5.85 thf(fact_6575_even__and__iff,axiom,
% 5.52/5.85 ! [A: code_integer,B: code_integer] :
% 5.52/5.85 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 5.52/5.85 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.85 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % even_and_iff
% 5.52/5.85 thf(fact_6576_even__and__iff,axiom,
% 5.52/5.85 ! [A: int,B: int] :
% 5.52/5.85 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.52/5.85 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.85 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % even_and_iff
% 5.52/5.85 thf(fact_6577_even__and__iff,axiom,
% 5.52/5.85 ! [A: nat,B: nat] :
% 5.52/5.85 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.52/5.85 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.85 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % even_and_iff
% 5.52/5.85 thf(fact_6578_sum_OatLeast0__atMost__Suc,axiom,
% 5.52/5.85 ! [G: nat > rat,N: nat] :
% 5.52/5.85 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.atLeast0_atMost_Suc
% 5.52/5.85 thf(fact_6579_sum_OatLeast0__atMost__Suc,axiom,
% 5.52/5.85 ! [G: nat > int,N: nat] :
% 5.52/5.85 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.atLeast0_atMost_Suc
% 5.52/5.85 thf(fact_6580_sum_OatLeast0__atMost__Suc,axiom,
% 5.52/5.85 ! [G: nat > complex,N: nat] :
% 5.52/5.85 ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.atLeast0_atMost_Suc
% 5.52/5.85 thf(fact_6581_sum_OatLeast0__atMost__Suc,axiom,
% 5.52/5.85 ! [G: nat > nat,N: nat] :
% 5.52/5.85 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.atLeast0_atMost_Suc
% 5.52/5.85 thf(fact_6582_sum_OatLeast0__atMost__Suc,axiom,
% 5.52/5.85 ! [G: nat > real,N: nat] :
% 5.52/5.85 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.atLeast0_atMost_Suc
% 5.52/5.85 thf(fact_6583_even__and__iff__int,axiom,
% 5.52/5.85 ! [K: int,L: int] :
% 5.52/5.85 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.52/5.85 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.52/5.85 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % even_and_iff_int
% 5.52/5.85 thf(fact_6584_sum_Onat__ivl__Suc_H,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > rat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.nat_ivl_Suc'
% 5.52/5.85 thf(fact_6585_sum_Onat__ivl__Suc_H,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > int] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.85 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.nat_ivl_Suc'
% 5.52/5.85 thf(fact_6586_sum_Onat__ivl__Suc_H,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > complex] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.85 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_complex @ ( G @ ( suc @ N ) ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.nat_ivl_Suc'
% 5.52/5.85 thf(fact_6587_sum_Onat__ivl__Suc_H,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.85 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.nat_ivl_Suc'
% 5.52/5.85 thf(fact_6588_sum_Onat__ivl__Suc_H,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > real] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.85 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.nat_ivl_Suc'
% 5.52/5.85 thf(fact_6589_sum_OatLeast__Suc__atMost,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > rat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.atLeast_Suc_atMost
% 5.52/5.85 thf(fact_6590_sum_OatLeast__Suc__atMost,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > int] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.atLeast_Suc_atMost
% 5.52/5.85 thf(fact_6591_sum_OatLeast__Suc__atMost,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > complex] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( plus_plus_complex @ ( G @ M ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.atLeast_Suc_atMost
% 5.52/5.85 thf(fact_6592_sum_OatLeast__Suc__atMost,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.atLeast_Suc_atMost
% 5.52/5.85 thf(fact_6593_sum_OatLeast__Suc__atMost,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > real] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.atLeast_Suc_atMost
% 5.52/5.85 thf(fact_6594_ln__ge__iff,axiom,
% 5.52/5.85 ! [X2: real,Y2: real] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_eq_real @ Y2 @ ( ln_ln_real @ X2 ) )
% 5.52/5.85 = ( ord_less_eq_real @ ( exp_real @ Y2 ) @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % ln_ge_iff
% 5.52/5.85 thf(fact_6595_numeral__inc,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( numera6690914467698888265omplex @ ( inc @ X2 ) )
% 5.52/5.85 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X2 ) @ one_one_complex ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_inc
% 5.52/5.85 thf(fact_6596_numeral__inc,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( numeral_numeral_real @ ( inc @ X2 ) )
% 5.52/5.85 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_inc
% 5.52/5.85 thf(fact_6597_numeral__inc,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( numeral_numeral_rat @ ( inc @ X2 ) )
% 5.52/5.85 = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_inc
% 5.52/5.85 thf(fact_6598_numeral__inc,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( numeral_numeral_nat @ ( inc @ X2 ) )
% 5.52/5.85 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_inc
% 5.52/5.85 thf(fact_6599_numeral__inc,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( numeral_numeral_int @ ( inc @ X2 ) )
% 5.52/5.85 = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_inc
% 5.52/5.85 thf(fact_6600_sum_OSuc__reindex__ivl,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > rat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ M )
% 5.52/5.85 @ ( groups2906978787729119204at_rat
% 5.52/5.85 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.Suc_reindex_ivl
% 5.52/5.85 thf(fact_6601_sum_OSuc__reindex__ivl,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > int] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_int @ ( G @ M )
% 5.52/5.85 @ ( groups3539618377306564664at_int
% 5.52/5.85 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.Suc_reindex_ivl
% 5.52/5.85 thf(fact_6602_sum_OSuc__reindex__ivl,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > complex] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_complex @ ( G @ M )
% 5.52/5.85 @ ( groups2073611262835488442omplex
% 5.52/5.85 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.Suc_reindex_ivl
% 5.52/5.85 thf(fact_6603_sum_OSuc__reindex__ivl,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_nat @ ( G @ M )
% 5.52/5.85 @ ( groups3542108847815614940at_nat
% 5.52/5.85 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.Suc_reindex_ivl
% 5.52/5.85 thf(fact_6604_sum_OSuc__reindex__ivl,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > real] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ M )
% 5.52/5.85 @ ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.Suc_reindex_ivl
% 5.52/5.85 thf(fact_6605_sum__Suc__diff,axiom,
% 5.52/5.85 ! [M: nat,N: nat,F: nat > complex] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.85 => ( ( groups2073611262835488442omplex
% 5.52/5.85 @ ^ [I4: nat] : ( minus_minus_complex @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_complex @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_Suc_diff
% 5.52/5.85 thf(fact_6606_sum__Suc__diff,axiom,
% 5.52/5.85 ! [M: nat,N: nat,F: nat > rat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat
% 5.52/5.85 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_Suc_diff
% 5.52/5.85 thf(fact_6607_sum__Suc__diff,axiom,
% 5.52/5.85 ! [M: nat,N: nat,F: nat > int] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.85 => ( ( groups3539618377306564664at_int
% 5.52/5.85 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_Suc_diff
% 5.52/5.85 thf(fact_6608_sum__Suc__diff,axiom,
% 5.52/5.85 ! [M: nat,N: nat,F: nat > real] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.85 => ( ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_Suc_diff
% 5.52/5.85 thf(fact_6609_and__one__eq,axiom,
% 5.52/5.85 ! [A: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.52/5.85 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_one_eq
% 5.52/5.85 thf(fact_6610_and__one__eq,axiom,
% 5.52/5.85 ! [A: nat] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.52/5.85 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_one_eq
% 5.52/5.85 thf(fact_6611_one__and__eq,axiom,
% 5.52/5.85 ! [A: int] :
% 5.52/5.85 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.52/5.85 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % one_and_eq
% 5.52/5.85 thf(fact_6612_one__and__eq,axiom,
% 5.52/5.85 ! [A: nat] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.52/5.85 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % one_and_eq
% 5.52/5.85 thf(fact_6613_exp__le,axiom,
% 5.52/5.85 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_le
% 5.52/5.85 thf(fact_6614_sum_Oub__add__nat,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > rat,P6: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.52/5.85 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.ub_add_nat
% 5.52/5.85 thf(fact_6615_sum_Oub__add__nat,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.52/5.85 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.52/5.85 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.ub_add_nat
% 5.52/5.85 thf(fact_6616_sum_Oub__add__nat,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > complex,P6: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.52/5.85 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.52/5.85 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.ub_add_nat
% 5.52/5.85 thf(fact_6617_sum_Oub__add__nat,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.52/5.85 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.52/5.85 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.ub_add_nat
% 5.52/5.85 thf(fact_6618_sum_Oub__add__nat,axiom,
% 5.52/5.85 ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.52/5.85 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.52/5.85 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.ub_add_nat
% 5.52/5.85 thf(fact_6619_set__encode__def,axiom,
% 5.52/5.85 ( nat_set_encode
% 5.52/5.85 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % set_encode_def
% 5.52/5.85 thf(fact_6620_tanh__altdef,axiom,
% 5.52/5.85 ( tanh_real
% 5.52/5.85 = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % tanh_altdef
% 5.52/5.85 thf(fact_6621_tanh__altdef,axiom,
% 5.52/5.85 ( tanh_complex
% 5.52/5.85 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % tanh_altdef
% 5.52/5.85 thf(fact_6622_exp__half__le2,axiom,
% 5.52/5.85 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_half_le2
% 5.52/5.85 thf(fact_6623_exp__double,axiom,
% 5.52/5.85 ! [Z: complex] :
% 5.52/5.85 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.52/5.85 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_double
% 5.52/5.85 thf(fact_6624_exp__double,axiom,
% 5.52/5.85 ! [Z: real] :
% 5.52/5.85 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.52/5.85 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_double
% 5.52/5.85 thf(fact_6625_sum__natinterval__diff,axiom,
% 5.52/5.85 ! [M: nat,N: nat,F: nat > complex] :
% 5.52/5.85 ( ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups2073611262835488442omplex
% 5.52/5.85 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.52/5.85 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups2073611262835488442omplex
% 5.52/5.85 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = zero_zero_complex ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_natinterval_diff
% 5.52/5.85 thf(fact_6626_sum__natinterval__diff,axiom,
% 5.52/5.85 ! [M: nat,N: nat,F: nat > rat] :
% 5.52/5.85 ( ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat
% 5.52/5.85 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.52/5.85 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat
% 5.52/5.85 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = zero_zero_rat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_natinterval_diff
% 5.52/5.85 thf(fact_6627_sum__natinterval__diff,axiom,
% 5.52/5.85 ! [M: nat,N: nat,F: nat > int] :
% 5.52/5.85 ( ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups3539618377306564664at_int
% 5.52/5.85 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.52/5.85 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups3539618377306564664at_int
% 5.52/5.85 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = zero_zero_int ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_natinterval_diff
% 5.52/5.85 thf(fact_6628_sum__natinterval__diff,axiom,
% 5.52/5.85 ! [M: nat,N: nat,F: nat > real] :
% 5.52/5.85 ( ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.52/5.85 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = zero_zero_real ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_natinterval_diff
% 5.52/5.85 thf(fact_6629_sum__telescope_H_H,axiom,
% 5.52/5.85 ! [M: nat,N: nat,F: nat > complex] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups2073611262835488442omplex
% 5.52/5.85 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.52/5.85 = ( minus_minus_complex @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_telescope''
% 5.52/5.85 thf(fact_6630_sum__telescope_H_H,axiom,
% 5.52/5.85 ! [M: nat,N: nat,F: nat > rat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat
% 5.52/5.85 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.52/5.85 = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_telescope''
% 5.52/5.85 thf(fact_6631_sum__telescope_H_H,axiom,
% 5.52/5.85 ! [M: nat,N: nat,F: nat > int] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups3539618377306564664at_int
% 5.52/5.85 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.52/5.85 = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_telescope''
% 5.52/5.85 thf(fact_6632_sum__telescope_H_H,axiom,
% 5.52/5.85 ! [M: nat,N: nat,F: nat > real] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.52/5.85 = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_telescope''
% 5.52/5.85 thf(fact_6633_mask__eq__sum__exp,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 5.52/5.85 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.85 @ ( collect_nat
% 5.52/5.85 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mask_eq_sum_exp
% 5.52/5.85 thf(fact_6634_mask__eq__sum__exp,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 5.52/5.85 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.85 @ ( collect_nat
% 5.52/5.85 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mask_eq_sum_exp
% 5.52/5.85 thf(fact_6635_sum__gp__multiplied,axiom,
% 5.52/5.85 ! [M: nat,N: nat,X2: complex] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.52/5.85 = ( minus_minus_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_gp_multiplied
% 5.52/5.85 thf(fact_6636_sum__gp__multiplied,axiom,
% 5.52/5.85 ! [M: nat,N: nat,X2: rat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.52/5.85 = ( minus_minus_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_gp_multiplied
% 5.52/5.85 thf(fact_6637_sum__gp__multiplied,axiom,
% 5.52/5.85 ! [M: nat,N: nat,X2: int] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.52/5.85 = ( minus_minus_int @ ( power_power_int @ X2 @ M ) @ ( power_power_int @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_gp_multiplied
% 5.52/5.85 thf(fact_6638_sum__gp__multiplied,axiom,
% 5.52/5.85 ! [M: nat,N: nat,X2: real] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.52/5.85 = ( minus_minus_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_gp_multiplied
% 5.52/5.85 thf(fact_6639_sum_Oin__pairs,axiom,
% 5.52/5.85 ! [G: nat > rat,M: nat,N: nat] :
% 5.52/5.85 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.52/5.85 = ( groups2906978787729119204at_rat
% 5.52/5.85 @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.in_pairs
% 5.52/5.85 thf(fact_6640_sum_Oin__pairs,axiom,
% 5.52/5.85 ! [G: nat > int,M: nat,N: nat] :
% 5.52/5.85 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.52/5.85 = ( groups3539618377306564664at_int
% 5.52/5.85 @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.in_pairs
% 5.52/5.85 thf(fact_6641_sum_Oin__pairs,axiom,
% 5.52/5.85 ! [G: nat > complex,M: nat,N: nat] :
% 5.52/5.85 ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.52/5.85 = ( groups2073611262835488442omplex
% 5.52/5.85 @ ^ [I4: nat] : ( plus_plus_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.in_pairs
% 5.52/5.85 thf(fact_6642_sum_Oin__pairs,axiom,
% 5.52/5.85 ! [G: nat > nat,M: nat,N: nat] :
% 5.52/5.85 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.52/5.85 = ( groups3542108847815614940at_nat
% 5.52/5.85 @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.in_pairs
% 5.52/5.85 thf(fact_6643_sum_Oin__pairs,axiom,
% 5.52/5.85 ! [G: nat > real,M: nat,N: nat] :
% 5.52/5.85 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.52/5.85 = ( groups6591440286371151544t_real
% 5.52/5.85 @ ^ [I4: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.in_pairs
% 5.52/5.85 thf(fact_6644_unbounded__k__infinite,axiom,
% 5.52/5.85 ! [K: nat,S3: set_nat] :
% 5.52/5.85 ( ! [M4: nat] :
% 5.52/5.85 ( ( ord_less_nat @ K @ M4 )
% 5.52/5.85 => ? [N7: nat] :
% 5.52/5.85 ( ( ord_less_nat @ M4 @ N7 )
% 5.52/5.85 & ( member_nat @ N7 @ S3 ) ) )
% 5.52/5.85 => ~ ( finite_finite_nat @ S3 ) ) ).
% 5.52/5.85
% 5.52/5.85 % unbounded_k_infinite
% 5.52/5.85 thf(fact_6645_infinite__nat__iff__unbounded,axiom,
% 5.52/5.85 ! [S3: set_nat] :
% 5.52/5.85 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.52/5.85 = ( ! [M3: nat] :
% 5.52/5.85 ? [N3: nat] :
% 5.52/5.85 ( ( ord_less_nat @ M3 @ N3 )
% 5.52/5.85 & ( member_nat @ N3 @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % infinite_nat_iff_unbounded
% 5.52/5.85 thf(fact_6646_infinite__nat__iff__unbounded__le,axiom,
% 5.52/5.85 ! [S3: set_nat] :
% 5.52/5.85 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.52/5.85 = ( ! [M3: nat] :
% 5.52/5.85 ? [N3: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.85 & ( member_nat @ N3 @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % infinite_nat_iff_unbounded_le
% 5.52/5.85 thf(fact_6647_exp__bound,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.52/5.85 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_bound
% 5.52/5.85 thf(fact_6648_mask__eq__sum__exp__nat,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.52/5.85 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.85 @ ( collect_nat
% 5.52/5.85 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mask_eq_sum_exp_nat
% 5.52/5.85 thf(fact_6649_and__int__rec,axiom,
% 5.52/5.85 ( bit_se725231765392027082nd_int
% 5.52/5.85 = ( ^ [K2: int,L2: int] :
% 5.52/5.85 ( plus_plus_int
% 5.52/5.85 @ ( zero_n2684676970156552555ol_int
% 5.52/5.85 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.52/5.85 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.52/5.85 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_int_rec
% 5.52/5.85 thf(fact_6650_gauss__sum__nat,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( groups3542108847815614940at_nat
% 5.52/5.85 @ ^ [X: nat] : X
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.52/5.85 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % gauss_sum_nat
% 5.52/5.85 thf(fact_6651_real__exp__bound__lemma,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.85 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_exp_bound_lemma
% 5.52/5.85 thf(fact_6652_arith__series__nat,axiom,
% 5.52/5.85 ! [A: nat,D2: nat,N: nat] :
% 5.52/5.85 ( ( groups3542108847815614940at_nat
% 5.52/5.85 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I4 @ D2 ) )
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.52/5.85 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % arith_series_nat
% 5.52/5.85 thf(fact_6653_Sum__Icc__nat,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( groups3542108847815614940at_nat
% 5.52/5.85 @ ^ [X: nat] : X
% 5.52/5.85 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % Sum_Icc_nat
% 5.52/5.85 thf(fact_6654_exp__lower__Taylor__quadratic,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( divide_divide_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_lower_Taylor_quadratic
% 5.52/5.85 thf(fact_6655_and__int_Oelims,axiom,
% 5.52/5.85 ! [X2: int,Xa2: int,Y2: int] :
% 5.52/5.85 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa2 )
% 5.52/5.85 = Y2 )
% 5.52/5.85 => ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.52/5.85 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.52/5.85 => ( Y2
% 5.52/5.85 = ( uminus_uminus_int
% 5.52/5.85 @ ( zero_n2684676970156552555ol_int
% 5.52/5.85 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.52/5.85 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.52/5.85 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.52/5.85 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.52/5.85 => ( Y2
% 5.52/5.85 = ( plus_plus_int
% 5.52/5.85 @ ( zero_n2684676970156552555ol_int
% 5.52/5.85 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.52/5.85 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.52/5.85 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_int.elims
% 5.52/5.85 thf(fact_6656_and__int_Osimps,axiom,
% 5.52/5.85 ( bit_se725231765392027082nd_int
% 5.52/5.85 = ( ^ [K2: int,L2: int] :
% 5.52/5.85 ( if_int
% 5.52/5.85 @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.52/5.85 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.52/5.85 @ ( uminus_uminus_int
% 5.52/5.85 @ ( zero_n2684676970156552555ol_int
% 5.52/5.85 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.52/5.85 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.52/5.85 @ ( plus_plus_int
% 5.52/5.85 @ ( zero_n2684676970156552555ol_int
% 5.52/5.85 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.52/5.85 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.52/5.85 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_int.simps
% 5.52/5.85 thf(fact_6657_sum__gp,axiom,
% 5.52/5.85 ! [N: nat,M: nat,X2: complex] :
% 5.52/5.85 ( ( ( ord_less_nat @ N @ M )
% 5.52/5.85 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = zero_zero_complex ) )
% 5.52/5.85 & ( ~ ( ord_less_nat @ N @ M )
% 5.52/5.85 => ( ( ( X2 = one_one_complex )
% 5.52/5.85 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.52/5.85 & ( ( X2 != one_one_complex )
% 5.52/5.85 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_gp
% 5.52/5.85 thf(fact_6658_sum__gp,axiom,
% 5.52/5.85 ! [N: nat,M: nat,X2: rat] :
% 5.52/5.85 ( ( ( ord_less_nat @ N @ M )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = zero_zero_rat ) )
% 5.52/5.85 & ( ~ ( ord_less_nat @ N @ M )
% 5.52/5.85 => ( ( ( X2 = one_one_rat )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.52/5.85 & ( ( X2 != one_one_rat )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_gp
% 5.52/5.85 thf(fact_6659_sum__gp,axiom,
% 5.52/5.85 ! [N: nat,M: nat,X2: real] :
% 5.52/5.85 ( ( ( ord_less_nat @ N @ M )
% 5.52/5.85 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = zero_zero_real ) )
% 5.52/5.85 & ( ~ ( ord_less_nat @ N @ M )
% 5.52/5.85 => ( ( ( X2 = one_one_real )
% 5.52/5.85 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.52/5.85 & ( ( X2 != one_one_real )
% 5.52/5.85 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.85 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum_gp
% 5.52/5.85 thf(fact_6660_log__base__10__eq1,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.85 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_base_10_eq1
% 5.52/5.85 thf(fact_6661_signed__take__bit__eq__take__bit__minus,axiom,
% 5.52/5.85 ( bit_ri631733984087533419it_int
% 5.52/5.85 = ( ^ [N3: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ K2 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N3 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % signed_take_bit_eq_take_bit_minus
% 5.52/5.85 thf(fact_6662_gauss__sum__from__Suc__0,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.52/5.85 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % gauss_sum_from_Suc_0
% 5.52/5.85 thf(fact_6663_gauss__sum__from__Suc__0,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.52/5.85 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % gauss_sum_from_Suc_0
% 5.52/5.85 thf(fact_6664_of__nat__eq__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ( semiri1314217659103216013at_int @ M )
% 5.52/5.85 = ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.85 = ( M = N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_iff
% 5.52/5.85 thf(fact_6665_of__nat__eq__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ( semiri5074537144036343181t_real @ M )
% 5.52/5.85 = ( semiri5074537144036343181t_real @ N ) )
% 5.52/5.85 = ( M = N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_iff
% 5.52/5.85 thf(fact_6666_of__nat__eq__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.52/5.85 = ( semiri1316708129612266289at_nat @ N ) )
% 5.52/5.85 = ( M = N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_iff
% 5.52/5.85 thf(fact_6667_of__nat__eq__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ( semiri681578069525770553at_rat @ M )
% 5.52/5.85 = ( semiri681578069525770553at_rat @ N ) )
% 5.52/5.85 = ( M = N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_iff
% 5.52/5.85 thf(fact_6668_of__nat__eq__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ( semiri4216267220026989637d_enat @ M )
% 5.52/5.85 = ( semiri4216267220026989637d_enat @ N ) )
% 5.52/5.85 = ( M = N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_iff
% 5.52/5.85 thf(fact_6669_int__eq__iff__numeral,axiom,
% 5.52/5.85 ! [M: nat,V: num] :
% 5.52/5.85 ( ( ( semiri1314217659103216013at_int @ M )
% 5.52/5.85 = ( numeral_numeral_int @ V ) )
% 5.52/5.85 = ( M
% 5.52/5.85 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % int_eq_iff_numeral
% 5.52/5.85 thf(fact_6670_bit__0__eq,axiom,
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ zero_zero_int )
% 5.52/5.85 = bot_bot_nat_o ) ).
% 5.52/5.85
% 5.52/5.85 % bit_0_eq
% 5.52/5.85 thf(fact_6671_bit__0__eq,axiom,
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ zero_zero_nat )
% 5.52/5.85 = bot_bot_nat_o ) ).
% 5.52/5.85
% 5.52/5.85 % bit_0_eq
% 5.52/5.85 thf(fact_6672_abs__of__nat,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.52/5.85 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % abs_of_nat
% 5.52/5.85 thf(fact_6673_abs__of__nat,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.85 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % abs_of_nat
% 5.52/5.85 thf(fact_6674_abs__of__nat,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.52/5.85 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % abs_of_nat
% 5.52/5.85 thf(fact_6675_abs__of__nat,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.52/5.85 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % abs_of_nat
% 5.52/5.85 thf(fact_6676_height__double__log__univ__size,axiom,
% 5.52/5.85 ! [U: real,Deg: nat,T: vEBT_VEBT] :
% 5.52/5.85 ( ( U
% 5.52/5.85 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Deg ) )
% 5.52/5.85 => ( ( vEBT_invar_vebt @ T @ Deg )
% 5.52/5.85 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_height @ T ) ) @ ( plus_plus_real @ one_one_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % height_double_log_univ_size
% 5.52/5.85 thf(fact_6677_of__nat__eq__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( ( semiri1314217659103216013at_int @ M )
% 5.52/5.85 = zero_zero_int )
% 5.52/5.85 = ( M = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_0_iff
% 5.52/5.85 thf(fact_6678_of__nat__eq__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( ( semiri5074537144036343181t_real @ M )
% 5.52/5.85 = zero_zero_real )
% 5.52/5.85 = ( M = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_0_iff
% 5.52/5.85 thf(fact_6679_of__nat__eq__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.52/5.85 = zero_zero_nat )
% 5.52/5.85 = ( M = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_0_iff
% 5.52/5.85 thf(fact_6680_of__nat__eq__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( ( semiri681578069525770553at_rat @ M )
% 5.52/5.85 = zero_zero_rat )
% 5.52/5.85 = ( M = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_0_iff
% 5.52/5.85 thf(fact_6681_of__nat__eq__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( ( semiri4216267220026989637d_enat @ M )
% 5.52/5.85 = zero_z5237406670263579293d_enat )
% 5.52/5.85 = ( M = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_0_iff
% 5.52/5.85 thf(fact_6682_of__nat__0__eq__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( zero_zero_int
% 5.52/5.85 = ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.85 = ( zero_zero_nat = N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_eq_iff
% 5.52/5.85 thf(fact_6683_of__nat__0__eq__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( zero_zero_real
% 5.52/5.85 = ( semiri5074537144036343181t_real @ N ) )
% 5.52/5.85 = ( zero_zero_nat = N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_eq_iff
% 5.52/5.85 thf(fact_6684_of__nat__0__eq__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( zero_zero_nat
% 5.52/5.85 = ( semiri1316708129612266289at_nat @ N ) )
% 5.52/5.85 = ( zero_zero_nat = N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_eq_iff
% 5.52/5.85 thf(fact_6685_of__nat__0__eq__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( zero_zero_rat
% 5.52/5.85 = ( semiri681578069525770553at_rat @ N ) )
% 5.52/5.85 = ( zero_zero_nat = N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_eq_iff
% 5.52/5.85 thf(fact_6686_of__nat__0__eq__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( zero_z5237406670263579293d_enat
% 5.52/5.85 = ( semiri4216267220026989637d_enat @ N ) )
% 5.52/5.85 = ( zero_zero_nat = N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_eq_iff
% 5.52/5.85 thf(fact_6687_of__nat__0,axiom,
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.52/5.85 = zero_zero_int ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0
% 5.52/5.85 thf(fact_6688_of__nat__0,axiom,
% 5.52/5.85 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.52/5.85 = zero_zero_real ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0
% 5.52/5.85 thf(fact_6689_of__nat__0,axiom,
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.52/5.85 = zero_zero_nat ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0
% 5.52/5.85 thf(fact_6690_of__nat__0,axiom,
% 5.52/5.85 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.52/5.85 = zero_zero_rat ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0
% 5.52/5.85 thf(fact_6691_of__nat__0,axiom,
% 5.52/5.85 ( ( semiri4216267220026989637d_enat @ zero_zero_nat )
% 5.52/5.85 = zero_z5237406670263579293d_enat ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0
% 5.52/5.85 thf(fact_6692_of__nat__less__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.85 = ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_iff
% 5.52/5.85 thf(fact_6693_of__nat__less__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.52/5.85 = ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_iff
% 5.52/5.85 thf(fact_6694_of__nat__less__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.52/5.85 = ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_iff
% 5.52/5.85 thf(fact_6695_of__nat__less__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.52/5.85 = ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_iff
% 5.52/5.85 thf(fact_6696_of__nat__less__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_le72135733267957522d_enat @ ( semiri4216267220026989637d_enat @ M ) @ ( semiri4216267220026989637d_enat @ N ) )
% 5.52/5.85 = ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_iff
% 5.52/5.85 thf(fact_6697_of__nat__numeral,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( numera6690914467698888265omplex @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_numeral
% 5.52/5.85 thf(fact_6698_of__nat__numeral,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( numeral_numeral_int @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_numeral
% 5.52/5.85 thf(fact_6699_of__nat__numeral,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( numeral_numeral_real @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_numeral
% 5.52/5.85 thf(fact_6700_of__nat__numeral,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( numeral_numeral_nat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_numeral
% 5.52/5.85 thf(fact_6701_of__nat__numeral,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( numeral_numeral_rat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_numeral
% 5.52/5.85 thf(fact_6702_of__nat__numeral,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( semiri4216267220026989637d_enat @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( numera1916890842035813515d_enat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_numeral
% 5.52/5.85 thf(fact_6703_of__nat__le__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.52/5.85 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_iff
% 5.52/5.85 thf(fact_6704_of__nat__le__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_le2932123472753598470d_enat @ ( semiri4216267220026989637d_enat @ M ) @ ( semiri4216267220026989637d_enat @ N ) )
% 5.52/5.85 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_iff
% 5.52/5.85 thf(fact_6705_of__nat__le__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.52/5.85 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_iff
% 5.52/5.85 thf(fact_6706_of__nat__le__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.52/5.85 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_iff
% 5.52/5.85 thf(fact_6707_of__nat__le__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.85 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_iff
% 5.52/5.85 thf(fact_6708_of__nat__add,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 5.52/5.85 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_add
% 5.52/5.85 thf(fact_6709_of__nat__add,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 5.52/5.85 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_add
% 5.52/5.85 thf(fact_6710_of__nat__add,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 5.52/5.85 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_add
% 5.52/5.85 thf(fact_6711_of__nat__add,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 5.52/5.85 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_add
% 5.52/5.85 thf(fact_6712_of__nat__add,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 5.52/5.85 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_add
% 5.52/5.85 thf(fact_6713_of__nat__add,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri4216267220026989637d_enat @ ( plus_plus_nat @ M @ N ) )
% 5.52/5.85 = ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ M ) @ ( semiri4216267220026989637d_enat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_add
% 5.52/5.85 thf(fact_6714_of__nat__eq__1__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( ( semiri8010041392384452111omplex @ N )
% 5.52/5.85 = one_one_complex )
% 5.52/5.85 = ( N = one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_1_iff
% 5.52/5.85 thf(fact_6715_of__nat__eq__1__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( ( semiri1314217659103216013at_int @ N )
% 5.52/5.85 = one_one_int )
% 5.52/5.85 = ( N = one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_1_iff
% 5.52/5.85 thf(fact_6716_of__nat__eq__1__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( ( semiri5074537144036343181t_real @ N )
% 5.52/5.85 = one_one_real )
% 5.52/5.85 = ( N = one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_1_iff
% 5.52/5.85 thf(fact_6717_of__nat__eq__1__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.52/5.85 = one_one_nat )
% 5.52/5.85 = ( N = one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_1_iff
% 5.52/5.85 thf(fact_6718_of__nat__eq__1__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( ( semiri681578069525770553at_rat @ N )
% 5.52/5.85 = one_one_rat )
% 5.52/5.85 = ( N = one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_1_iff
% 5.52/5.85 thf(fact_6719_of__nat__eq__1__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( ( semiri4216267220026989637d_enat @ N )
% 5.52/5.85 = one_on7984719198319812577d_enat )
% 5.52/5.85 = ( N = one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_1_iff
% 5.52/5.85 thf(fact_6720_of__nat__1__eq__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( one_one_complex
% 5.52/5.85 = ( semiri8010041392384452111omplex @ N ) )
% 5.52/5.85 = ( N = one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_1_eq_iff
% 5.52/5.85 thf(fact_6721_of__nat__1__eq__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( one_one_int
% 5.52/5.85 = ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.85 = ( N = one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_1_eq_iff
% 5.52/5.85 thf(fact_6722_of__nat__1__eq__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( one_one_real
% 5.52/5.85 = ( semiri5074537144036343181t_real @ N ) )
% 5.52/5.85 = ( N = one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_1_eq_iff
% 5.52/5.85 thf(fact_6723_of__nat__1__eq__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( one_one_nat
% 5.52/5.85 = ( semiri1316708129612266289at_nat @ N ) )
% 5.52/5.85 = ( N = one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_1_eq_iff
% 5.52/5.85 thf(fact_6724_of__nat__1__eq__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( one_one_rat
% 5.52/5.85 = ( semiri681578069525770553at_rat @ N ) )
% 5.52/5.85 = ( N = one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_1_eq_iff
% 5.52/5.85 thf(fact_6725_of__nat__1__eq__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( one_on7984719198319812577d_enat
% 5.52/5.85 = ( semiri4216267220026989637d_enat @ N ) )
% 5.52/5.85 = ( N = one_one_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_1_eq_iff
% 5.52/5.85 thf(fact_6726_of__nat__1,axiom,
% 5.52/5.85 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.52/5.85 = one_one_complex ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_1
% 5.52/5.85 thf(fact_6727_of__nat__1,axiom,
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.52/5.85 = one_one_int ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_1
% 5.52/5.85 thf(fact_6728_of__nat__1,axiom,
% 5.52/5.85 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.52/5.85 = one_one_real ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_1
% 5.52/5.85 thf(fact_6729_of__nat__1,axiom,
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.52/5.85 = one_one_nat ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_1
% 5.52/5.85 thf(fact_6730_of__nat__1,axiom,
% 5.52/5.85 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.52/5.85 = one_one_rat ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_1
% 5.52/5.85 thf(fact_6731_of__nat__1,axiom,
% 5.52/5.85 ( ( semiri4216267220026989637d_enat @ one_one_nat )
% 5.52/5.85 = one_on7984719198319812577d_enat ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_1
% 5.52/5.85 thf(fact_6732_of__nat__mult,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 5.52/5.85 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mult
% 5.52/5.85 thf(fact_6733_of__nat__mult,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 5.52/5.85 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mult
% 5.52/5.85 thf(fact_6734_of__nat__mult,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 5.52/5.85 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mult
% 5.52/5.85 thf(fact_6735_of__nat__mult,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 5.52/5.85 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mult
% 5.52/5.85 thf(fact_6736_of__nat__mult,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri4216267220026989637d_enat @ ( times_times_nat @ M @ N ) )
% 5.52/5.85 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ M ) @ ( semiri4216267220026989637d_enat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mult
% 5.52/5.85 thf(fact_6737_of__nat__power,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 5.52/5.85 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power
% 5.52/5.85 thf(fact_6738_of__nat__power,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 5.52/5.85 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power
% 5.52/5.85 thf(fact_6739_of__nat__power,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 5.52/5.85 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power
% 5.52/5.85 thf(fact_6740_of__nat__power,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 5.52/5.85 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power
% 5.52/5.85 thf(fact_6741_of__nat__power,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 5.52/5.85 = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power
% 5.52/5.85 thf(fact_6742_of__nat__power,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri4216267220026989637d_enat @ ( power_power_nat @ M @ N ) )
% 5.52/5.85 = ( power_8040749407984259932d_enat @ ( semiri4216267220026989637d_enat @ M ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power
% 5.52/5.85 thf(fact_6743_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.52/5.85 = ( semiri8010041392384452111omplex @ X2 ) )
% 5.52/5.85 = ( ( power_power_nat @ B @ W )
% 5.52/5.85 = X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6744_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.52/5.85 = ( semiri1314217659103216013at_int @ X2 ) )
% 5.52/5.85 = ( ( power_power_nat @ B @ W )
% 5.52/5.85 = X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6745_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.52/5.85 = ( semiri5074537144036343181t_real @ X2 ) )
% 5.52/5.85 = ( ( power_power_nat @ B @ W )
% 5.52/5.85 = X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6746_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.52/5.85 = ( semiri1316708129612266289at_nat @ X2 ) )
% 5.52/5.85 = ( ( power_power_nat @ B @ W )
% 5.52/5.85 = X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6747_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W )
% 5.52/5.85 = ( semiri681578069525770553at_rat @ X2 ) )
% 5.52/5.85 = ( ( power_power_nat @ B @ W )
% 5.52/5.85 = X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6748_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ( power_8040749407984259932d_enat @ ( semiri4216267220026989637d_enat @ B ) @ W )
% 5.52/5.85 = ( semiri4216267220026989637d_enat @ X2 ) )
% 5.52/5.85 = ( ( power_power_nat @ B @ W )
% 5.52/5.85 = X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_eq_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6749_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ( semiri8010041392384452111omplex @ X2 )
% 5.52/5.85 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.52/5.85 = ( X2
% 5.52/5.85 = ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_eq_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6750_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ( semiri1314217659103216013at_int @ X2 )
% 5.52/5.85 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.52/5.85 = ( X2
% 5.52/5.85 = ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_eq_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6751_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ( semiri5074537144036343181t_real @ X2 )
% 5.52/5.85 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.52/5.85 = ( X2
% 5.52/5.85 = ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_eq_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6752_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ( semiri1316708129612266289at_nat @ X2 )
% 5.52/5.85 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.52/5.85 = ( X2
% 5.52/5.85 = ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_eq_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6753_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ( semiri681578069525770553at_rat @ X2 )
% 5.52/5.85 = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.52/5.85 = ( X2
% 5.52/5.85 = ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_eq_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6754_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ( semiri4216267220026989637d_enat @ X2 )
% 5.52/5.85 = ( power_8040749407984259932d_enat @ ( semiri4216267220026989637d_enat @ B ) @ W ) )
% 5.52/5.85 = ( X2
% 5.52/5.85 = ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_eq_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6755_negative__zless,axiom,
% 5.52/5.85 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.52/5.85
% 5.52/5.85 % negative_zless
% 5.52/5.85 thf(fact_6756_of__nat__of__bool,axiom,
% 5.52/5.85 ! [P: $o] :
% 5.52/5.85 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.52/5.85 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_of_bool
% 5.52/5.85 thf(fact_6757_of__nat__of__bool,axiom,
% 5.52/5.85 ! [P: $o] :
% 5.52/5.85 ( ( semiri681578069525770553at_rat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.52/5.85 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_of_bool
% 5.52/5.85 thf(fact_6758_of__nat__of__bool,axiom,
% 5.52/5.85 ! [P: $o] :
% 5.52/5.85 ( ( semiri4216267220026989637d_enat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.52/5.85 = ( zero_n1046097342994218471d_enat @ P ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_of_bool
% 5.52/5.85 thf(fact_6759_of__nat__of__bool,axiom,
% 5.52/5.85 ! [P: $o] :
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.52/5.85 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_of_bool
% 5.52/5.85 thf(fact_6760_of__nat__of__bool,axiom,
% 5.52/5.85 ! [P: $o] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.52/5.85 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_of_bool
% 5.52/5.85 thf(fact_6761_of__nat__of__bool,axiom,
% 5.52/5.85 ! [P: $o] :
% 5.52/5.85 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.52/5.85 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_of_bool
% 5.52/5.85 thf(fact_6762_of__nat__le__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.52/5.85 = ( M = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_0_iff
% 5.52/5.85 thf(fact_6763_of__nat__le__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( ord_le2932123472753598470d_enat @ ( semiri4216267220026989637d_enat @ M ) @ zero_z5237406670263579293d_enat )
% 5.52/5.85 = ( M = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_0_iff
% 5.52/5.85 thf(fact_6764_of__nat__le__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.52/5.85 = ( M = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_0_iff
% 5.52/5.85 thf(fact_6765_of__nat__le__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.52/5.85 = ( M = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_0_iff
% 5.52/5.85 thf(fact_6766_of__nat__le__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.52/5.85 = ( M = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_0_iff
% 5.52/5.85 thf(fact_6767_of__nat__Suc,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.52/5.85 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_Suc
% 5.52/5.85 thf(fact_6768_of__nat__Suc,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.52/5.85 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_Suc
% 5.52/5.85 thf(fact_6769_of__nat__Suc,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.52/5.85 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_Suc
% 5.52/5.85 thf(fact_6770_of__nat__Suc,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.52/5.85 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_Suc
% 5.52/5.85 thf(fact_6771_of__nat__Suc,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.52/5.85 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_Suc
% 5.52/5.85 thf(fact_6772_of__nat__Suc,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ( ( semiri4216267220026989637d_enat @ ( suc @ M ) )
% 5.52/5.85 = ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( semiri4216267220026989637d_enat @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_Suc
% 5.52/5.85 thf(fact_6773_and__nat__numerals_I1_J,axiom,
% 5.52/5.85 ! [Y2: num] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.52/5.85 = zero_zero_nat ) ).
% 5.52/5.85
% 5.52/5.85 % and_nat_numerals(1)
% 5.52/5.85 thf(fact_6774_and__nat__numerals_I3_J,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.52/5.85 = zero_zero_nat ) ).
% 5.52/5.85
% 5.52/5.85 % and_nat_numerals(3)
% 5.52/5.85 thf(fact_6775_sum_Oinsert,axiom,
% 5.52/5.85 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.52/5.85 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.85 => ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.85 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert
% 5.52/5.85 thf(fact_6776_sum_Oinsert,axiom,
% 5.52/5.85 ! [A2: set_real,X2: real,G: real > real] :
% 5.52/5.85 ( ( finite_finite_real @ A2 )
% 5.52/5.85 => ( ~ ( member_real @ X2 @ A2 )
% 5.52/5.85 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert
% 5.52/5.85 thf(fact_6777_sum_Oinsert,axiom,
% 5.52/5.85 ! [A2: set_int,X2: int,G: int > real] :
% 5.52/5.85 ( ( finite_finite_int @ A2 )
% 5.52/5.85 => ( ~ ( member_int @ X2 @ A2 )
% 5.52/5.85 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert
% 5.52/5.85 thf(fact_6778_sum_Oinsert,axiom,
% 5.52/5.85 ! [A2: set_complex,X2: complex,G: complex > real] :
% 5.52/5.85 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.85 => ( ~ ( member_complex @ X2 @ A2 )
% 5.52/5.85 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert
% 5.52/5.85 thf(fact_6779_sum_Oinsert,axiom,
% 5.52/5.85 ! [A2: set_Extended_enat,X2: extended_enat,G: extended_enat > real] :
% 5.52/5.85 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.85 => ( ~ ( member_Extended_enat @ X2 @ A2 )
% 5.52/5.85 => ( ( groups4148127829035722712t_real @ G @ ( insert_Extended_enat @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ X2 ) @ ( groups4148127829035722712t_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert
% 5.52/5.85 thf(fact_6780_sum_Oinsert,axiom,
% 5.52/5.85 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.52/5.85 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.85 => ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.85 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert
% 5.52/5.85 thf(fact_6781_sum_Oinsert,axiom,
% 5.52/5.85 ! [A2: set_real,X2: real,G: real > rat] :
% 5.52/5.85 ( ( finite_finite_real @ A2 )
% 5.52/5.85 => ( ~ ( member_real @ X2 @ A2 )
% 5.52/5.85 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert
% 5.52/5.85 thf(fact_6782_sum_Oinsert,axiom,
% 5.52/5.85 ! [A2: set_nat,X2: nat,G: nat > rat] :
% 5.52/5.85 ( ( finite_finite_nat @ A2 )
% 5.52/5.85 => ( ~ ( member_nat @ X2 @ A2 )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert
% 5.52/5.85 thf(fact_6783_sum_Oinsert,axiom,
% 5.52/5.85 ! [A2: set_int,X2: int,G: int > rat] :
% 5.52/5.85 ( ( finite_finite_int @ A2 )
% 5.52/5.85 => ( ~ ( member_int @ X2 @ A2 )
% 5.52/5.85 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert
% 5.52/5.85 thf(fact_6784_sum_Oinsert,axiom,
% 5.52/5.85 ! [A2: set_complex,X2: complex,G: complex > rat] :
% 5.52/5.85 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.85 => ( ~ ( member_complex @ X2 @ A2 )
% 5.52/5.85 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert
% 5.52/5.85 thf(fact_6785_bit__numeral__Bit0__Suc__iff,axiom,
% 5.52/5.85 ! [M: num,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( suc @ N ) )
% 5.52/5.85 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_numeral_Bit0_Suc_iff
% 5.52/5.85 thf(fact_6786_bit__numeral__Bit0__Suc__iff,axiom,
% 5.52/5.85 ! [M: num,N: nat] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( suc @ N ) )
% 5.52/5.85 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_numeral_Bit0_Suc_iff
% 5.52/5.85 thf(fact_6787_real__of__nat__less__numeral__iff,axiom,
% 5.52/5.85 ! [N: nat,W: num] :
% 5.52/5.85 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 5.52/5.85 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_of_nat_less_numeral_iff
% 5.52/5.85 thf(fact_6788_numeral__less__real__of__nat__iff,axiom,
% 5.52/5.85 ! [W: num,N: nat] :
% 5.52/5.85 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.52/5.85 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_less_real_of_nat_iff
% 5.52/5.85 thf(fact_6789_bit__numeral__Bit1__Suc__iff,axiom,
% 5.52/5.85 ! [M: num,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( suc @ N ) )
% 5.52/5.85 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_numeral_Bit1_Suc_iff
% 5.52/5.85 thf(fact_6790_bit__numeral__Bit1__Suc__iff,axiom,
% 5.52/5.85 ! [M: num,N: nat] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( suc @ N ) )
% 5.52/5.85 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_numeral_Bit1_Suc_iff
% 5.52/5.85 thf(fact_6791_numeral__le__real__of__nat__iff,axiom,
% 5.52/5.85 ! [N: num,M: nat] :
% 5.52/5.85 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.52/5.85 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_le_real_of_nat_iff
% 5.52/5.85 thf(fact_6792_zero__less__log__cancel__iff,axiom,
% 5.52/5.85 ! [A: real,X2: real] :
% 5.52/5.85 ( ( ord_less_real @ one_one_real @ A )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X2 ) )
% 5.52/5.85 = ( ord_less_real @ one_one_real @ X2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % zero_less_log_cancel_iff
% 5.52/5.85 thf(fact_6793_log__less__zero__cancel__iff,axiom,
% 5.52/5.85 ! [A: real,X2: real] :
% 5.52/5.85 ( ( ord_less_real @ one_one_real @ A )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_real @ ( log @ A @ X2 ) @ zero_zero_real )
% 5.52/5.85 = ( ord_less_real @ X2 @ one_one_real ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_less_zero_cancel_iff
% 5.52/5.85 thf(fact_6794_one__less__log__cancel__iff,axiom,
% 5.52/5.85 ! [A: real,X2: real] :
% 5.52/5.85 ( ( ord_less_real @ one_one_real @ A )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X2 ) )
% 5.52/5.85 = ( ord_less_real @ A @ X2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % one_less_log_cancel_iff
% 5.52/5.85 thf(fact_6795_log__less__one__cancel__iff,axiom,
% 5.52/5.85 ! [A: real,X2: real] :
% 5.52/5.85 ( ( ord_less_real @ one_one_real @ A )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_real @ ( log @ A @ X2 ) @ one_one_real )
% 5.52/5.85 = ( ord_less_real @ X2 @ A ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_less_one_cancel_iff
% 5.52/5.85 thf(fact_6796_log__less__cancel__iff,axiom,
% 5.52/5.85 ! [A: real,X2: real,Y2: real] :
% 5.52/5.85 ( ( ord_less_real @ one_one_real @ A )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.85 => ( ( ord_less_real @ ( log @ A @ X2 ) @ ( log @ A @ Y2 ) )
% 5.52/5.85 = ( ord_less_real @ X2 @ Y2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_less_cancel_iff
% 5.52/5.85 thf(fact_6797_log__eq__one,axiom,
% 5.52/5.85 ! [A: real] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.85 => ( ( A != one_one_real )
% 5.52/5.85 => ( ( log @ A @ A )
% 5.52/5.85 = one_one_real ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_eq_one
% 5.52/5.85 thf(fact_6798_signed__take__bit__nonnegative__iff,axiom,
% 5.52/5.85 ! [N: nat,K: int] :
% 5.52/5.85 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.52/5.85 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % signed_take_bit_nonnegative_iff
% 5.52/5.85 thf(fact_6799_signed__take__bit__negative__iff,axiom,
% 5.52/5.85 ! [N: nat,K: int] :
% 5.52/5.85 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 5.52/5.85 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % signed_take_bit_negative_iff
% 5.52/5.85 thf(fact_6800_of__nat__0__less__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.85 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_less_iff
% 5.52/5.85 thf(fact_6801_of__nat__0__less__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.52/5.85 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_less_iff
% 5.52/5.85 thf(fact_6802_of__nat__0__less__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.52/5.85 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_less_iff
% 5.52/5.85 thf(fact_6803_of__nat__0__less__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.52/5.85 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_less_iff
% 5.52/5.85 thf(fact_6804_of__nat__0__less__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( semiri4216267220026989637d_enat @ N ) )
% 5.52/5.85 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_less_iff
% 5.52/5.85 thf(fact_6805_and__nat__numerals_I2_J,axiom,
% 5.52/5.85 ! [Y2: num] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.52/5.85 = one_one_nat ) ).
% 5.52/5.85
% 5.52/5.85 % and_nat_numerals(2)
% 5.52/5.85 thf(fact_6806_and__nat__numerals_I4_J,axiom,
% 5.52/5.85 ! [X2: num] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.52/5.85 = one_one_nat ) ).
% 5.52/5.85
% 5.52/5.85 % and_nat_numerals(4)
% 5.52/5.85 thf(fact_6807_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.52/5.85 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6808_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.52/5.85 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6809_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.52/5.85 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6810_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.52/5.85 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6811_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.52/5.85 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_less_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6812_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.52/5.85 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_less_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6813_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.52/5.85 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_less_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6814_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.52/5.85 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_less_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6815_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [Y2: nat,X2: num,N: nat] :
% 5.52/5.85 ( ( ( semiri8010041392384452111omplex @ Y2 )
% 5.52/5.85 = ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N ) )
% 5.52/5.85 = ( Y2
% 5.52/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_of_nat_eq_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6816_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [Y2: nat,X2: num,N: nat] :
% 5.52/5.85 ( ( ( semiri1314217659103216013at_int @ Y2 )
% 5.52/5.85 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.52/5.85 = ( Y2
% 5.52/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_of_nat_eq_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6817_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [Y2: nat,X2: num,N: nat] :
% 5.52/5.85 ( ( ( semiri5074537144036343181t_real @ Y2 )
% 5.52/5.85 = ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.52/5.85 = ( Y2
% 5.52/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_of_nat_eq_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6818_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [Y2: nat,X2: num,N: nat] :
% 5.52/5.85 ( ( ( semiri1316708129612266289at_nat @ Y2 )
% 5.52/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.52/5.85 = ( Y2
% 5.52/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_of_nat_eq_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6819_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [Y2: nat,X2: num,N: nat] :
% 5.52/5.85 ( ( ( semiri681578069525770553at_rat @ Y2 )
% 5.52/5.85 = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.52/5.85 = ( Y2
% 5.52/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_of_nat_eq_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6820_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [Y2: nat,X2: num,N: nat] :
% 5.52/5.85 ( ( ( semiri4216267220026989637d_enat @ Y2 )
% 5.52/5.85 = ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ X2 ) @ N ) )
% 5.52/5.85 = ( Y2
% 5.52/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_of_nat_eq_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6821_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: num,N: nat,Y2: nat] :
% 5.52/5.85 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N )
% 5.52/5.85 = ( semiri8010041392384452111omplex @ Y2 ) )
% 5.52/5.85 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.52/5.85 = Y2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_eq_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6822_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: num,N: nat,Y2: nat] :
% 5.52/5.85 ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.52/5.85 = ( semiri1314217659103216013at_int @ Y2 ) )
% 5.52/5.85 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.52/5.85 = Y2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_eq_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6823_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: num,N: nat,Y2: nat] :
% 5.52/5.85 ( ( ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N )
% 5.52/5.85 = ( semiri5074537144036343181t_real @ Y2 ) )
% 5.52/5.85 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.52/5.85 = Y2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_eq_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6824_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: num,N: nat,Y2: nat] :
% 5.52/5.85 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.52/5.85 = ( semiri1316708129612266289at_nat @ Y2 ) )
% 5.52/5.85 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.52/5.85 = Y2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_eq_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6825_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: num,N: nat,Y2: nat] :
% 5.52/5.85 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 5.52/5.85 = ( semiri681578069525770553at_rat @ Y2 ) )
% 5.52/5.85 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.52/5.85 = Y2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_eq_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6826_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: num,N: nat,Y2: nat] :
% 5.52/5.85 ( ( ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ X2 ) @ N )
% 5.52/5.85 = ( semiri4216267220026989637d_enat @ Y2 ) )
% 5.52/5.85 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.52/5.85 = Y2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_eq_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6827_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.52/5.85 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_le_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6828_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.52/5.85 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_le_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6829_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.52/5.85 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_le_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6830_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,B: nat,W: nat] :
% 5.52/5.85 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.52/5.85 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_power_le_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6831_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.52/5.85 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6832_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.52/5.85 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6833_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.52/5.85 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6834_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.52/5.85 ! [B: nat,W: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.52/5.85 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_of_nat_power_cancel_iff
% 5.52/5.85 thf(fact_6835_log__le__cancel__iff,axiom,
% 5.52/5.85 ! [A: real,X2: real,Y2: real] :
% 5.52/5.85 ( ( ord_less_real @ one_one_real @ A )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.85 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ ( log @ A @ Y2 ) )
% 5.52/5.85 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_le_cancel_iff
% 5.52/5.85 thf(fact_6836_log__le__one__cancel__iff,axiom,
% 5.52/5.85 ! [A: real,X2: real] :
% 5.52/5.85 ( ( ord_less_real @ one_one_real @ A )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ one_one_real )
% 5.52/5.85 = ( ord_less_eq_real @ X2 @ A ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_le_one_cancel_iff
% 5.52/5.85 thf(fact_6837_one__le__log__cancel__iff,axiom,
% 5.52/5.85 ! [A: real,X2: real] :
% 5.52/5.85 ( ( ord_less_real @ one_one_real @ A )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X2 ) )
% 5.52/5.85 = ( ord_less_eq_real @ A @ X2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % one_le_log_cancel_iff
% 5.52/5.85 thf(fact_6838_log__le__zero__cancel__iff,axiom,
% 5.52/5.85 ! [A: real,X2: real] :
% 5.52/5.85 ( ( ord_less_real @ one_one_real @ A )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ zero_zero_real )
% 5.52/5.85 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_le_zero_cancel_iff
% 5.52/5.85 thf(fact_6839_zero__le__log__cancel__iff,axiom,
% 5.52/5.85 ! [A: real,X2: real] :
% 5.52/5.85 ( ( ord_less_real @ one_one_real @ A )
% 5.52/5.85 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X2 ) )
% 5.52/5.85 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % zero_le_log_cancel_iff
% 5.52/5.85 thf(fact_6840_log__pow__cancel,axiom,
% 5.52/5.85 ! [A: real,B: nat] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.85 => ( ( A != one_one_real )
% 5.52/5.85 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.52/5.85 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_pow_cancel
% 5.52/5.85 thf(fact_6841_bit__numeral__simps_I2_J,axiom,
% 5.52/5.85 ! [W: num,N: num] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_numeral_simps(2)
% 5.52/5.85 thf(fact_6842_bit__numeral__simps_I2_J,axiom,
% 5.52/5.85 ! [W: num,N: num] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_numeral_simps(2)
% 5.52/5.85 thf(fact_6843_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.52/5.85 ! [W: num,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 5.52/5.85 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_minus_numeral_Bit0_Suc_iff
% 5.52/5.85 thf(fact_6844_bit__numeral__simps_I3_J,axiom,
% 5.52/5.85 ! [W: num,N: num] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_numeral_simps(3)
% 5.52/5.85 thf(fact_6845_bit__numeral__simps_I3_J,axiom,
% 5.52/5.85 ! [W: num,N: num] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_numeral_simps(3)
% 5.52/5.85 thf(fact_6846_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.52/5.85 ! [W: num,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 5.52/5.85 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_minus_numeral_Bit1_Suc_iff
% 5.52/5.85 thf(fact_6847_of__nat__zero__less__power__iff,axiom,
% 5.52/5.85 ! [X2: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X2 ) @ N ) )
% 5.52/5.85 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.52/5.85 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_zero_less_power_iff
% 5.52/5.85 thf(fact_6848_of__nat__zero__less__power__iff,axiom,
% 5.52/5.85 ! [X2: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X2 ) @ N ) )
% 5.52/5.85 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.52/5.85 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_zero_less_power_iff
% 5.52/5.85 thf(fact_6849_of__nat__zero__less__power__iff,axiom,
% 5.52/5.85 ! [X2: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ N ) )
% 5.52/5.85 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.52/5.85 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_zero_less_power_iff
% 5.52/5.85 thf(fact_6850_of__nat__zero__less__power__iff,axiom,
% 5.52/5.85 ! [X2: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X2 ) @ N ) )
% 5.52/5.85 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.52/5.85 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_zero_less_power_iff
% 5.52/5.85 thf(fact_6851_bit__0,axiom,
% 5.52/5.85 ! [A: code_integer] :
% 5.52/5.85 ( ( bit_se9216721137139052372nteger @ A @ zero_zero_nat )
% 5.52/5.85 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_0
% 5.52/5.85 thf(fact_6852_bit__0,axiom,
% 5.52/5.85 ! [A: int] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ A @ zero_zero_nat )
% 5.52/5.85 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_0
% 5.52/5.85 thf(fact_6853_bit__0,axiom,
% 5.52/5.85 ! [A: nat] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ A @ zero_zero_nat )
% 5.52/5.85 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_0
% 5.52/5.85 thf(fact_6854_and__Suc__0__eq,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.52/5.85 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % and_Suc_0_eq
% 5.52/5.85 thf(fact_6855_Suc__0__and__eq,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.52/5.85 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % Suc_0_and_eq
% 5.52/5.85 thf(fact_6856_bit__minus__numeral__int_I1_J,axiom,
% 5.52/5.85 ! [W: num,N: num] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_minus_numeral_int(1)
% 5.52/5.85 thf(fact_6857_bit__minus__numeral__int_I2_J,axiom,
% 5.52/5.85 ! [W: num,N: num] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_minus_numeral_int(2)
% 5.52/5.85 thf(fact_6858_even__of__nat,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.52/5.85 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % even_of_nat
% 5.52/5.85 thf(fact_6859_even__of__nat,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.85 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % even_of_nat
% 5.52/5.85 thf(fact_6860_even__of__nat,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.52/5.85 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % even_of_nat
% 5.52/5.85 thf(fact_6861_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,I: num,N: nat] :
% 5.52/5.85 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.52/5.85 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6862_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,I: num,N: nat] :
% 5.52/5.85 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.52/5.85 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6863_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,I: num,N: nat] :
% 5.52/5.85 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.52/5.85 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6864_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,I: num,N: nat] :
% 5.52/5.85 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.52/5.85 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6865_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [I: num,N: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.52/5.85 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_less_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6866_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [I: num,N: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.52/5.85 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_less_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6867_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [I: num,N: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.52/5.85 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_less_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6868_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [I: num,N: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.52/5.85 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_less_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6869_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,I: num,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.52/5.85 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6870_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,I: num,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.52/5.85 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6871_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,I: num,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.52/5.85 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6872_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.52/5.85 ! [X2: nat,I: num,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.52/5.85 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_le_numeral_power_cancel_iff
% 5.52/5.85 thf(fact_6873_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [I: num,N: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.52/5.85 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_le_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6874_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [I: num,N: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.52/5.85 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_le_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6875_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [I: num,N: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.52/5.85 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_le_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6876_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.52/5.85 ! [I: num,N: nat,X2: nat] :
% 5.52/5.85 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.52/5.85 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % numeral_power_le_of_nat_cancel_iff
% 5.52/5.85 thf(fact_6877_bit__mod__2__iff,axiom,
% 5.52/5.85 ! [A: code_integer,N: nat] :
% 5.52/5.85 ( ( bit_se9216721137139052372nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N )
% 5.52/5.85 = ( ( N = zero_zero_nat )
% 5.52/5.85 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_mod_2_iff
% 5.52/5.85 thf(fact_6878_bit__mod__2__iff,axiom,
% 5.52/5.85 ! [A: int,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N )
% 5.52/5.85 = ( ( N = zero_zero_nat )
% 5.52/5.85 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_mod_2_iff
% 5.52/5.85 thf(fact_6879_bit__mod__2__iff,axiom,
% 5.52/5.85 ! [A: nat,N: nat] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.52/5.85 = ( ( N = zero_zero_nat )
% 5.52/5.85 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_mod_2_iff
% 5.52/5.85 thf(fact_6880_bit__of__nat__iff__bit,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( semiri1314217659103216013at_int @ M ) @ N )
% 5.52/5.85 = ( bit_se1148574629649215175it_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_of_nat_iff_bit
% 5.52/5.85 thf(fact_6881_bit__of__nat__iff__bit,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ ( semiri1316708129612266289at_nat @ M ) @ N )
% 5.52/5.85 = ( bit_se1148574629649215175it_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_of_nat_iff_bit
% 5.52/5.85 thf(fact_6882_bit__numeral__iff,axiom,
% 5.52/5.85 ! [M: num,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N )
% 5.52/5.85 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_numeral_iff
% 5.52/5.85 thf(fact_6883_bit__numeral__iff,axiom,
% 5.52/5.85 ! [M: num,N: nat] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N )
% 5.52/5.85 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_numeral_iff
% 5.52/5.85 thf(fact_6884_bit__disjunctive__add__iff,axiom,
% 5.52/5.85 ! [A: int,B: int,N: nat] :
% 5.52/5.85 ( ! [N2: nat] :
% 5.52/5.85 ( ~ ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.52/5.85 | ~ ( bit_se1146084159140164899it_int @ B @ N2 ) )
% 5.52/5.85 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.52/5.85 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.52/5.85 | ( bit_se1146084159140164899it_int @ B @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_disjunctive_add_iff
% 5.52/5.85 thf(fact_6885_bit__disjunctive__add__iff,axiom,
% 5.52/5.85 ! [A: nat,B: nat,N: nat] :
% 5.52/5.85 ( ! [N2: nat] :
% 5.52/5.85 ( ~ ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.52/5.85 | ~ ( bit_se1148574629649215175it_nat @ B @ N2 ) )
% 5.52/5.85 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.52/5.85 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.52/5.85 | ( bit_se1148574629649215175it_nat @ B @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_disjunctive_add_iff
% 5.52/5.85 thf(fact_6886_real__arch__simple,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ? [N2: nat] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_arch_simple
% 5.52/5.85 thf(fact_6887_real__arch__simple,axiom,
% 5.52/5.85 ! [X2: rat] :
% 5.52/5.85 ? [N2: nat] : ( ord_less_eq_rat @ X2 @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_arch_simple
% 5.52/5.85 thf(fact_6888_reals__Archimedean2,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ? [N2: nat] : ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % reals_Archimedean2
% 5.52/5.85 thf(fact_6889_reals__Archimedean2,axiom,
% 5.52/5.85 ! [X2: rat] :
% 5.52/5.85 ? [N2: nat] : ( ord_less_rat @ X2 @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % reals_Archimedean2
% 5.52/5.85 thf(fact_6890_mult__of__nat__commute,axiom,
% 5.52/5.85 ! [X2: nat,Y2: int] :
% 5.52/5.85 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X2 ) @ Y2 )
% 5.52/5.85 = ( times_times_int @ Y2 @ ( semiri1314217659103216013at_int @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mult_of_nat_commute
% 5.52/5.85 thf(fact_6891_mult__of__nat__commute,axiom,
% 5.52/5.85 ! [X2: nat,Y2: real] :
% 5.52/5.85 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ Y2 )
% 5.52/5.85 = ( times_times_real @ Y2 @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mult_of_nat_commute
% 5.52/5.85 thf(fact_6892_mult__of__nat__commute,axiom,
% 5.52/5.85 ! [X2: nat,Y2: nat] :
% 5.52/5.85 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ Y2 )
% 5.52/5.85 = ( times_times_nat @ Y2 @ ( semiri1316708129612266289at_nat @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mult_of_nat_commute
% 5.52/5.85 thf(fact_6893_mult__of__nat__commute,axiom,
% 5.52/5.85 ! [X2: nat,Y2: rat] :
% 5.52/5.85 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X2 ) @ Y2 )
% 5.52/5.85 = ( times_times_rat @ Y2 @ ( semiri681578069525770553at_rat @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mult_of_nat_commute
% 5.52/5.85 thf(fact_6894_mult__of__nat__commute,axiom,
% 5.52/5.85 ! [X2: nat,Y2: extended_enat] :
% 5.52/5.85 ( ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ X2 ) @ Y2 )
% 5.52/5.85 = ( times_7803423173614009249d_enat @ Y2 @ ( semiri4216267220026989637d_enat @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mult_of_nat_commute
% 5.52/5.85 thf(fact_6895_bit__and__iff,axiom,
% 5.52/5.85 ! [A: int,B: int,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ N )
% 5.52/5.85 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.52/5.85 & ( bit_se1146084159140164899it_int @ B @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_and_iff
% 5.52/5.85 thf(fact_6896_bit__and__iff,axiom,
% 5.52/5.85 ! [A: nat,B: nat,N: nat] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ N )
% 5.52/5.85 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.52/5.85 & ( bit_se1148574629649215175it_nat @ B @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_and_iff
% 5.52/5.85 thf(fact_6897_of__nat__and__eq,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.52/5.85 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_and_eq
% 5.52/5.85 thf(fact_6898_of__nat__and__eq,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.52/5.85 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_and_eq
% 5.52/5.85 thf(fact_6899_bit__and__int__iff,axiom,
% 5.52/5.85 ! [K: int,L: int,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ N )
% 5.52/5.85 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.52/5.85 & ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_and_int_iff
% 5.52/5.85 thf(fact_6900_bit__unset__bit__iff,axiom,
% 5.52/5.85 ! [M: nat,A: int,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( bit_se4203085406695923979it_int @ M @ A ) @ N )
% 5.52/5.85 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.52/5.85 & ( M != N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_unset_bit_iff
% 5.52/5.85 thf(fact_6901_bit__unset__bit__iff,axiom,
% 5.52/5.85 ! [M: nat,A: nat,N: nat] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ ( bit_se4205575877204974255it_nat @ M @ A ) @ N )
% 5.52/5.85 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.52/5.85 & ( M != N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_unset_bit_iff
% 5.52/5.85 thf(fact_6902_log__of__power__eq,axiom,
% 5.52/5.85 ! [M: nat,B: real,N: nat] :
% 5.52/5.85 ( ( ( semiri5074537144036343181t_real @ M )
% 5.52/5.85 = ( power_power_real @ B @ N ) )
% 5.52/5.85 => ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.85 => ( ( semiri5074537144036343181t_real @ N )
% 5.52/5.85 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_of_power_eq
% 5.52/5.85 thf(fact_6903_less__log__of__power,axiom,
% 5.52/5.85 ! [B: real,N: nat,M: real] :
% 5.52/5.85 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 5.52/5.85 => ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.85 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % less_log_of_power
% 5.52/5.85 thf(fact_6904_of__nat__less__of__int__iff,axiom,
% 5.52/5.85 ! [N: nat,X2: int] :
% 5.52/5.85 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X2 ) )
% 5.52/5.85 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_of_int_iff
% 5.52/5.85 thf(fact_6905_of__nat__less__of__int__iff,axiom,
% 5.52/5.85 ! [N: nat,X2: int] :
% 5.52/5.85 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X2 ) )
% 5.52/5.85 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_of_int_iff
% 5.52/5.85 thf(fact_6906_of__nat__less__of__int__iff,axiom,
% 5.52/5.85 ! [N: nat,X2: int] :
% 5.52/5.85 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.52/5.85 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_of_int_iff
% 5.52/5.85 thf(fact_6907_le__log__of__power,axiom,
% 5.52/5.85 ! [B: real,N: nat,M: real] :
% 5.52/5.85 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 5.52/5.85 => ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.85 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % le_log_of_power
% 5.52/5.85 thf(fact_6908_log__base__pow,axiom,
% 5.52/5.85 ! [A: real,N: nat,X2: real] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.85 => ( ( log @ ( power_power_real @ A @ N ) @ X2 )
% 5.52/5.85 = ( divide_divide_real @ ( log @ A @ X2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_base_pow
% 5.52/5.85 thf(fact_6909_log__nat__power,axiom,
% 5.52/5.85 ! [X2: real,B: real,N: nat] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ( ( log @ B @ ( power_power_real @ X2 @ N ) )
% 5.52/5.85 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_nat_power
% 5.52/5.85 thf(fact_6910_not__bit__1__Suc,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % not_bit_1_Suc
% 5.52/5.85 thf(fact_6911_not__bit__1__Suc,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % not_bit_1_Suc
% 5.52/5.85 thf(fact_6912_bit__1__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ one_one_int @ N )
% 5.52/5.85 = ( N = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_1_iff
% 5.52/5.85 thf(fact_6913_bit__1__iff,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N )
% 5.52/5.85 = ( N = zero_zero_nat ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_1_iff
% 5.52/5.85 thf(fact_6914_bit__numeral__simps_I1_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_numeral_simps(1)
% 5.52/5.85 thf(fact_6915_bit__numeral__simps_I1_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_numeral_simps(1)
% 5.52/5.85 thf(fact_6916_of__nat__0__le__iff,axiom,
% 5.52/5.85 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_le_iff
% 5.52/5.85 thf(fact_6917_of__nat__0__le__iff,axiom,
% 5.52/5.85 ! [N: nat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( semiri4216267220026989637d_enat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_le_iff
% 5.52/5.85 thf(fact_6918_of__nat__0__le__iff,axiom,
% 5.52/5.85 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_le_iff
% 5.52/5.85 thf(fact_6919_of__nat__0__le__iff,axiom,
% 5.52/5.85 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_le_iff
% 5.52/5.85 thf(fact_6920_of__nat__0__le__iff,axiom,
% 5.52/5.85 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_0_le_iff
% 5.52/5.85 thf(fact_6921_of__nat__less__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_0_iff
% 5.52/5.85 thf(fact_6922_of__nat__less__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_0_iff
% 5.52/5.85 thf(fact_6923_of__nat__less__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_0_iff
% 5.52/5.85 thf(fact_6924_of__nat__less__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_0_iff
% 5.52/5.85 thf(fact_6925_of__nat__less__0__iff,axiom,
% 5.52/5.85 ! [M: nat] :
% 5.52/5.85 ~ ( ord_le72135733267957522d_enat @ ( semiri4216267220026989637d_enat @ M ) @ zero_z5237406670263579293d_enat ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_0_iff
% 5.52/5.85 thf(fact_6926_bit__take__bit__iff,axiom,
% 5.52/5.85 ! [M: nat,A: int,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M @ A ) @ N )
% 5.52/5.85 = ( ( ord_less_nat @ N @ M )
% 5.52/5.85 & ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_take_bit_iff
% 5.52/5.85 thf(fact_6927_bit__take__bit__iff,axiom,
% 5.52/5.85 ! [M: nat,A: nat,N: nat] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M @ A ) @ N )
% 5.52/5.85 = ( ( ord_less_nat @ N @ M )
% 5.52/5.85 & ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_take_bit_iff
% 5.52/5.85 thf(fact_6928_of__nat__neq__0,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.52/5.85 != zero_zero_int ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_neq_0
% 5.52/5.85 thf(fact_6929_of__nat__neq__0,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.52/5.85 != zero_zero_real ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_neq_0
% 5.52/5.85 thf(fact_6930_of__nat__neq__0,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.52/5.85 != zero_zero_nat ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_neq_0
% 5.52/5.85 thf(fact_6931_of__nat__neq__0,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.52/5.85 != zero_zero_rat ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_neq_0
% 5.52/5.85 thf(fact_6932_of__nat__neq__0,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( semiri4216267220026989637d_enat @ ( suc @ N ) )
% 5.52/5.85 != zero_z5237406670263579293d_enat ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_neq_0
% 5.52/5.85 thf(fact_6933_bit__of__bool__iff,axiom,
% 5.52/5.85 ! [B: $o,N: nat] :
% 5.52/5.85 ( ( bit_se9216721137139052372nteger @ ( zero_n356916108424825756nteger @ B ) @ N )
% 5.52/5.85 = ( B
% 5.52/5.85 & ( N = zero_zero_nat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_of_bool_iff
% 5.52/5.85 thf(fact_6934_bit__of__bool__iff,axiom,
% 5.52/5.85 ! [B: $o,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( zero_n2684676970156552555ol_int @ B ) @ N )
% 5.52/5.85 = ( B
% 5.52/5.85 & ( N = zero_zero_nat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_of_bool_iff
% 5.52/5.85 thf(fact_6935_bit__of__bool__iff,axiom,
% 5.52/5.85 ! [B: $o,N: nat] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ N )
% 5.52/5.85 = ( B
% 5.52/5.85 & ( N = zero_zero_nat ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_of_bool_iff
% 5.52/5.85 thf(fact_6936_div__mult2__eq_H,axiom,
% 5.52/5.85 ! [A: int,M: nat,N: nat] :
% 5.52/5.85 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.52/5.85 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % div_mult2_eq'
% 5.52/5.85 thf(fact_6937_div__mult2__eq_H,axiom,
% 5.52/5.85 ! [A: nat,M: nat,N: nat] :
% 5.52/5.85 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.52/5.85 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % div_mult2_eq'
% 5.52/5.85 thf(fact_6938_less__imp__of__nat__less,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_nat @ M @ N )
% 5.52/5.85 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % less_imp_of_nat_less
% 5.52/5.85 thf(fact_6939_less__imp__of__nat__less,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_nat @ M @ N )
% 5.52/5.85 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % less_imp_of_nat_less
% 5.52/5.85 thf(fact_6940_less__imp__of__nat__less,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_nat @ M @ N )
% 5.52/5.85 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % less_imp_of_nat_less
% 5.52/5.85 thf(fact_6941_less__imp__of__nat__less,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_nat @ M @ N )
% 5.52/5.85 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % less_imp_of_nat_less
% 5.52/5.85 thf(fact_6942_less__imp__of__nat__less,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_nat @ M @ N )
% 5.52/5.85 => ( ord_le72135733267957522d_enat @ ( semiri4216267220026989637d_enat @ M ) @ ( semiri4216267220026989637d_enat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % less_imp_of_nat_less
% 5.52/5.85 thf(fact_6943_of__nat__less__imp__less,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.85 => ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_imp_less
% 5.52/5.85 thf(fact_6944_of__nat__less__imp__less,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.52/5.85 => ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_imp_less
% 5.52/5.85 thf(fact_6945_of__nat__less__imp__less,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.52/5.85 => ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_imp_less
% 5.52/5.85 thf(fact_6946_of__nat__less__imp__less,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.52/5.85 => ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_imp_less
% 5.52/5.85 thf(fact_6947_of__nat__less__imp__less,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_le72135733267957522d_enat @ ( semiri4216267220026989637d_enat @ M ) @ ( semiri4216267220026989637d_enat @ N ) )
% 5.52/5.85 => ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_less_imp_less
% 5.52/5.85 thf(fact_6948_of__nat__mono,axiom,
% 5.52/5.85 ! [I: nat,J: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.52/5.85 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mono
% 5.52/5.85 thf(fact_6949_of__nat__mono,axiom,
% 5.52/5.85 ! [I: nat,J: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.52/5.85 => ( ord_le2932123472753598470d_enat @ ( semiri4216267220026989637d_enat @ I ) @ ( semiri4216267220026989637d_enat @ J ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mono
% 5.52/5.85 thf(fact_6950_of__nat__mono,axiom,
% 5.52/5.85 ! [I: nat,J: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.52/5.85 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mono
% 5.52/5.85 thf(fact_6951_of__nat__mono,axiom,
% 5.52/5.85 ! [I: nat,J: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.52/5.85 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mono
% 5.52/5.85 thf(fact_6952_of__nat__mono,axiom,
% 5.52/5.85 ! [I: nat,J: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.52/5.85 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mono
% 5.52/5.85 thf(fact_6953_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 5.52/5.85 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.52/5.85 thf(fact_6954_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 5.52/5.85 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.52/5.85 thf(fact_6955_of__nat__dvd__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.52/5.85 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_dvd_iff
% 5.52/5.85 thf(fact_6956_of__nat__dvd__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.85 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_dvd_iff
% 5.52/5.85 thf(fact_6957_of__nat__dvd__iff,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.52/5.85 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_dvd_iff
% 5.52/5.85 thf(fact_6958_signed__take__bit__eq__if__positive,axiom,
% 5.52/5.85 ! [A: int,N: nat] :
% 5.52/5.85 ( ~ ( bit_se1146084159140164899it_int @ A @ N )
% 5.52/5.85 => ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.52/5.85 = ( bit_se2923211474154528505it_int @ N @ A ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % signed_take_bit_eq_if_positive
% 5.52/5.85 thf(fact_6959_int__ops_I3_J,axiom,
% 5.52/5.85 ! [N: num] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.52/5.85 = ( numeral_numeral_int @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % int_ops(3)
% 5.52/5.85 thf(fact_6960_nat__int__comparison_I2_J,axiom,
% 5.52/5.85 ( ord_less_nat
% 5.52/5.85 = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % nat_int_comparison(2)
% 5.52/5.85 thf(fact_6961_nat__int__comparison_I3_J,axiom,
% 5.52/5.85 ( ord_less_eq_nat
% 5.52/5.85 = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % nat_int_comparison(3)
% 5.52/5.85 thf(fact_6962_zle__int,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.85 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % zle_int
% 5.52/5.85 thf(fact_6963_int__ops_I2_J,axiom,
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.52/5.85 = one_one_int ) ).
% 5.52/5.85
% 5.52/5.85 % int_ops(2)
% 5.52/5.85 thf(fact_6964_of__nat__mod,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 5.52/5.85 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mod
% 5.52/5.85 thf(fact_6965_of__nat__mod,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.52/5.85 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mod
% 5.52/5.85 thf(fact_6966_int__plus,axiom,
% 5.52/5.85 ! [N: nat,M: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 5.52/5.85 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % int_plus
% 5.52/5.85 thf(fact_6967_int__ops_I5_J,axiom,
% 5.52/5.85 ! [A: nat,B: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.52/5.85 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % int_ops(5)
% 5.52/5.85 thf(fact_6968_zadd__int__left,axiom,
% 5.52/5.85 ! [M: nat,N: nat,Z: int] :
% 5.52/5.85 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 5.52/5.85 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 5.52/5.85
% 5.52/5.85 % zadd_int_left
% 5.52/5.85 thf(fact_6969_int__ops_I7_J,axiom,
% 5.52/5.85 ! [A: nat,B: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.52/5.85 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % int_ops(7)
% 5.52/5.85 thf(fact_6970_not__int__zless__negative,axiom,
% 5.52/5.85 ! [N: nat,M: nat] :
% 5.52/5.85 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % not_int_zless_negative
% 5.52/5.85 thf(fact_6971_zdiv__int,axiom,
% 5.52/5.85 ! [A: nat,B: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.52/5.85 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % zdiv_int
% 5.52/5.85 thf(fact_6972_of__nat__max,axiom,
% 5.52/5.85 ! [X2: nat,Y2: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.52/5.85 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_max
% 5.52/5.85 thf(fact_6973_of__nat__max,axiom,
% 5.52/5.85 ! [X2: nat,Y2: nat] :
% 5.52/5.85 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.52/5.85 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( semiri5074537144036343181t_real @ Y2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_max
% 5.52/5.85 thf(fact_6974_of__nat__max,axiom,
% 5.52/5.85 ! [X2: nat,Y2: nat] :
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.52/5.85 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( semiri1316708129612266289at_nat @ Y2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_max
% 5.52/5.85 thf(fact_6975_of__nat__max,axiom,
% 5.52/5.85 ! [X2: nat,Y2: nat] :
% 5.52/5.85 ( ( semiri681578069525770553at_rat @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.52/5.85 = ( ord_max_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( semiri681578069525770553at_rat @ Y2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_max
% 5.52/5.85 thf(fact_6976_of__nat__max,axiom,
% 5.52/5.85 ! [X2: nat,Y2: nat] :
% 5.52/5.85 ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.52/5.85 = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X2 ) @ ( semiri4216267220026989637d_enat @ Y2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_max
% 5.52/5.85 thf(fact_6977_log2__of__power__eq,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( M
% 5.52/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.85 => ( ( semiri5074537144036343181t_real @ N )
% 5.52/5.85 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log2_of_power_eq
% 5.52/5.85 thf(fact_6978_log__of__power__less,axiom,
% 5.52/5.85 ! [M: nat,B: real,N: nat] :
% 5.52/5.85 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.52/5.85 => ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.85 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.85 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_of_power_less
% 5.52/5.85 thf(fact_6979_zmod__int,axiom,
% 5.52/5.85 ! [A: nat,B: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 5.52/5.85 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % zmod_int
% 5.52/5.85 thf(fact_6980_take__bit__of__nat,axiom,
% 5.52/5.85 ! [N: nat,M: nat] :
% 5.52/5.85 ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 5.52/5.85 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_of_nat
% 5.52/5.85 thf(fact_6981_take__bit__of__nat,axiom,
% 5.52/5.85 ! [N: nat,M: nat] :
% 5.52/5.85 ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 5.52/5.85 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % take_bit_of_nat
% 5.52/5.85 thf(fact_6982_nat__less__as__int,axiom,
% 5.52/5.85 ( ord_less_nat
% 5.52/5.85 = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % nat_less_as_int
% 5.52/5.85 thf(fact_6983_of__nat__mask__eq,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.52/5.85 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mask_eq
% 5.52/5.85 thf(fact_6984_of__nat__mask__eq,axiom,
% 5.52/5.85 ! [N: nat] :
% 5.52/5.85 ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.52/5.85 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_mask_eq
% 5.52/5.85 thf(fact_6985_nat__leq__as__int,axiom,
% 5.52/5.85 ( ord_less_eq_nat
% 5.52/5.85 = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % nat_leq_as_int
% 5.52/5.85 thf(fact_6986_log__of__power__le,axiom,
% 5.52/5.85 ! [M: nat,B: real,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.52/5.85 => ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.85 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.85 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_of_power_le
% 5.52/5.85 thf(fact_6987_ex__less__of__nat__mult,axiom,
% 5.52/5.85 ! [X2: real,Y2: real] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ? [N2: nat] : ( ord_less_real @ Y2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % ex_less_of_nat_mult
% 5.52/5.85 thf(fact_6988_ex__less__of__nat__mult,axiom,
% 5.52/5.85 ! [X2: rat,Y2: rat] :
% 5.52/5.85 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.52/5.85 => ? [N2: nat] : ( ord_less_rat @ Y2 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % ex_less_of_nat_mult
% 5.52/5.85 thf(fact_6989_of__nat__diff,axiom,
% 5.52/5.85 ! [N: nat,M: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.85 => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_diff
% 5.52/5.85 thf(fact_6990_of__nat__diff,axiom,
% 5.52/5.85 ! [N: nat,M: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.85 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_diff
% 5.52/5.85 thf(fact_6991_of__nat__diff,axiom,
% 5.52/5.85 ! [N: nat,M: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.85 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_diff
% 5.52/5.85 thf(fact_6992_of__nat__diff,axiom,
% 5.52/5.85 ! [N: nat,M: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.85 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_diff
% 5.52/5.85 thf(fact_6993_of__nat__diff,axiom,
% 5.52/5.85 ! [N: nat,M: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.85 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 5.52/5.85 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % of_nat_diff
% 5.52/5.85 thf(fact_6994_bit__not__int__iff_H,axiom,
% 5.52/5.85 ! [K: int,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 5.52/5.85 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_not_int_iff'
% 5.52/5.85 thf(fact_6995_finite__ranking__induct,axiom,
% 5.52/5.85 ! [S3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > rat] :
% 5.52/5.85 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.52/5.85 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.52/5.85 => ( ! [X4: vEBT_VEBT,S4: set_VEBT_VEBT] :
% 5.52/5.85 ( ( finite5795047828879050333T_VEBT @ S4 )
% 5.52/5.85 => ( ! [Y4: vEBT_VEBT] :
% 5.52/5.85 ( ( member_VEBT_VEBT @ Y4 @ S4 )
% 5.52/5.85 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( P @ S4 )
% 5.52/5.85 => ( P @ ( insert_VEBT_VEBT @ X4 @ S4 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_ranking_induct
% 5.52/5.85 thf(fact_6996_finite__ranking__induct,axiom,
% 5.52/5.85 ! [S3: set_real,P: set_real > $o,F: real > rat] :
% 5.52/5.85 ( ( finite_finite_real @ S3 )
% 5.52/5.85 => ( ( P @ bot_bot_set_real )
% 5.52/5.85 => ( ! [X4: real,S4: set_real] :
% 5.52/5.85 ( ( finite_finite_real @ S4 )
% 5.52/5.85 => ( ! [Y4: real] :
% 5.52/5.85 ( ( member_real @ Y4 @ S4 )
% 5.52/5.85 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( P @ S4 )
% 5.52/5.85 => ( P @ ( insert_real @ X4 @ S4 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_ranking_induct
% 5.52/5.85 thf(fact_6997_finite__ranking__induct,axiom,
% 5.52/5.85 ! [S3: set_complex,P: set_complex > $o,F: complex > rat] :
% 5.52/5.85 ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.85 => ( ( P @ bot_bot_set_complex )
% 5.52/5.85 => ( ! [X4: complex,S4: set_complex] :
% 5.52/5.85 ( ( finite3207457112153483333omplex @ S4 )
% 5.52/5.85 => ( ! [Y4: complex] :
% 5.52/5.85 ( ( member_complex @ Y4 @ S4 )
% 5.52/5.85 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( P @ S4 )
% 5.52/5.85 => ( P @ ( insert_complex @ X4 @ S4 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_ranking_induct
% 5.52/5.85 thf(fact_6998_finite__ranking__induct,axiom,
% 5.52/5.85 ! [S3: set_nat,P: set_nat > $o,F: nat > rat] :
% 5.52/5.85 ( ( finite_finite_nat @ S3 )
% 5.52/5.85 => ( ( P @ bot_bot_set_nat )
% 5.52/5.85 => ( ! [X4: nat,S4: set_nat] :
% 5.52/5.85 ( ( finite_finite_nat @ S4 )
% 5.52/5.85 => ( ! [Y4: nat] :
% 5.52/5.85 ( ( member_nat @ Y4 @ S4 )
% 5.52/5.85 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( P @ S4 )
% 5.52/5.85 => ( P @ ( insert_nat @ X4 @ S4 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_ranking_induct
% 5.52/5.85 thf(fact_6999_finite__ranking__induct,axiom,
% 5.52/5.85 ! [S3: set_int,P: set_int > $o,F: int > rat] :
% 5.52/5.85 ( ( finite_finite_int @ S3 )
% 5.52/5.85 => ( ( P @ bot_bot_set_int )
% 5.52/5.85 => ( ! [X4: int,S4: set_int] :
% 5.52/5.85 ( ( finite_finite_int @ S4 )
% 5.52/5.85 => ( ! [Y4: int] :
% 5.52/5.85 ( ( member_int @ Y4 @ S4 )
% 5.52/5.85 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( P @ S4 )
% 5.52/5.85 => ( P @ ( insert_int @ X4 @ S4 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_ranking_induct
% 5.52/5.85 thf(fact_7000_finite__ranking__induct,axiom,
% 5.52/5.85 ! [S3: set_Extended_enat,P: set_Extended_enat > $o,F: extended_enat > rat] :
% 5.52/5.85 ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.85 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.52/5.85 => ( ! [X4: extended_enat,S4: set_Extended_enat] :
% 5.52/5.85 ( ( finite4001608067531595151d_enat @ S4 )
% 5.52/5.85 => ( ! [Y4: extended_enat] :
% 5.52/5.85 ( ( member_Extended_enat @ Y4 @ S4 )
% 5.52/5.85 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( P @ S4 )
% 5.52/5.85 => ( P @ ( insert_Extended_enat @ X4 @ S4 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_ranking_induct
% 5.52/5.85 thf(fact_7001_finite__ranking__induct,axiom,
% 5.52/5.85 ! [S3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > num] :
% 5.52/5.85 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.52/5.85 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.52/5.85 => ( ! [X4: vEBT_VEBT,S4: set_VEBT_VEBT] :
% 5.52/5.85 ( ( finite5795047828879050333T_VEBT @ S4 )
% 5.52/5.85 => ( ! [Y4: vEBT_VEBT] :
% 5.52/5.85 ( ( member_VEBT_VEBT @ Y4 @ S4 )
% 5.52/5.85 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( P @ S4 )
% 5.52/5.85 => ( P @ ( insert_VEBT_VEBT @ X4 @ S4 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_ranking_induct
% 5.52/5.85 thf(fact_7002_finite__ranking__induct,axiom,
% 5.52/5.85 ! [S3: set_real,P: set_real > $o,F: real > num] :
% 5.52/5.85 ( ( finite_finite_real @ S3 )
% 5.52/5.85 => ( ( P @ bot_bot_set_real )
% 5.52/5.85 => ( ! [X4: real,S4: set_real] :
% 5.52/5.85 ( ( finite_finite_real @ S4 )
% 5.52/5.85 => ( ! [Y4: real] :
% 5.52/5.85 ( ( member_real @ Y4 @ S4 )
% 5.52/5.85 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( P @ S4 )
% 5.52/5.85 => ( P @ ( insert_real @ X4 @ S4 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_ranking_induct
% 5.52/5.85 thf(fact_7003_finite__ranking__induct,axiom,
% 5.52/5.85 ! [S3: set_complex,P: set_complex > $o,F: complex > num] :
% 5.52/5.85 ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.85 => ( ( P @ bot_bot_set_complex )
% 5.52/5.85 => ( ! [X4: complex,S4: set_complex] :
% 5.52/5.85 ( ( finite3207457112153483333omplex @ S4 )
% 5.52/5.85 => ( ! [Y4: complex] :
% 5.52/5.85 ( ( member_complex @ Y4 @ S4 )
% 5.52/5.85 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( P @ S4 )
% 5.52/5.85 => ( P @ ( insert_complex @ X4 @ S4 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_ranking_induct
% 5.52/5.85 thf(fact_7004_finite__ranking__induct,axiom,
% 5.52/5.85 ! [S3: set_nat,P: set_nat > $o,F: nat > num] :
% 5.52/5.85 ( ( finite_finite_nat @ S3 )
% 5.52/5.85 => ( ( P @ bot_bot_set_nat )
% 5.52/5.85 => ( ! [X4: nat,S4: set_nat] :
% 5.52/5.85 ( ( finite_finite_nat @ S4 )
% 5.52/5.85 => ( ! [Y4: nat] :
% 5.52/5.85 ( ( member_nat @ Y4 @ S4 )
% 5.52/5.85 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 5.52/5.85 => ( ( P @ S4 )
% 5.52/5.85 => ( P @ ( insert_nat @ X4 @ S4 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_ranking_induct
% 5.52/5.85 thf(fact_7005_finite__linorder__min__induct,axiom,
% 5.52/5.85 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.52/5.85 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.85 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.52/5.85 => ( ! [B2: extended_enat,A7: set_Extended_enat] :
% 5.52/5.85 ( ( finite4001608067531595151d_enat @ A7 )
% 5.52/5.85 => ( ! [X6: extended_enat] :
% 5.52/5.85 ( ( member_Extended_enat @ X6 @ A7 )
% 5.52/5.85 => ( ord_le72135733267957522d_enat @ B2 @ X6 ) )
% 5.52/5.85 => ( ( P @ A7 )
% 5.52/5.85 => ( P @ ( insert_Extended_enat @ B2 @ A7 ) ) ) ) )
% 5.52/5.85 => ( P @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_linorder_min_induct
% 5.52/5.85 thf(fact_7006_finite__linorder__min__induct,axiom,
% 5.52/5.85 ! [A2: set_real,P: set_real > $o] :
% 5.52/5.85 ( ( finite_finite_real @ A2 )
% 5.52/5.85 => ( ( P @ bot_bot_set_real )
% 5.52/5.85 => ( ! [B2: real,A7: set_real] :
% 5.52/5.85 ( ( finite_finite_real @ A7 )
% 5.52/5.85 => ( ! [X6: real] :
% 5.52/5.85 ( ( member_real @ X6 @ A7 )
% 5.52/5.85 => ( ord_less_real @ B2 @ X6 ) )
% 5.52/5.85 => ( ( P @ A7 )
% 5.52/5.85 => ( P @ ( insert_real @ B2 @ A7 ) ) ) ) )
% 5.52/5.85 => ( P @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_linorder_min_induct
% 5.52/5.85 thf(fact_7007_finite__linorder__min__induct,axiom,
% 5.52/5.85 ! [A2: set_rat,P: set_rat > $o] :
% 5.52/5.85 ( ( finite_finite_rat @ A2 )
% 5.52/5.85 => ( ( P @ bot_bot_set_rat )
% 5.52/5.85 => ( ! [B2: rat,A7: set_rat] :
% 5.52/5.85 ( ( finite_finite_rat @ A7 )
% 5.52/5.85 => ( ! [X6: rat] :
% 5.52/5.85 ( ( member_rat @ X6 @ A7 )
% 5.52/5.85 => ( ord_less_rat @ B2 @ X6 ) )
% 5.52/5.85 => ( ( P @ A7 )
% 5.52/5.85 => ( P @ ( insert_rat @ B2 @ A7 ) ) ) ) )
% 5.52/5.85 => ( P @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_linorder_min_induct
% 5.52/5.85 thf(fact_7008_finite__linorder__min__induct,axiom,
% 5.52/5.85 ! [A2: set_num,P: set_num > $o] :
% 5.52/5.85 ( ( finite_finite_num @ A2 )
% 5.52/5.85 => ( ( P @ bot_bot_set_num )
% 5.52/5.85 => ( ! [B2: num,A7: set_num] :
% 5.52/5.85 ( ( finite_finite_num @ A7 )
% 5.52/5.85 => ( ! [X6: num] :
% 5.52/5.85 ( ( member_num @ X6 @ A7 )
% 5.52/5.85 => ( ord_less_num @ B2 @ X6 ) )
% 5.52/5.85 => ( ( P @ A7 )
% 5.52/5.85 => ( P @ ( insert_num @ B2 @ A7 ) ) ) ) )
% 5.52/5.85 => ( P @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_linorder_min_induct
% 5.52/5.85 thf(fact_7009_finite__linorder__min__induct,axiom,
% 5.52/5.85 ! [A2: set_nat,P: set_nat > $o] :
% 5.52/5.85 ( ( finite_finite_nat @ A2 )
% 5.52/5.85 => ( ( P @ bot_bot_set_nat )
% 5.52/5.85 => ( ! [B2: nat,A7: set_nat] :
% 5.52/5.85 ( ( finite_finite_nat @ A7 )
% 5.52/5.85 => ( ! [X6: nat] :
% 5.52/5.85 ( ( member_nat @ X6 @ A7 )
% 5.52/5.85 => ( ord_less_nat @ B2 @ X6 ) )
% 5.52/5.85 => ( ( P @ A7 )
% 5.52/5.85 => ( P @ ( insert_nat @ B2 @ A7 ) ) ) ) )
% 5.52/5.85 => ( P @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_linorder_min_induct
% 5.52/5.85 thf(fact_7010_finite__linorder__min__induct,axiom,
% 5.52/5.85 ! [A2: set_int,P: set_int > $o] :
% 5.52/5.85 ( ( finite_finite_int @ A2 )
% 5.52/5.85 => ( ( P @ bot_bot_set_int )
% 5.52/5.85 => ( ! [B2: int,A7: set_int] :
% 5.52/5.85 ( ( finite_finite_int @ A7 )
% 5.52/5.85 => ( ! [X6: int] :
% 5.52/5.85 ( ( member_int @ X6 @ A7 )
% 5.52/5.85 => ( ord_less_int @ B2 @ X6 ) )
% 5.52/5.85 => ( ( P @ A7 )
% 5.52/5.85 => ( P @ ( insert_int @ B2 @ A7 ) ) ) ) )
% 5.52/5.85 => ( P @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_linorder_min_induct
% 5.52/5.85 thf(fact_7011_finite__linorder__max__induct,axiom,
% 5.52/5.85 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.52/5.85 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.85 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.52/5.85 => ( ! [B2: extended_enat,A7: set_Extended_enat] :
% 5.52/5.85 ( ( finite4001608067531595151d_enat @ A7 )
% 5.52/5.85 => ( ! [X6: extended_enat] :
% 5.52/5.85 ( ( member_Extended_enat @ X6 @ A7 )
% 5.52/5.85 => ( ord_le72135733267957522d_enat @ X6 @ B2 ) )
% 5.52/5.85 => ( ( P @ A7 )
% 5.52/5.85 => ( P @ ( insert_Extended_enat @ B2 @ A7 ) ) ) ) )
% 5.52/5.85 => ( P @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_linorder_max_induct
% 5.52/5.85 thf(fact_7012_finite__linorder__max__induct,axiom,
% 5.52/5.85 ! [A2: set_real,P: set_real > $o] :
% 5.52/5.85 ( ( finite_finite_real @ A2 )
% 5.52/5.85 => ( ( P @ bot_bot_set_real )
% 5.52/5.85 => ( ! [B2: real,A7: set_real] :
% 5.52/5.85 ( ( finite_finite_real @ A7 )
% 5.52/5.85 => ( ! [X6: real] :
% 5.52/5.85 ( ( member_real @ X6 @ A7 )
% 5.52/5.85 => ( ord_less_real @ X6 @ B2 ) )
% 5.52/5.85 => ( ( P @ A7 )
% 5.52/5.85 => ( P @ ( insert_real @ B2 @ A7 ) ) ) ) )
% 5.52/5.85 => ( P @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_linorder_max_induct
% 5.52/5.85 thf(fact_7013_finite__linorder__max__induct,axiom,
% 5.52/5.85 ! [A2: set_rat,P: set_rat > $o] :
% 5.52/5.85 ( ( finite_finite_rat @ A2 )
% 5.52/5.85 => ( ( P @ bot_bot_set_rat )
% 5.52/5.85 => ( ! [B2: rat,A7: set_rat] :
% 5.52/5.85 ( ( finite_finite_rat @ A7 )
% 5.52/5.85 => ( ! [X6: rat] :
% 5.52/5.85 ( ( member_rat @ X6 @ A7 )
% 5.52/5.85 => ( ord_less_rat @ X6 @ B2 ) )
% 5.52/5.85 => ( ( P @ A7 )
% 5.52/5.85 => ( P @ ( insert_rat @ B2 @ A7 ) ) ) ) )
% 5.52/5.85 => ( P @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_linorder_max_induct
% 5.52/5.85 thf(fact_7014_finite__linorder__max__induct,axiom,
% 5.52/5.85 ! [A2: set_num,P: set_num > $o] :
% 5.52/5.85 ( ( finite_finite_num @ A2 )
% 5.52/5.85 => ( ( P @ bot_bot_set_num )
% 5.52/5.85 => ( ! [B2: num,A7: set_num] :
% 5.52/5.85 ( ( finite_finite_num @ A7 )
% 5.52/5.85 => ( ! [X6: num] :
% 5.52/5.85 ( ( member_num @ X6 @ A7 )
% 5.52/5.85 => ( ord_less_num @ X6 @ B2 ) )
% 5.52/5.85 => ( ( P @ A7 )
% 5.52/5.85 => ( P @ ( insert_num @ B2 @ A7 ) ) ) ) )
% 5.52/5.85 => ( P @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_linorder_max_induct
% 5.52/5.85 thf(fact_7015_finite__linorder__max__induct,axiom,
% 5.52/5.85 ! [A2: set_nat,P: set_nat > $o] :
% 5.52/5.85 ( ( finite_finite_nat @ A2 )
% 5.52/5.85 => ( ( P @ bot_bot_set_nat )
% 5.52/5.85 => ( ! [B2: nat,A7: set_nat] :
% 5.52/5.85 ( ( finite_finite_nat @ A7 )
% 5.52/5.85 => ( ! [X6: nat] :
% 5.52/5.85 ( ( member_nat @ X6 @ A7 )
% 5.52/5.85 => ( ord_less_nat @ X6 @ B2 ) )
% 5.52/5.85 => ( ( P @ A7 )
% 5.52/5.85 => ( P @ ( insert_nat @ B2 @ A7 ) ) ) ) )
% 5.52/5.85 => ( P @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_linorder_max_induct
% 5.52/5.85 thf(fact_7016_finite__linorder__max__induct,axiom,
% 5.52/5.85 ! [A2: set_int,P: set_int > $o] :
% 5.52/5.85 ( ( finite_finite_int @ A2 )
% 5.52/5.85 => ( ( P @ bot_bot_set_int )
% 5.52/5.85 => ( ! [B2: int,A7: set_int] :
% 5.52/5.85 ( ( finite_finite_int @ A7 )
% 5.52/5.85 => ( ! [X6: int] :
% 5.52/5.85 ( ( member_int @ X6 @ A7 )
% 5.52/5.85 => ( ord_less_int @ X6 @ B2 ) )
% 5.52/5.85 => ( ( P @ A7 )
% 5.52/5.85 => ( P @ ( insert_int @ B2 @ A7 ) ) ) ) )
% 5.52/5.85 => ( P @ A2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_linorder_max_induct
% 5.52/5.85 thf(fact_7017_exp__of__nat__mult,axiom,
% 5.52/5.85 ! [N: nat,X2: complex] :
% 5.52/5.85 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X2 ) )
% 5.52/5.85 = ( power_power_complex @ ( exp_complex @ X2 ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_of_nat_mult
% 5.52/5.85 thf(fact_7018_exp__of__nat__mult,axiom,
% 5.52/5.85 ! [N: nat,X2: real] :
% 5.52/5.85 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) )
% 5.52/5.85 = ( power_power_real @ ( exp_real @ X2 ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_of_nat_mult
% 5.52/5.85 thf(fact_7019_exp__of__nat2__mult,axiom,
% 5.52/5.85 ! [X2: complex,N: nat] :
% 5.52/5.85 ( ( exp_complex @ ( times_times_complex @ X2 @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.52/5.85 = ( power_power_complex @ ( exp_complex @ X2 ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_of_nat2_mult
% 5.52/5.85 thf(fact_7020_exp__of__nat2__mult,axiom,
% 5.52/5.85 ! [X2: real,N: nat] :
% 5.52/5.85 ( ( exp_real @ ( times_times_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.52/5.85 = ( power_power_real @ ( exp_real @ X2 ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_of_nat2_mult
% 5.52/5.85 thf(fact_7021_sum_Oinsert__if,axiom,
% 5.52/5.85 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.52/5.85 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.85 => ( ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.85 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.85 = ( groups2240296850493347238T_real @ G @ A2 ) ) )
% 5.52/5.85 & ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.85 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert_if
% 5.52/5.85 thf(fact_7022_sum_Oinsert__if,axiom,
% 5.52/5.85 ! [A2: set_real,X2: real,G: real > real] :
% 5.52/5.85 ( ( finite_finite_real @ A2 )
% 5.52/5.85 => ( ( ( member_real @ X2 @ A2 )
% 5.52/5.85 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X2 @ A2 ) )
% 5.52/5.85 = ( groups8097168146408367636l_real @ G @ A2 ) ) )
% 5.52/5.85 & ( ~ ( member_real @ X2 @ A2 )
% 5.52/5.85 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert_if
% 5.52/5.85 thf(fact_7023_sum_Oinsert__if,axiom,
% 5.52/5.85 ! [A2: set_int,X2: int,G: int > real] :
% 5.52/5.85 ( ( finite_finite_int @ A2 )
% 5.52/5.85 => ( ( ( member_int @ X2 @ A2 )
% 5.52/5.85 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.85 = ( groups8778361861064173332t_real @ G @ A2 ) ) )
% 5.52/5.85 & ( ~ ( member_int @ X2 @ A2 )
% 5.52/5.85 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert_if
% 5.52/5.85 thf(fact_7024_sum_Oinsert__if,axiom,
% 5.52/5.85 ! [A2: set_complex,X2: complex,G: complex > real] :
% 5.52/5.85 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.85 => ( ( ( member_complex @ X2 @ A2 )
% 5.52/5.85 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.85 = ( groups5808333547571424918x_real @ G @ A2 ) ) )
% 5.52/5.85 & ( ~ ( member_complex @ X2 @ A2 )
% 5.52/5.85 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert_if
% 5.52/5.85 thf(fact_7025_sum_Oinsert__if,axiom,
% 5.52/5.85 ! [A2: set_Extended_enat,X2: extended_enat,G: extended_enat > real] :
% 5.52/5.85 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.85 => ( ( ( member_Extended_enat @ X2 @ A2 )
% 5.52/5.85 => ( ( groups4148127829035722712t_real @ G @ ( insert_Extended_enat @ X2 @ A2 ) )
% 5.52/5.85 = ( groups4148127829035722712t_real @ G @ A2 ) ) )
% 5.52/5.85 & ( ~ ( member_Extended_enat @ X2 @ A2 )
% 5.52/5.85 => ( ( groups4148127829035722712t_real @ G @ ( insert_Extended_enat @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_real @ ( G @ X2 ) @ ( groups4148127829035722712t_real @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert_if
% 5.52/5.85 thf(fact_7026_sum_Oinsert__if,axiom,
% 5.52/5.85 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.52/5.85 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.85 => ( ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.85 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.85 = ( groups136491112297645522BT_rat @ G @ A2 ) ) )
% 5.52/5.85 & ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.85 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert_if
% 5.52/5.85 thf(fact_7027_sum_Oinsert__if,axiom,
% 5.52/5.85 ! [A2: set_real,X2: real,G: real > rat] :
% 5.52/5.85 ( ( finite_finite_real @ A2 )
% 5.52/5.85 => ( ( ( member_real @ X2 @ A2 )
% 5.52/5.85 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X2 @ A2 ) )
% 5.52/5.85 = ( groups1300246762558778688al_rat @ G @ A2 ) ) )
% 5.52/5.85 & ( ~ ( member_real @ X2 @ A2 )
% 5.52/5.85 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert_if
% 5.52/5.85 thf(fact_7028_sum_Oinsert__if,axiom,
% 5.52/5.85 ! [A2: set_nat,X2: nat,G: nat > rat] :
% 5.52/5.85 ( ( finite_finite_nat @ A2 )
% 5.52/5.85 => ( ( ( member_nat @ X2 @ A2 )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.52/5.85 = ( groups2906978787729119204at_rat @ G @ A2 ) ) )
% 5.52/5.85 & ( ~ ( member_nat @ X2 @ A2 )
% 5.52/5.85 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert_if
% 5.52/5.85 thf(fact_7029_sum_Oinsert__if,axiom,
% 5.52/5.85 ! [A2: set_int,X2: int,G: int > rat] :
% 5.52/5.85 ( ( finite_finite_int @ A2 )
% 5.52/5.85 => ( ( ( member_int @ X2 @ A2 )
% 5.52/5.85 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.85 = ( groups3906332499630173760nt_rat @ G @ A2 ) ) )
% 5.52/5.85 & ( ~ ( member_int @ X2 @ A2 )
% 5.52/5.85 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert_if
% 5.52/5.85 thf(fact_7030_sum_Oinsert__if,axiom,
% 5.52/5.85 ! [A2: set_complex,X2: complex,G: complex > rat] :
% 5.52/5.85 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.85 => ( ( ( member_complex @ X2 @ A2 )
% 5.52/5.85 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.85 = ( groups5058264527183730370ex_rat @ G @ A2 ) ) )
% 5.52/5.85 & ( ~ ( member_complex @ X2 @ A2 )
% 5.52/5.85 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.85 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % sum.insert_if
% 5.52/5.85 thf(fact_7031_reals__Archimedean3,axiom,
% 5.52/5.85 ! [X2: real] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.85 => ! [Y4: real] :
% 5.52/5.85 ? [N2: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % reals_Archimedean3
% 5.52/5.85 thf(fact_7032_int__cases4,axiom,
% 5.52/5.85 ! [M: int] :
% 5.52/5.85 ( ! [N2: nat] :
% 5.52/5.85 ( M
% 5.52/5.85 != ( semiri1314217659103216013at_int @ N2 ) )
% 5.52/5.85 => ~ ! [N2: nat] :
% 5.52/5.85 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.52/5.85 => ( M
% 5.52/5.85 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % int_cases4
% 5.52/5.85 thf(fact_7033_real__of__nat__div4,axiom,
% 5.52/5.85 ! [N: nat,X2: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_of_nat_div4
% 5.52/5.85 thf(fact_7034_zless__iff__Suc__zadd,axiom,
% 5.52/5.85 ( ord_less_int
% 5.52/5.85 = ( ^ [W2: int,Z2: int] :
% 5.52/5.85 ? [N3: nat] :
% 5.52/5.85 ( Z2
% 5.52/5.85 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % zless_iff_Suc_zadd
% 5.52/5.85 thf(fact_7035_real__of__nat__div,axiom,
% 5.52/5.85 ! [D2: nat,N: nat] :
% 5.52/5.85 ( ( dvd_dvd_nat @ D2 @ N )
% 5.52/5.85 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D2 ) )
% 5.52/5.85 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_of_nat_div
% 5.52/5.85 thf(fact_7036_less__log2__of__power,axiom,
% 5.52/5.85 ! [N: nat,M: nat] :
% 5.52/5.85 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.52/5.85 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % less_log2_of_power
% 5.52/5.85 thf(fact_7037_le__log2__of__power,axiom,
% 5.52/5.85 ! [N: nat,M: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.52/5.85 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % le_log2_of_power
% 5.52/5.85 thf(fact_7038_flip__bit__eq__if,axiom,
% 5.52/5.85 ( bit_se2159334234014336723it_int
% 5.52/5.85 = ( ^ [N3: nat,A4: int] : ( if_nat_int_int @ ( bit_se1146084159140164899it_int @ A4 @ N3 ) @ bit_se4203085406695923979it_int @ bit_se7879613467334960850it_int @ N3 @ A4 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % flip_bit_eq_if
% 5.52/5.85 thf(fact_7039_flip__bit__eq__if,axiom,
% 5.52/5.85 ( bit_se2161824704523386999it_nat
% 5.52/5.85 = ( ^ [N3: nat,A4: nat] : ( if_nat_nat_nat @ ( bit_se1148574629649215175it_nat @ A4 @ N3 ) @ bit_se4205575877204974255it_nat @ bit_se7882103937844011126it_nat @ N3 @ A4 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % flip_bit_eq_if
% 5.52/5.85 thf(fact_7040_log2__of__power__less,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.85 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.85 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log2_of_power_less
% 5.52/5.85 thf(fact_7041_log__base__change,axiom,
% 5.52/5.85 ! [A: real,B: real,X2: real] :
% 5.52/5.85 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.85 => ( ( A != one_one_real )
% 5.52/5.85 => ( ( log @ B @ X2 )
% 5.52/5.85 = ( divide_divide_real @ ( log @ A @ X2 ) @ ( log @ A @ B ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log_base_change
% 5.52/5.85 thf(fact_7042_mod__mult2__eq_H,axiom,
% 5.52/5.85 ! [A: int,M: nat,N: nat] :
% 5.52/5.85 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.52/5.85 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mod_mult2_eq'
% 5.52/5.85 thf(fact_7043_mod__mult2__eq_H,axiom,
% 5.52/5.85 ! [A: nat,M: nat,N: nat] :
% 5.52/5.85 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.52/5.85 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % mod_mult2_eq'
% 5.52/5.85 thf(fact_7044_bit__imp__take__bit__positive,axiom,
% 5.52/5.85 ! [N: nat,M: nat,K: int] :
% 5.52/5.85 ( ( ord_less_nat @ N @ M )
% 5.52/5.85 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.52/5.85 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_imp_take_bit_positive
% 5.52/5.85 thf(fact_7045_field__char__0__class_Oof__nat__div,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 5.52/5.85 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % field_char_0_class.of_nat_div
% 5.52/5.85 thf(fact_7046_field__char__0__class_Oof__nat__div,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 5.52/5.85 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % field_char_0_class.of_nat_div
% 5.52/5.85 thf(fact_7047_field__char__0__class_Oof__nat__div,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 5.52/5.85 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % field_char_0_class.of_nat_div
% 5.52/5.85 thf(fact_7048_bit__concat__bit__iff,axiom,
% 5.52/5.85 ! [M: nat,K: int,L: int,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 5.52/5.85 = ( ( ( ord_less_nat @ N @ M )
% 5.52/5.85 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.52/5.85 | ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.85 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_concat_bit_iff
% 5.52/5.85 thf(fact_7049_pos__int__cases,axiom,
% 5.52/5.85 ! [K: int] :
% 5.52/5.85 ( ( ord_less_int @ zero_zero_int @ K )
% 5.52/5.85 => ~ ! [N2: nat] :
% 5.52/5.85 ( ( K
% 5.52/5.85 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.52/5.85 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % pos_int_cases
% 5.52/5.85 thf(fact_7050_zero__less__imp__eq__int,axiom,
% 5.52/5.85 ! [K: int] :
% 5.52/5.85 ( ( ord_less_int @ zero_zero_int @ K )
% 5.52/5.85 => ? [N2: nat] :
% 5.52/5.85 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.52/5.85 & ( K
% 5.52/5.85 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % zero_less_imp_eq_int
% 5.52/5.85 thf(fact_7051_int__cases3,axiom,
% 5.52/5.85 ! [K: int] :
% 5.52/5.85 ( ( K != zero_zero_int )
% 5.52/5.85 => ( ! [N2: nat] :
% 5.52/5.85 ( ( K
% 5.52/5.85 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.52/5.85 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.52/5.85 => ~ ! [N2: nat] :
% 5.52/5.85 ( ( K
% 5.52/5.85 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.52/5.85 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % int_cases3
% 5.52/5.85 thf(fact_7052_nat__less__real__le,axiom,
% 5.52/5.85 ( ord_less_nat
% 5.52/5.85 = ( ^ [N3: nat,M3: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % nat_less_real_le
% 5.52/5.85 thf(fact_7053_nat__le__real__less,axiom,
% 5.52/5.85 ( ord_less_eq_nat
% 5.52/5.85 = ( ^ [N3: nat,M3: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M3 ) @ one_one_real ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % nat_le_real_less
% 5.52/5.85 thf(fact_7054_zmult__zless__mono2__lemma,axiom,
% 5.52/5.85 ! [I: int,J: int,K: nat] :
% 5.52/5.85 ( ( ord_less_int @ I @ J )
% 5.52/5.85 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.85 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % zmult_zless_mono2_lemma
% 5.52/5.85 thf(fact_7055_negD,axiom,
% 5.52/5.85 ! [X2: int] :
% 5.52/5.85 ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.52/5.85 => ? [N2: nat] :
% 5.52/5.85 ( X2
% 5.52/5.85 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % negD
% 5.52/5.85 thf(fact_7056_negative__zless__0,axiom,
% 5.52/5.85 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.52/5.85
% 5.52/5.85 % negative_zless_0
% 5.52/5.85 thf(fact_7057_log2__of__power__le,axiom,
% 5.52/5.85 ! [M: nat,N: nat] :
% 5.52/5.85 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.85 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.85 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % log2_of_power_le
% 5.52/5.85 thf(fact_7058_finite__induct__select,axiom,
% 5.52/5.85 ! [S3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 5.52/5.85 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.52/5.85 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.52/5.85 => ( ! [T3: set_VEBT_VEBT] :
% 5.52/5.85 ( ( ord_le3480810397992357184T_VEBT @ T3 @ S3 )
% 5.52/5.85 => ( ( P @ T3 )
% 5.52/5.85 => ? [X6: vEBT_VEBT] :
% 5.52/5.85 ( ( member_VEBT_VEBT @ X6 @ ( minus_5127226145743854075T_VEBT @ S3 @ T3 ) )
% 5.52/5.85 & ( P @ ( insert_VEBT_VEBT @ X6 @ T3 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_induct_select
% 5.52/5.85 thf(fact_7059_finite__induct__select,axiom,
% 5.52/5.85 ! [S3: set_complex,P: set_complex > $o] :
% 5.52/5.85 ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.85 => ( ( P @ bot_bot_set_complex )
% 5.52/5.85 => ( ! [T3: set_complex] :
% 5.52/5.85 ( ( ord_less_set_complex @ T3 @ S3 )
% 5.52/5.85 => ( ( P @ T3 )
% 5.52/5.85 => ? [X6: complex] :
% 5.52/5.85 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ S3 @ T3 ) )
% 5.52/5.85 & ( P @ ( insert_complex @ X6 @ T3 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_induct_select
% 5.52/5.85 thf(fact_7060_finite__induct__select,axiom,
% 5.52/5.85 ! [S3: set_nat,P: set_nat > $o] :
% 5.52/5.85 ( ( finite_finite_nat @ S3 )
% 5.52/5.85 => ( ( P @ bot_bot_set_nat )
% 5.52/5.85 => ( ! [T3: set_nat] :
% 5.52/5.85 ( ( ord_less_set_nat @ T3 @ S3 )
% 5.52/5.85 => ( ( P @ T3 )
% 5.52/5.85 => ? [X6: nat] :
% 5.52/5.85 ( ( member_nat @ X6 @ ( minus_minus_set_nat @ S3 @ T3 ) )
% 5.52/5.85 & ( P @ ( insert_nat @ X6 @ T3 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_induct_select
% 5.52/5.85 thf(fact_7061_finite__induct__select,axiom,
% 5.52/5.85 ! [S3: set_int,P: set_int > $o] :
% 5.52/5.85 ( ( finite_finite_int @ S3 )
% 5.52/5.85 => ( ( P @ bot_bot_set_int )
% 5.52/5.85 => ( ! [T3: set_int] :
% 5.52/5.85 ( ( ord_less_set_int @ T3 @ S3 )
% 5.52/5.85 => ( ( P @ T3 )
% 5.52/5.85 => ? [X6: int] :
% 5.52/5.85 ( ( member_int @ X6 @ ( minus_minus_set_int @ S3 @ T3 ) )
% 5.52/5.85 & ( P @ ( insert_int @ X6 @ T3 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_induct_select
% 5.52/5.85 thf(fact_7062_finite__induct__select,axiom,
% 5.52/5.85 ! [S3: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.52/5.85 ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.85 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.52/5.85 => ( ! [T3: set_Extended_enat] :
% 5.52/5.85 ( ( ord_le2529575680413868914d_enat @ T3 @ S3 )
% 5.52/5.85 => ( ( P @ T3 )
% 5.52/5.85 => ? [X6: extended_enat] :
% 5.52/5.85 ( ( member_Extended_enat @ X6 @ ( minus_925952699566721837d_enat @ S3 @ T3 ) )
% 5.52/5.85 & ( P @ ( insert_Extended_enat @ X6 @ T3 ) ) ) ) )
% 5.52/5.85 => ( P @ S3 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % finite_induct_select
% 5.52/5.85 thf(fact_7063_psubset__insert__iff,axiom,
% 5.52/5.85 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 5.52/5.85 ( ( ord_le3480810397992357184T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ B4 ) )
% 5.52/5.85 = ( ( ( member_VEBT_VEBT @ X2 @ B4 )
% 5.52/5.85 => ( ord_le3480810397992357184T_VEBT @ A2 @ B4 ) )
% 5.52/5.85 & ( ~ ( member_VEBT_VEBT @ X2 @ B4 )
% 5.52/5.85 => ( ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.85 => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) @ B4 ) )
% 5.52/5.85 & ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.85 => ( ord_le4337996190870823476T_VEBT @ A2 @ B4 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % psubset_insert_iff
% 5.52/5.85 thf(fact_7064_psubset__insert__iff,axiom,
% 5.52/5.85 ! [A2: set_option_nat,X2: option_nat,B4: set_option_nat] :
% 5.52/5.85 ( ( ord_le1792839605950587050on_nat @ A2 @ ( insert_option_nat @ X2 @ B4 ) )
% 5.52/5.85 = ( ( ( member_option_nat @ X2 @ B4 )
% 5.52/5.85 => ( ord_le1792839605950587050on_nat @ A2 @ B4 ) )
% 5.52/5.85 & ( ~ ( member_option_nat @ X2 @ B4 )
% 5.52/5.85 => ( ( ( member_option_nat @ X2 @ A2 )
% 5.52/5.85 => ( ord_le1792839605950587050on_nat @ ( minus_5999362281193037231on_nat @ A2 @ ( insert_option_nat @ X2 @ bot_bo5009843511495006442on_nat ) ) @ B4 ) )
% 5.52/5.85 & ( ~ ( member_option_nat @ X2 @ A2 )
% 5.52/5.85 => ( ord_le6937355464348597430on_nat @ A2 @ B4 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % psubset_insert_iff
% 5.52/5.85 thf(fact_7065_psubset__insert__iff,axiom,
% 5.52/5.85 ! [A2: set_real,X2: real,B4: set_real] :
% 5.52/5.85 ( ( ord_less_set_real @ A2 @ ( insert_real @ X2 @ B4 ) )
% 5.52/5.85 = ( ( ( member_real @ X2 @ B4 )
% 5.52/5.85 => ( ord_less_set_real @ A2 @ B4 ) )
% 5.52/5.85 & ( ~ ( member_real @ X2 @ B4 )
% 5.52/5.85 => ( ( ( member_real @ X2 @ A2 )
% 5.52/5.85 => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B4 ) )
% 5.52/5.85 & ( ~ ( member_real @ X2 @ A2 )
% 5.52/5.85 => ( ord_less_eq_set_real @ A2 @ B4 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % psubset_insert_iff
% 5.52/5.85 thf(fact_7066_psubset__insert__iff,axiom,
% 5.52/5.85 ! [A2: set_set_nat_rat,X2: set_nat_rat,B4: set_set_nat_rat] :
% 5.52/5.85 ( ( ord_le1311537459589289991at_rat @ A2 @ ( insert_set_nat_rat @ X2 @ B4 ) )
% 5.52/5.85 = ( ( ( member_set_nat_rat @ X2 @ B4 )
% 5.52/5.85 => ( ord_le1311537459589289991at_rat @ A2 @ B4 ) )
% 5.52/5.85 & ( ~ ( member_set_nat_rat @ X2 @ B4 )
% 5.52/5.85 => ( ( ( member_set_nat_rat @ X2 @ A2 )
% 5.52/5.85 => ( ord_le1311537459589289991at_rat @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ X2 @ bot_bo6797373522285170759at_rat ) ) @ B4 ) )
% 5.52/5.85 & ( ~ ( member_set_nat_rat @ X2 @ A2 )
% 5.52/5.85 => ( ord_le4375437777232675859at_rat @ A2 @ B4 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % psubset_insert_iff
% 5.52/5.85 thf(fact_7067_psubset__insert__iff,axiom,
% 5.52/5.85 ! [A2: set_int,X2: int,B4: set_int] :
% 5.52/5.85 ( ( ord_less_set_int @ A2 @ ( insert_int @ X2 @ B4 ) )
% 5.52/5.85 = ( ( ( member_int @ X2 @ B4 )
% 5.52/5.85 => ( ord_less_set_int @ A2 @ B4 ) )
% 5.52/5.85 & ( ~ ( member_int @ X2 @ B4 )
% 5.52/5.85 => ( ( ( member_int @ X2 @ A2 )
% 5.52/5.85 => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B4 ) )
% 5.52/5.85 & ( ~ ( member_int @ X2 @ A2 )
% 5.52/5.85 => ( ord_less_eq_set_int @ A2 @ B4 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % psubset_insert_iff
% 5.52/5.85 thf(fact_7068_psubset__insert__iff,axiom,
% 5.52/5.85 ! [A2: set_Extended_enat,X2: extended_enat,B4: set_Extended_enat] :
% 5.52/5.85 ( ( ord_le2529575680413868914d_enat @ A2 @ ( insert_Extended_enat @ X2 @ B4 ) )
% 5.52/5.85 = ( ( ( member_Extended_enat @ X2 @ B4 )
% 5.52/5.85 => ( ord_le2529575680413868914d_enat @ A2 @ B4 ) )
% 5.52/5.85 & ( ~ ( member_Extended_enat @ X2 @ B4 )
% 5.52/5.85 => ( ( ( member_Extended_enat @ X2 @ A2 )
% 5.52/5.85 => ( ord_le2529575680413868914d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) @ B4 ) )
% 5.52/5.85 & ( ~ ( member_Extended_enat @ X2 @ A2 )
% 5.52/5.85 => ( ord_le7203529160286727270d_enat @ A2 @ B4 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % psubset_insert_iff
% 5.52/5.85 thf(fact_7069_psubset__insert__iff,axiom,
% 5.52/5.85 ! [A2: set_nat,X2: nat,B4: set_nat] :
% 5.52/5.85 ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X2 @ B4 ) )
% 5.52/5.85 = ( ( ( member_nat @ X2 @ B4 )
% 5.52/5.85 => ( ord_less_set_nat @ A2 @ B4 ) )
% 5.52/5.85 & ( ~ ( member_nat @ X2 @ B4 )
% 5.52/5.85 => ( ( ( member_nat @ X2 @ A2 )
% 5.52/5.85 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B4 ) )
% 5.52/5.85 & ( ~ ( member_nat @ X2 @ A2 )
% 5.52/5.85 => ( ord_less_eq_set_nat @ A2 @ B4 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % psubset_insert_iff
% 5.52/5.85 thf(fact_7070_int__ops_I6_J,axiom,
% 5.52/5.85 ! [A: nat,B: nat] :
% 5.52/5.85 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.52/5.85 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.52/5.85 = zero_zero_int ) )
% 5.52/5.85 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.52/5.85 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.52/5.85 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % int_ops(6)
% 5.52/5.85 thf(fact_7071_real__of__nat__div__aux,axiom,
% 5.52/5.85 ! [X2: nat,D2: nat] :
% 5.52/5.85 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( semiri5074537144036343181t_real @ D2 ) )
% 5.52/5.85 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X2 @ D2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X2 @ D2 ) ) @ ( semiri5074537144036343181t_real @ D2 ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % real_of_nat_div_aux
% 5.52/5.85 thf(fact_7072_simp__from__to,axiom,
% 5.52/5.85 ( set_or1266510415728281911st_int
% 5.52/5.85 = ( ^ [I4: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I4 ) @ bot_bot_set_int @ ( insert_int @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % simp_from_to
% 5.52/5.85 thf(fact_7073_signed__take__bit__eq__concat__bit,axiom,
% 5.52/5.85 ( bit_ri631733984087533419it_int
% 5.52/5.85 = ( ^ [N3: nat,K2: int] : ( bit_concat_bit @ N3 @ K2 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N3 ) ) ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % signed_take_bit_eq_concat_bit
% 5.52/5.85 thf(fact_7074_exp__eq__0__imp__not__bit,axiom,
% 5.52/5.85 ! [N: nat,A: int] :
% 5.52/5.85 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.52/5.85 = zero_zero_int )
% 5.52/5.85 => ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_eq_0_imp_not_bit
% 5.52/5.85 thf(fact_7075_exp__eq__0__imp__not__bit,axiom,
% 5.52/5.85 ! [N: nat,A: nat] :
% 5.52/5.85 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.85 = zero_zero_nat )
% 5.52/5.85 => ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % exp_eq_0_imp_not_bit
% 5.52/5.85 thf(fact_7076_bit__Suc,axiom,
% 5.52/5.85 ! [A: int,N: nat] :
% 5.52/5.85 ( ( bit_se1146084159140164899it_int @ A @ ( suc @ N ) )
% 5.52/5.85 = ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_Suc
% 5.52/5.85 thf(fact_7077_bit__Suc,axiom,
% 5.52/5.85 ! [A: nat,N: nat] :
% 5.52/5.85 ( ( bit_se1148574629649215175it_nat @ A @ ( suc @ N ) )
% 5.52/5.85 = ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N ) ) ).
% 5.52/5.85
% 5.52/5.85 % bit_Suc
% 5.52/5.85 thf(fact_7078_stable__imp__bit__iff__odd,axiom,
% 5.52/5.85 ! [A: code_integer,N: nat] :
% 5.52/5.85 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.85 = A )
% 5.52/5.85 => ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.52/5.85 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % stable_imp_bit_iff_odd
% 5.52/5.85 thf(fact_7079_stable__imp__bit__iff__odd,axiom,
% 5.52/5.85 ! [A: int,N: nat] :
% 5.52/5.85 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.85 = A )
% 5.52/5.85 => ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.52/5.85 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % stable_imp_bit_iff_odd
% 5.52/5.85 thf(fact_7080_stable__imp__bit__iff__odd,axiom,
% 5.52/5.85 ! [A: nat,N: nat] :
% 5.52/5.85 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.85 = A )
% 5.52/5.85 => ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.52/5.85 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.52/5.85
% 5.52/5.85 % stable_imp_bit_iff_odd
% 5.52/5.85 thf(fact_7081_bit__iff__idd__imp__stable,axiom,
% 5.52/5.85 ! [A: code_integer] :
% 5.52/5.85 ( ! [N2: nat] :
% 5.52/5.85 ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 5.52/5.85 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.52/5.85 => ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.86 = A ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_iff_idd_imp_stable
% 5.52/5.86 thf(fact_7082_bit__iff__idd__imp__stable,axiom,
% 5.52/5.86 ! [A: int] :
% 5.52/5.86 ( ! [N2: nat] :
% 5.52/5.86 ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.52/5.86 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.52/5.86 => ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.86 = A ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_iff_idd_imp_stable
% 5.52/5.86 thf(fact_7083_bit__iff__idd__imp__stable,axiom,
% 5.52/5.86 ! [A: nat] :
% 5.52/5.86 ( ! [N2: nat] :
% 5.52/5.86 ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.52/5.86 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.52/5.86 => ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.86 = A ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_iff_idd_imp_stable
% 5.52/5.86 thf(fact_7084_log__mult,axiom,
% 5.52/5.86 ! [A: real,X2: real,Y2: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.86 => ( ( A != one_one_real )
% 5.52/5.86 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.86 => ( ( log @ A @ ( times_times_real @ X2 @ Y2 ) )
% 5.52/5.86 = ( plus_plus_real @ ( log @ A @ X2 ) @ ( log @ A @ Y2 ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % log_mult
% 5.52/5.86 thf(fact_7085_log__divide,axiom,
% 5.52/5.86 ! [A: real,X2: real,Y2: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.86 => ( ( A != one_one_real )
% 5.52/5.86 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.86 => ( ( log @ A @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.52/5.86 = ( minus_minus_real @ ( log @ A @ X2 ) @ ( log @ A @ Y2 ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % log_divide
% 5.52/5.86 thf(fact_7086_int__bit__bound,axiom,
% 5.52/5.86 ! [K: int] :
% 5.52/5.86 ~ ! [N2: nat] :
% 5.52/5.86 ( ! [M2: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N2 @ M2 )
% 5.52/5.86 => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 5.52/5.86 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) )
% 5.52/5.86 => ~ ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.52/5.86 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 5.52/5.86 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % int_bit_bound
% 5.52/5.86 thf(fact_7087_nat__approx__posE,axiom,
% 5.52/5.86 ! [E: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ E )
% 5.52/5.86 => ~ ! [N2: nat] :
% 5.52/5.86 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ E ) ) ).
% 5.52/5.86
% 5.52/5.86 % nat_approx_posE
% 5.52/5.86 thf(fact_7088_nat__approx__posE,axiom,
% 5.52/5.86 ! [E: rat] :
% 5.52/5.86 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.52/5.86 => ~ ! [N2: nat] :
% 5.52/5.86 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) ) @ E ) ) ).
% 5.52/5.86
% 5.52/5.86 % nat_approx_posE
% 5.52/5.86 thf(fact_7089_of__nat__less__two__power,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_nat_less_two_power
% 5.52/5.86 thf(fact_7090_of__nat__less__two__power,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_nat_less_two_power
% 5.52/5.86 thf(fact_7091_of__nat__less__two__power,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_nat_less_two_power
% 5.52/5.86 thf(fact_7092_inverse__of__nat__le,axiom,
% 5.52/5.86 ! [N: nat,M: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.86 => ( ( N != zero_zero_nat )
% 5.52/5.86 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % inverse_of_nat_le
% 5.52/5.86 thf(fact_7093_inverse__of__nat__le,axiom,
% 5.52/5.86 ! [N: nat,M: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.86 => ( ( N != zero_zero_nat )
% 5.52/5.86 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % inverse_of_nat_le
% 5.52/5.86 thf(fact_7094_insert__bound__size__univ,axiom,
% 5.52/5.86 ! [T: vEBT_VEBT,N: nat,U: real,X2: nat] :
% 5.52/5.86 ( ( vEBT_invar_vebt @ T @ N )
% 5.52/5.86 => ( ( U
% 5.52/5.86 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.86 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_i_n_s_e_r_t @ T @ X2 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % insert_bound_size_univ
% 5.52/5.86 thf(fact_7095_member__bound__size__univ,axiom,
% 5.52/5.86 ! [T: vEBT_VEBT,N: nat,U: real,X2: nat] :
% 5.52/5.86 ( ( vEBT_invar_vebt @ T @ N )
% 5.52/5.86 => ( ( U
% 5.52/5.86 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.86 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_m_e_m_b_e_r @ T @ X2 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % member_bound_size_univ
% 5.52/5.86 thf(fact_7096_exp__divide__power__eq,axiom,
% 5.52/5.86 ! [N: nat,X2: complex] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X2 @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 5.52/5.86 = ( exp_complex @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % exp_divide_power_eq
% 5.52/5.86 thf(fact_7097_exp__divide__power__eq,axiom,
% 5.52/5.86 ! [N: nat,X2: real] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.52/5.86 = ( exp_real @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % exp_divide_power_eq
% 5.52/5.86 thf(fact_7098_real__archimedian__rdiv__eq__0,axiom,
% 5.52/5.86 ! [X2: real,C: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.52/5.86 => ( ! [M4: nat] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 5.52/5.86 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X2 ) @ C ) )
% 5.52/5.86 => ( X2 = zero_zero_real ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % real_archimedian_rdiv_eq_0
% 5.52/5.86 thf(fact_7099_sum_Oinsert__remove,axiom,
% 5.52/5.86 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,X2: vEBT_VEBT] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.86 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.86 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.insert_remove
% 5.52/5.86 thf(fact_7100_sum_Oinsert__remove,axiom,
% 5.52/5.86 ! [A2: set_complex,G: complex > real,X2: complex] :
% 5.52/5.86 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.86 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.86 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.insert_remove
% 5.52/5.86 thf(fact_7101_sum_Oinsert__remove,axiom,
% 5.52/5.86 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > rat,X2: vEBT_VEBT] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.86 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.86 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.insert_remove
% 5.52/5.86 thf(fact_7102_sum_Oinsert__remove,axiom,
% 5.52/5.86 ! [A2: set_complex,G: complex > rat,X2: complex] :
% 5.52/5.86 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.86 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.86 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.insert_remove
% 5.52/5.86 thf(fact_7103_sum_Oinsert__remove,axiom,
% 5.52/5.86 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > nat,X2: vEBT_VEBT] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.86 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.86 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.insert_remove
% 5.52/5.86 thf(fact_7104_sum_Oinsert__remove,axiom,
% 5.52/5.86 ! [A2: set_complex,G: complex > nat,X2: complex] :
% 5.52/5.86 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.86 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.86 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.insert_remove
% 5.52/5.86 thf(fact_7105_sum_Oinsert__remove,axiom,
% 5.52/5.86 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > int,X2: vEBT_VEBT] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.86 => ( ( groups769130701875090982BT_int @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.86 = ( plus_plus_int @ ( G @ X2 ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.insert_remove
% 5.52/5.86 thf(fact_7106_sum_Oinsert__remove,axiom,
% 5.52/5.86 ! [A2: set_complex,G: complex > int,X2: complex] :
% 5.52/5.86 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.86 => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.86 = ( plus_plus_int @ ( G @ X2 ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.insert_remove
% 5.52/5.86 thf(fact_7107_sum_Oinsert__remove,axiom,
% 5.52/5.86 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > complex,X2: vEBT_VEBT] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.86 => ( ( groups1794756597179926696omplex @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.86 = ( plus_plus_complex @ ( G @ X2 ) @ ( groups1794756597179926696omplex @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.insert_remove
% 5.52/5.86 thf(fact_7108_sum_Oinsert__remove,axiom,
% 5.52/5.86 ! [A2: set_nat,G: nat > rat,X2: nat] :
% 5.52/5.86 ( ( finite_finite_nat @ A2 )
% 5.52/5.86 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.52/5.86 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.insert_remove
% 5.52/5.86 thf(fact_7109_sum_Oremove,axiom,
% 5.52/5.86 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.86 => ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.86 => ( ( groups2240296850493347238T_real @ G @ A2 )
% 5.52/5.86 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.remove
% 5.52/5.86 thf(fact_7110_sum_Oremove,axiom,
% 5.52/5.86 ! [A2: set_real,X2: real,G: real > real] :
% 5.52/5.86 ( ( finite_finite_real @ A2 )
% 5.52/5.86 => ( ( member_real @ X2 @ A2 )
% 5.52/5.86 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.52/5.86 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.remove
% 5.52/5.86 thf(fact_7111_sum_Oremove,axiom,
% 5.52/5.86 ! [A2: set_complex,X2: complex,G: complex > real] :
% 5.52/5.86 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.86 => ( ( member_complex @ X2 @ A2 )
% 5.52/5.86 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.52/5.86 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.remove
% 5.52/5.86 thf(fact_7112_sum_Oremove,axiom,
% 5.52/5.86 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.86 => ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.86 => ( ( groups136491112297645522BT_rat @ G @ A2 )
% 5.52/5.86 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.remove
% 5.52/5.86 thf(fact_7113_sum_Oremove,axiom,
% 5.52/5.86 ! [A2: set_real,X2: real,G: real > rat] :
% 5.52/5.86 ( ( finite_finite_real @ A2 )
% 5.52/5.86 => ( ( member_real @ X2 @ A2 )
% 5.52/5.86 => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 5.52/5.86 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.remove
% 5.52/5.86 thf(fact_7114_sum_Oremove,axiom,
% 5.52/5.86 ! [A2: set_complex,X2: complex,G: complex > rat] :
% 5.52/5.86 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.86 => ( ( member_complex @ X2 @ A2 )
% 5.52/5.86 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.52/5.86 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.remove
% 5.52/5.86 thf(fact_7115_sum_Oremove,axiom,
% 5.52/5.86 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.86 => ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.86 => ( ( groups771621172384141258BT_nat @ G @ A2 )
% 5.52/5.86 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.remove
% 5.52/5.86 thf(fact_7116_sum_Oremove,axiom,
% 5.52/5.86 ! [A2: set_real,X2: real,G: real > nat] :
% 5.52/5.86 ( ( finite_finite_real @ A2 )
% 5.52/5.86 => ( ( member_real @ X2 @ A2 )
% 5.52/5.86 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.52/5.86 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.remove
% 5.52/5.86 thf(fact_7117_sum_Oremove,axiom,
% 5.52/5.86 ! [A2: set_complex,X2: complex,G: complex > nat] :
% 5.52/5.86 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.86 => ( ( member_complex @ X2 @ A2 )
% 5.52/5.86 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.52/5.86 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.remove
% 5.52/5.86 thf(fact_7118_sum_Oremove,axiom,
% 5.52/5.86 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > int] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.86 => ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.86 => ( ( groups769130701875090982BT_int @ G @ A2 )
% 5.52/5.86 = ( plus_plus_int @ ( G @ X2 ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.remove
% 5.52/5.86 thf(fact_7119_neg__int__cases,axiom,
% 5.52/5.86 ! [K: int] :
% 5.52/5.86 ( ( ord_less_int @ K @ zero_zero_int )
% 5.52/5.86 => ~ ! [N2: nat] :
% 5.52/5.86 ( ( K
% 5.52/5.86 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.52/5.86 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % neg_int_cases
% 5.52/5.86 thf(fact_7120_zdiff__int__split,axiom,
% 5.52/5.86 ! [P: int > $o,X2: nat,Y2: nat] :
% 5.52/5.86 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X2 @ Y2 ) ) )
% 5.52/5.86 = ( ( ( ord_less_eq_nat @ Y2 @ X2 )
% 5.52/5.86 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) )
% 5.52/5.86 & ( ( ord_less_nat @ X2 @ Y2 )
% 5.52/5.86 => ( P @ zero_zero_int ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % zdiff_int_split
% 5.52/5.86 thf(fact_7121_real__of__nat__div2,axiom,
% 5.52/5.86 ! [N: nat,X2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % real_of_nat_div2
% 5.52/5.86 thf(fact_7122_real__of__nat__div3,axiom,
% 5.52/5.86 ! [N: nat,X2: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) ) @ one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % real_of_nat_div3
% 5.52/5.86 thf(fact_7123_ln__realpow,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ln_ln_real @ ( power_power_real @ X2 @ N ) )
% 5.52/5.86 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ln_realpow
% 5.52/5.86 thf(fact_7124_bit__iff__odd,axiom,
% 5.52/5.86 ( bit_se9216721137139052372nteger
% 5.52/5.86 = ( ^ [A4: code_integer,N3: nat] :
% 5.52/5.86 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A4 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_iff_odd
% 5.52/5.86 thf(fact_7125_bit__iff__odd,axiom,
% 5.52/5.86 ( bit_se1146084159140164899it_int
% 5.52/5.86 = ( ^ [A4: int,N3: nat] :
% 5.52/5.86 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_iff_odd
% 5.52/5.86 thf(fact_7126_bit__iff__odd,axiom,
% 5.52/5.86 ( bit_se1148574629649215175it_nat
% 5.52/5.86 = ( ^ [A4: nat,N3: nat] :
% 5.52/5.86 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_iff_odd
% 5.52/5.86 thf(fact_7127_sum_Odelta__remove,axiom,
% 5.52/5.86 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.52/5.86 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.52/5.86 => ( ( groups2240296850493347238T_real
% 5.52/5.86 @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( plus_plus_real @ ( B @ A ) @ ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.52/5.86 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.52/5.86 => ( ( groups2240296850493347238T_real
% 5.52/5.86 @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.delta_remove
% 5.52/5.86 thf(fact_7128_sum_Odelta__remove,axiom,
% 5.52/5.86 ! [S3: set_real,A: real,B: real > real,C: real > real] :
% 5.52/5.86 ( ( finite_finite_real @ S3 )
% 5.52/5.86 => ( ( ( member_real @ A @ S3 )
% 5.52/5.86 => ( ( groups8097168146408367636l_real
% 5.52/5.86 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( plus_plus_real @ ( B @ A ) @ ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.52/5.86 & ( ~ ( member_real @ A @ S3 )
% 5.52/5.86 => ( ( groups8097168146408367636l_real
% 5.52/5.86 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.delta_remove
% 5.52/5.86 thf(fact_7129_sum_Odelta__remove,axiom,
% 5.52/5.86 ! [S3: set_complex,A: complex,B: complex > real,C: complex > real] :
% 5.52/5.86 ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.86 => ( ( ( member_complex @ A @ S3 )
% 5.52/5.86 => ( ( groups5808333547571424918x_real
% 5.52/5.86 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.52/5.86 & ( ~ ( member_complex @ A @ S3 )
% 5.52/5.86 => ( ( groups5808333547571424918x_real
% 5.52/5.86 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.delta_remove
% 5.52/5.86 thf(fact_7130_sum_Odelta__remove,axiom,
% 5.52/5.86 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C: vEBT_VEBT > rat] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.52/5.86 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.52/5.86 => ( ( groups136491112297645522BT_rat
% 5.52/5.86 @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( plus_plus_rat @ ( B @ A ) @ ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.52/5.86 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.52/5.86 => ( ( groups136491112297645522BT_rat
% 5.52/5.86 @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.delta_remove
% 5.52/5.86 thf(fact_7131_sum_Odelta__remove,axiom,
% 5.52/5.86 ! [S3: set_real,A: real,B: real > rat,C: real > rat] :
% 5.52/5.86 ( ( finite_finite_real @ S3 )
% 5.52/5.86 => ( ( ( member_real @ A @ S3 )
% 5.52/5.86 => ( ( groups1300246762558778688al_rat
% 5.52/5.86 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( plus_plus_rat @ ( B @ A ) @ ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.52/5.86 & ( ~ ( member_real @ A @ S3 )
% 5.52/5.86 => ( ( groups1300246762558778688al_rat
% 5.52/5.86 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.delta_remove
% 5.52/5.86 thf(fact_7132_sum_Odelta__remove,axiom,
% 5.52/5.86 ! [S3: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 5.52/5.86 ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.86 => ( ( ( member_complex @ A @ S3 )
% 5.52/5.86 => ( ( groups5058264527183730370ex_rat
% 5.52/5.86 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.52/5.86 & ( ~ ( member_complex @ A @ S3 )
% 5.52/5.86 => ( ( groups5058264527183730370ex_rat
% 5.52/5.86 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.delta_remove
% 5.52/5.86 thf(fact_7133_sum_Odelta__remove,axiom,
% 5.52/5.86 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > nat,C: vEBT_VEBT > nat] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.52/5.86 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.52/5.86 => ( ( groups771621172384141258BT_nat
% 5.52/5.86 @ ^ [K2: vEBT_VEBT] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( plus_plus_nat @ ( B @ A ) @ ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.52/5.86 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.52/5.86 => ( ( groups771621172384141258BT_nat
% 5.52/5.86 @ ^ [K2: vEBT_VEBT] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.delta_remove
% 5.52/5.86 thf(fact_7134_sum_Odelta__remove,axiom,
% 5.52/5.86 ! [S3: set_real,A: real,B: real > nat,C: real > nat] :
% 5.52/5.86 ( ( finite_finite_real @ S3 )
% 5.52/5.86 => ( ( ( member_real @ A @ S3 )
% 5.52/5.86 => ( ( groups1935376822645274424al_nat
% 5.52/5.86 @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( plus_plus_nat @ ( B @ A ) @ ( groups1935376822645274424al_nat @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.52/5.86 & ( ~ ( member_real @ A @ S3 )
% 5.52/5.86 => ( ( groups1935376822645274424al_nat
% 5.52/5.86 @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( groups1935376822645274424al_nat @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.delta_remove
% 5.52/5.86 thf(fact_7135_sum_Odelta__remove,axiom,
% 5.52/5.86 ! [S3: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 5.52/5.86 ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.86 => ( ( ( member_complex @ A @ S3 )
% 5.52/5.86 => ( ( groups5693394587270226106ex_nat
% 5.52/5.86 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( plus_plus_nat @ ( B @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.52/5.86 & ( ~ ( member_complex @ A @ S3 )
% 5.52/5.86 => ( ( groups5693394587270226106ex_nat
% 5.52/5.86 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.delta_remove
% 5.52/5.86 thf(fact_7136_sum_Odelta__remove,axiom,
% 5.52/5.86 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > int,C: vEBT_VEBT > int] :
% 5.52/5.86 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.52/5.86 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.52/5.86 => ( ( groups769130701875090982BT_int
% 5.52/5.86 @ ^ [K2: vEBT_VEBT] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( plus_plus_int @ ( B @ A ) @ ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.52/5.86 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.52/5.86 => ( ( groups769130701875090982BT_int
% 5.52/5.86 @ ^ [K2: vEBT_VEBT] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.86 @ S3 )
% 5.52/5.86 = ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.delta_remove
% 5.52/5.86 thf(fact_7137_and__exp__eq__0__iff__not__bit,axiom,
% 5.52/5.86 ! [A: int,N: nat] :
% 5.52/5.86 ( ( ( bit_se725231765392027082nd_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.86 = zero_zero_int )
% 5.52/5.86 = ( ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % and_exp_eq_0_iff_not_bit
% 5.52/5.86 thf(fact_7138_and__exp__eq__0__iff__not__bit,axiom,
% 5.52/5.86 ! [A: nat,N: nat] :
% 5.52/5.86 ( ( ( bit_se727722235901077358nd_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.86 = zero_zero_nat )
% 5.52/5.86 = ( ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % and_exp_eq_0_iff_not_bit
% 5.52/5.86 thf(fact_7139_log__eq__div__ln__mult__log,axiom,
% 5.52/5.86 ! [A: real,B: real,X2: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.86 => ( ( A != one_one_real )
% 5.52/5.86 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.86 => ( ( B != one_one_real )
% 5.52/5.86 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( log @ A @ X2 )
% 5.52/5.86 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X2 ) ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % log_eq_div_ln_mult_log
% 5.52/5.86 thf(fact_7140_bit__int__def,axiom,
% 5.52/5.86 ( bit_se1146084159140164899it_int
% 5.52/5.86 = ( ^ [K2: int,N3: nat] :
% 5.52/5.86 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_int_def
% 5.52/5.86 thf(fact_7141_member__le__sum,axiom,
% 5.52/5.86 ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.52/5.86 ( ( member_VEBT_VEBT @ I @ A2 )
% 5.52/5.86 => ( ! [X4: vEBT_VEBT] :
% 5.52/5.86 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.52/5.86 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.86 => ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( F @ I ) @ ( groups2240296850493347238T_real @ F @ A2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % member_le_sum
% 5.52/5.86 thf(fact_7142_member__le__sum,axiom,
% 5.52/5.86 ! [I: real,A2: set_real,F: real > real] :
% 5.52/5.86 ( ( member_real @ I @ A2 )
% 5.52/5.86 => ( ! [X4: real] :
% 5.52/5.86 ( ( member_real @ X4 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.52/5.86 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.86 => ( ( finite_finite_real @ A2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % member_le_sum
% 5.52/5.86 thf(fact_7143_member__le__sum,axiom,
% 5.52/5.86 ! [I: complex,A2: set_complex,F: complex > real] :
% 5.52/5.86 ( ( member_complex @ I @ A2 )
% 5.52/5.86 => ( ! [X4: complex] :
% 5.52/5.86 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.52/5.86 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.86 => ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % member_le_sum
% 5.52/5.86 thf(fact_7144_member__le__sum,axiom,
% 5.52/5.86 ! [I: int,A2: set_int,F: int > real] :
% 5.52/5.86 ( ( member_int @ I @ A2 )
% 5.52/5.86 => ( ! [X4: int] :
% 5.52/5.86 ( ( member_int @ X4 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.52/5.86 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.86 => ( ( finite_finite_int @ A2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % member_le_sum
% 5.52/5.86 thf(fact_7145_member__le__sum,axiom,
% 5.52/5.86 ! [I: extended_enat,A2: set_Extended_enat,F: extended_enat > real] :
% 5.52/5.86 ( ( member_Extended_enat @ I @ A2 )
% 5.52/5.86 => ( ! [X4: extended_enat] :
% 5.52/5.86 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ I @ bot_bo7653980558646680370d_enat ) ) )
% 5.52/5.86 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.86 => ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( F @ I ) @ ( groups4148127829035722712t_real @ F @ A2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % member_le_sum
% 5.52/5.86 thf(fact_7146_member__le__sum,axiom,
% 5.52/5.86 ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.52/5.86 ( ( member_VEBT_VEBT @ I @ A2 )
% 5.52/5.86 => ( ! [X4: vEBT_VEBT] :
% 5.52/5.86 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.52/5.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.86 => ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.86 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % member_le_sum
% 5.52/5.86 thf(fact_7147_member__le__sum,axiom,
% 5.52/5.86 ! [I: real,A2: set_real,F: real > rat] :
% 5.52/5.86 ( ( member_real @ I @ A2 )
% 5.52/5.86 => ( ! [X4: real] :
% 5.52/5.86 ( ( member_real @ X4 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.52/5.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.86 => ( ( finite_finite_real @ A2 )
% 5.52/5.86 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % member_le_sum
% 5.52/5.86 thf(fact_7148_member__le__sum,axiom,
% 5.52/5.86 ! [I: complex,A2: set_complex,F: complex > rat] :
% 5.52/5.86 ( ( member_complex @ I @ A2 )
% 5.52/5.86 => ( ! [X4: complex] :
% 5.52/5.86 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.52/5.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.86 => ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.86 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % member_le_sum
% 5.52/5.86 thf(fact_7149_member__le__sum,axiom,
% 5.52/5.86 ! [I: nat,A2: set_nat,F: nat > rat] :
% 5.52/5.86 ( ( member_nat @ I @ A2 )
% 5.52/5.86 => ( ! [X4: nat] :
% 5.52/5.86 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 5.52/5.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.86 => ( ( finite_finite_nat @ A2 )
% 5.52/5.86 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % member_le_sum
% 5.52/5.86 thf(fact_7150_member__le__sum,axiom,
% 5.52/5.86 ! [I: int,A2: set_int,F: int > rat] :
% 5.52/5.86 ( ( member_int @ I @ A2 )
% 5.52/5.86 => ( ! [X4: int] :
% 5.52/5.86 ( ( member_int @ X4 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.52/5.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.52/5.86 => ( ( finite_finite_int @ A2 )
% 5.52/5.86 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % member_le_sum
% 5.52/5.86 thf(fact_7151_linear__plus__1__le__power,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X2 @ one_one_real ) @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % linear_plus_1_le_power
% 5.52/5.86 thf(fact_7152_Bernoulli__inequality,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X2 ) @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Bernoulli_inequality
% 5.52/5.86 thf(fact_7153_even__bit__succ__iff,axiom,
% 5.52/5.86 ! [A: code_integer,N: nat] :
% 5.52/5.86 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.86 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N )
% 5.52/5.86 = ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.52/5.86 | ( N = zero_zero_nat ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % even_bit_succ_iff
% 5.52/5.86 thf(fact_7154_even__bit__succ__iff,axiom,
% 5.52/5.86 ! [A: int,N: nat] :
% 5.52/5.86 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.86 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N )
% 5.52/5.86 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.52/5.86 | ( N = zero_zero_nat ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % even_bit_succ_iff
% 5.52/5.86 thf(fact_7155_even__bit__succ__iff,axiom,
% 5.52/5.86 ! [A: nat,N: nat] :
% 5.52/5.86 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.86 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N )
% 5.52/5.86 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.52/5.86 | ( N = zero_zero_nat ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % even_bit_succ_iff
% 5.52/5.86 thf(fact_7156_odd__bit__iff__bit__pred,axiom,
% 5.52/5.86 ! [A: code_integer,N: nat] :
% 5.52/5.86 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.52/5.86 => ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.52/5.86 = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N )
% 5.52/5.86 | ( N = zero_zero_nat ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % odd_bit_iff_bit_pred
% 5.52/5.86 thf(fact_7157_odd__bit__iff__bit__pred,axiom,
% 5.52/5.86 ! [A: int,N: nat] :
% 5.52/5.86 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.52/5.86 => ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.52/5.86 = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N )
% 5.52/5.86 | ( N = zero_zero_nat ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % odd_bit_iff_bit_pred
% 5.52/5.86 thf(fact_7158_odd__bit__iff__bit__pred,axiom,
% 5.52/5.86 ! [A: nat,N: nat] :
% 5.52/5.86 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.52/5.86 => ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.52/5.86 = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N )
% 5.52/5.86 | ( N = zero_zero_nat ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % odd_bit_iff_bit_pred
% 5.52/5.86 thf(fact_7159_bit__sum__mult__2__cases,axiom,
% 5.52/5.86 ! [A: code_integer,B: code_integer,N: nat] :
% 5.52/5.86 ( ! [J2: nat] :
% 5.52/5.86 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J2 ) )
% 5.52/5.86 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.52/5.86 = ( ( ( N = zero_zero_nat )
% 5.52/5.86 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.86 & ( ( N != zero_zero_nat )
% 5.52/5.86 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_sum_mult_2_cases
% 5.52/5.86 thf(fact_7160_bit__sum__mult__2__cases,axiom,
% 5.52/5.86 ! [A: int,B: int,N: nat] :
% 5.52/5.86 ( ! [J2: nat] :
% 5.52/5.86 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J2 ) )
% 5.52/5.86 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.52/5.86 = ( ( ( N = zero_zero_nat )
% 5.52/5.86 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.86 & ( ( N != zero_zero_nat )
% 5.52/5.86 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_sum_mult_2_cases
% 5.52/5.86 thf(fact_7161_bit__sum__mult__2__cases,axiom,
% 5.52/5.86 ! [A: nat,B: nat,N: nat] :
% 5.52/5.86 ( ! [J2: nat] :
% 5.52/5.86 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J2 ) )
% 5.52/5.86 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.52/5.86 = ( ( ( N = zero_zero_nat )
% 5.52/5.86 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.52/5.86 & ( ( N != zero_zero_nat )
% 5.52/5.86 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_sum_mult_2_cases
% 5.52/5.86 thf(fact_7162_bit__rec,axiom,
% 5.52/5.86 ( bit_se9216721137139052372nteger
% 5.52/5.86 = ( ^ [A4: code_integer,N3: nat] :
% 5.52/5.86 ( ( ( N3 = zero_zero_nat )
% 5.52/5.86 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) )
% 5.52/5.86 & ( ( N3 != zero_zero_nat )
% 5.52/5.86 => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_rec
% 5.52/5.86 thf(fact_7163_bit__rec,axiom,
% 5.52/5.86 ( bit_se1146084159140164899it_int
% 5.52/5.86 = ( ^ [A4: int,N3: nat] :
% 5.52/5.86 ( ( ( N3 = zero_zero_nat )
% 5.52/5.86 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) )
% 5.52/5.86 & ( ( N3 != zero_zero_nat )
% 5.52/5.86 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_rec
% 5.52/5.86 thf(fact_7164_bit__rec,axiom,
% 5.52/5.86 ( bit_se1148574629649215175it_nat
% 5.52/5.86 = ( ^ [A4: nat,N3: nat] :
% 5.52/5.86 ( ( ( N3 = zero_zero_nat )
% 5.52/5.86 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) )
% 5.52/5.86 & ( ( N3 != zero_zero_nat )
% 5.52/5.86 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_rec
% 5.52/5.86 thf(fact_7165_and__nat__unfold,axiom,
% 5.52/5.86 ( bit_se727722235901077358nd_nat
% 5.52/5.86 = ( ^ [M3: nat,N3: nat] :
% 5.52/5.86 ( if_nat
% 5.52/5.86 @ ( ( M3 = zero_zero_nat )
% 5.52/5.86 | ( N3 = zero_zero_nat ) )
% 5.52/5.86 @ zero_zero_nat
% 5.52/5.86 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % and_nat_unfold
% 5.52/5.86 thf(fact_7166_and__nat__rec,axiom,
% 5.52/5.86 ( bit_se727722235901077358nd_nat
% 5.52/5.86 = ( ^ [M3: nat,N3: nat] :
% 5.52/5.86 ( plus_plus_nat
% 5.52/5.86 @ ( zero_n2687167440665602831ol_nat
% 5.52/5.86 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 5.52/5.86 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.52/5.86 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % and_nat_rec
% 5.52/5.86 thf(fact_7167_double__arith__series,axiom,
% 5.52/5.86 ! [A: complex,D2: complex,N: nat] :
% 5.52/5.86 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.52/5.86 @ ( groups2073611262835488442omplex
% 5.52/5.86 @ ^ [I4: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I4 ) @ D2 ) )
% 5.52/5.86 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.86 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_arith_series
% 5.52/5.86 thf(fact_7168_double__arith__series,axiom,
% 5.52/5.86 ! [A: int,D2: int,N: nat] :
% 5.52/5.86 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.52/5.86 @ ( groups3539618377306564664at_int
% 5.52/5.86 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D2 ) )
% 5.52/5.86 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.86 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_arith_series
% 5.52/5.86 thf(fact_7169_double__arith__series,axiom,
% 5.52/5.86 ! [A: rat,D2: rat,N: nat] :
% 5.52/5.86 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.52/5.86 @ ( groups2906978787729119204at_rat
% 5.52/5.86 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I4 ) @ D2 ) )
% 5.52/5.86 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.86 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_arith_series
% 5.52/5.86 thf(fact_7170_double__arith__series,axiom,
% 5.52/5.86 ! [A: extended_enat,D2: extended_enat,N: nat] :
% 5.52/5.86 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) )
% 5.52/5.86 @ ( groups7108830773950497114d_enat
% 5.52/5.86 @ ^ [I4: nat] : ( plus_p3455044024723400733d_enat @ A @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ I4 ) @ D2 ) )
% 5.52/5.86 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.86 = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ D2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_arith_series
% 5.52/5.86 thf(fact_7171_double__arith__series,axiom,
% 5.52/5.86 ! [A: nat,D2: nat,N: nat] :
% 5.52/5.86 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.52/5.86 @ ( groups3542108847815614940at_nat
% 5.52/5.86 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D2 ) )
% 5.52/5.86 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.86 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_arith_series
% 5.52/5.86 thf(fact_7172_double__arith__series,axiom,
% 5.52/5.86 ! [A: real,D2: real,N: nat] :
% 5.52/5.86 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [I4: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I4 ) @ D2 ) )
% 5.52/5.86 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.86 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_arith_series
% 5.52/5.86 thf(fact_7173_double__gauss__sum,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.86 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_gauss_sum
% 5.52/5.86 thf(fact_7174_double__gauss__sum,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.86 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_gauss_sum
% 5.52/5.86 thf(fact_7175_double__gauss__sum,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.86 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_gauss_sum
% 5.52/5.86 thf(fact_7176_double__gauss__sum,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.86 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_gauss_sum
% 5.52/5.86 thf(fact_7177_double__gauss__sum,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.86 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_gauss_sum
% 5.52/5.86 thf(fact_7178_double__gauss__sum,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.86 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_gauss_sum
% 5.52/5.86 thf(fact_7179_set__bit__eq,axiom,
% 5.52/5.86 ( bit_se7879613467334960850it_int
% 5.52/5.86 = ( ^ [N3: nat,K2: int] :
% 5.52/5.86 ( plus_plus_int @ K2
% 5.52/5.86 @ ( times_times_int
% 5.52/5.86 @ ( zero_n2684676970156552555ol_int
% 5.52/5.86 @ ~ ( bit_se1146084159140164899it_int @ K2 @ N3 ) )
% 5.52/5.86 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % set_bit_eq
% 5.52/5.86 thf(fact_7180_unset__bit__eq,axiom,
% 5.52/5.86 ( bit_se4203085406695923979it_int
% 5.52/5.86 = ( ^ [N3: nat,K2: int] : ( minus_minus_int @ K2 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N3 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % unset_bit_eq
% 5.52/5.86 thf(fact_7181_take__bit__Suc__from__most,axiom,
% 5.52/5.86 ! [N: nat,K: int] :
% 5.52/5.86 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 5.52/5.86 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % take_bit_Suc_from_most
% 5.52/5.86 thf(fact_7182_double__gauss__sum__from__Suc__0,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.52/5.86 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_gauss_sum_from_Suc_0
% 5.52/5.86 thf(fact_7183_double__gauss__sum__from__Suc__0,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.52/5.86 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_gauss_sum_from_Suc_0
% 5.52/5.86 thf(fact_7184_double__gauss__sum__from__Suc__0,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.52/5.86 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_gauss_sum_from_Suc_0
% 5.52/5.86 thf(fact_7185_double__gauss__sum__from__Suc__0,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.52/5.86 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_gauss_sum_from_Suc_0
% 5.52/5.86 thf(fact_7186_double__gauss__sum__from__Suc__0,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.52/5.86 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_gauss_sum_from_Suc_0
% 5.52/5.86 thf(fact_7187_double__gauss__sum__from__Suc__0,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.52/5.86 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % double_gauss_sum_from_Suc_0
% 5.52/5.86 thf(fact_7188_arith__series,axiom,
% 5.52/5.86 ! [A: int,D2: int,N: nat] :
% 5.52/5.86 ( ( groups3539618377306564664at_int
% 5.52/5.86 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D2 ) )
% 5.52/5.86 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.52/5.86 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % arith_series
% 5.52/5.86 thf(fact_7189_arith__series,axiom,
% 5.52/5.86 ! [A: nat,D2: nat,N: nat] :
% 5.52/5.86 ( ( groups3542108847815614940at_nat
% 5.52/5.86 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D2 ) )
% 5.52/5.86 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.52/5.86 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % arith_series
% 5.52/5.86 thf(fact_7190_gauss__sum,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.52/5.86 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % gauss_sum
% 5.52/5.86 thf(fact_7191_gauss__sum,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.52/5.86 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % gauss_sum
% 5.52/5.86 thf(fact_7192_sum__gp__offset,axiom,
% 5.52/5.86 ! [X2: complex,M: nat,N: nat] :
% 5.52/5.86 ( ( ( X2 = one_one_complex )
% 5.52/5.86 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.52/5.86 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 5.52/5.86 & ( ( X2 != one_one_complex )
% 5.52/5.86 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.52/5.86 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_gp_offset
% 5.52/5.86 thf(fact_7193_sum__gp__offset,axiom,
% 5.52/5.86 ! [X2: rat,M: nat,N: nat] :
% 5.52/5.86 ( ( ( X2 = one_one_rat )
% 5.52/5.86 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.52/5.86 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 5.52/5.86 & ( ( X2 != one_one_rat )
% 5.52/5.86 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.52/5.86 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_gp_offset
% 5.52/5.86 thf(fact_7194_sum__gp__offset,axiom,
% 5.52/5.86 ! [X2: real,M: nat,N: nat] :
% 5.52/5.86 ( ( ( X2 = one_one_real )
% 5.52/5.86 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.52/5.86 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 5.52/5.86 & ( ( X2 != one_one_real )
% 5.52/5.86 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.52/5.86 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_gp_offset
% 5.52/5.86 thf(fact_7195_Bernoulli__inequality__even,axiom,
% 5.52/5.86 ! [N: nat,X2: real] :
% 5.52/5.86 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.86 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X2 ) @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Bernoulli_inequality_even
% 5.52/5.86 thf(fact_7196_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.52/5.86 ! [N: nat,X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X2 )
% 5.52/5.86 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % exp_ge_one_plus_x_over_n_power_n
% 5.52/5.86 thf(fact_7197_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N ) )
% 5.52/5.86 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % exp_ge_one_minus_x_over_n_power_n
% 5.52/5.86 thf(fact_7198_log__base__10__eq2,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.86 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % log_base_10_eq2
% 5.52/5.86 thf(fact_7199_of__nat__code__if,axiom,
% 5.52/5.86 ( semiri8010041392384452111omplex
% 5.52/5.86 = ( ^ [N3: nat] :
% 5.52/5.86 ( if_complex @ ( N3 = zero_zero_nat ) @ zero_zero_complex
% 5.52/5.86 @ ( produc1917071388513777916omplex
% 5.52/5.86 @ ^ [M3: nat,Q4: nat] : ( if_complex @ ( Q4 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ one_one_complex ) )
% 5.52/5.86 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_nat_code_if
% 5.52/5.86 thf(fact_7200_of__nat__code__if,axiom,
% 5.52/5.86 ( semiri1314217659103216013at_int
% 5.52/5.86 = ( ^ [N3: nat] :
% 5.52/5.86 ( if_int @ ( N3 = zero_zero_nat ) @ zero_zero_int
% 5.52/5.86 @ ( produc6840382203811409530at_int
% 5.52/5.86 @ ^ [M3: nat,Q4: nat] : ( if_int @ ( Q4 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ one_one_int ) )
% 5.52/5.86 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_nat_code_if
% 5.52/5.86 thf(fact_7201_of__nat__code__if,axiom,
% 5.52/5.86 ( semiri5074537144036343181t_real
% 5.52/5.86 = ( ^ [N3: nat] :
% 5.52/5.86 ( if_real @ ( N3 = zero_zero_nat ) @ zero_zero_real
% 5.52/5.86 @ ( produc1703576794950452218t_real
% 5.52/5.86 @ ^ [M3: nat,Q4: nat] : ( if_real @ ( Q4 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ one_one_real ) )
% 5.52/5.86 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_nat_code_if
% 5.52/5.86 thf(fact_7202_of__nat__code__if,axiom,
% 5.52/5.86 ( semiri1316708129612266289at_nat
% 5.52/5.86 = ( ^ [N3: nat] :
% 5.52/5.86 ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat
% 5.52/5.86 @ ( produc6842872674320459806at_nat
% 5.52/5.86 @ ^ [M3: nat,Q4: nat] : ( if_nat @ ( Q4 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ one_one_nat ) )
% 5.52/5.86 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_nat_code_if
% 5.52/5.86 thf(fact_7203_of__nat__code__if,axiom,
% 5.52/5.86 ( semiri681578069525770553at_rat
% 5.52/5.86 = ( ^ [N3: nat] :
% 5.52/5.86 ( if_rat @ ( N3 = zero_zero_nat ) @ zero_zero_rat
% 5.52/5.86 @ ( produc6207742614233964070at_rat
% 5.52/5.86 @ ^ [M3: nat,Q4: nat] : ( if_rat @ ( Q4 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ one_one_rat ) )
% 5.52/5.86 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_nat_code_if
% 5.52/5.86 thf(fact_7204_of__nat__code__if,axiom,
% 5.52/5.86 ( semiri4216267220026989637d_enat
% 5.52/5.86 = ( ^ [N3: nat] :
% 5.52/5.86 ( if_Extended_enat @ ( N3 = zero_zero_nat ) @ zero_z5237406670263579293d_enat
% 5.52/5.86 @ ( produc2676513652042109336d_enat
% 5.52/5.86 @ ^ [M3: nat,Q4: nat] : ( if_Extended_enat @ ( Q4 = zero_zero_nat ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( semiri4216267220026989637d_enat @ M3 ) ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( semiri4216267220026989637d_enat @ M3 ) ) @ one_on7984719198319812577d_enat ) )
% 5.52/5.86 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_nat_code_if
% 5.52/5.86 thf(fact_7205_monoseq__arctan__series,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.52/5.86 => ( topolo6980174941875973593q_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % monoseq_arctan_series
% 5.52/5.86 thf(fact_7206_lemma__termdiff3,axiom,
% 5.52/5.86 ! [H2: real,Z: real,K5: real,N: nat] :
% 5.52/5.86 ( ( H2 != zero_zero_real )
% 5.52/5.86 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.52/5.86 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lemma_termdiff3
% 5.52/5.86 thf(fact_7207_lemma__termdiff3,axiom,
% 5.52/5.86 ! [H2: complex,Z: complex,K5: real,N: nat] :
% 5.52/5.86 ( ( H2 != zero_zero_complex )
% 5.52/5.86 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.52/5.86 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lemma_termdiff3
% 5.52/5.86 thf(fact_7208_log__ceil__idem,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.52/5.86 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.52/5.86 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % log_ceil_idem
% 5.52/5.86 thf(fact_7209_ln__series,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.52/5.86 => ( ( ln_ln_real @ X2 )
% 5.52/5.86 = ( suminf_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ one_one_real ) @ ( suc @ N3 ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ln_series
% 5.52/5.86 thf(fact_7210_lemma__termdiff2,axiom,
% 5.52/5.86 ! [H2: complex,Z: complex,N: nat] :
% 5.52/5.86 ( ( H2 != zero_zero_complex )
% 5.52/5.86 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.52/5.86 = ( times_times_complex @ H2
% 5.52/5.86 @ ( groups2073611262835488442omplex
% 5.52/5.86 @ ^ [P4: nat] :
% 5.52/5.86 ( groups2073611262835488442omplex
% 5.52/5.86 @ ^ [Q4: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q4 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lemma_termdiff2
% 5.52/5.86 thf(fact_7211_lemma__termdiff2,axiom,
% 5.52/5.86 ! [H2: rat,Z: rat,N: nat] :
% 5.52/5.86 ( ( H2 != zero_zero_rat )
% 5.52/5.86 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N ) @ ( power_power_rat @ Z @ N ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.52/5.86 = ( times_times_rat @ H2
% 5.52/5.86 @ ( groups2906978787729119204at_rat
% 5.52/5.86 @ ^ [P4: nat] :
% 5.52/5.86 ( groups2906978787729119204at_rat
% 5.52/5.86 @ ^ [Q4: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q4 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lemma_termdiff2
% 5.52/5.86 thf(fact_7212_lemma__termdiff2,axiom,
% 5.52/5.86 ! [H2: real,Z: real,N: nat] :
% 5.52/5.86 ( ( H2 != zero_zero_real )
% 5.52/5.86 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.52/5.86 = ( times_times_real @ H2
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [P4: nat] :
% 5.52/5.86 ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [Q4: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q4 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lemma_termdiff2
% 5.52/5.86 thf(fact_7213_lessThan__iff,axiom,
% 5.52/5.86 ! [I: set_nat_rat,K: set_nat_rat] :
% 5.52/5.86 ( ( member_set_nat_rat @ I @ ( set_or6234697943151750426at_rat @ K ) )
% 5.52/5.86 = ( ord_less_set_nat_rat @ I @ K ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_iff
% 5.52/5.86 thf(fact_7214_lessThan__iff,axiom,
% 5.52/5.86 ! [I: rat,K: rat] :
% 5.52/5.86 ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 5.52/5.86 = ( ord_less_rat @ I @ K ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_iff
% 5.52/5.86 thf(fact_7215_lessThan__iff,axiom,
% 5.52/5.86 ! [I: num,K: num] :
% 5.52/5.86 ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 5.52/5.86 = ( ord_less_num @ I @ K ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_iff
% 5.52/5.86 thf(fact_7216_lessThan__iff,axiom,
% 5.52/5.86 ! [I: int,K: int] :
% 5.52/5.86 ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 5.52/5.86 = ( ord_less_int @ I @ K ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_iff
% 5.52/5.86 thf(fact_7217_lessThan__iff,axiom,
% 5.52/5.86 ! [I: nat,K: nat] :
% 5.52/5.86 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 5.52/5.86 = ( ord_less_nat @ I @ K ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_iff
% 5.52/5.86 thf(fact_7218_lessThan__iff,axiom,
% 5.52/5.86 ! [I: real,K: real] :
% 5.52/5.86 ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 5.52/5.86 = ( ord_less_real @ I @ K ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_iff
% 5.52/5.86 thf(fact_7219_of__int__ceiling__cancel,axiom,
% 5.52/5.86 ! [X2: rat] :
% 5.52/5.86 ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.52/5.86 = X2 )
% 5.52/5.86 = ( ? [N3: int] :
% 5.52/5.86 ( X2
% 5.52/5.86 = ( ring_1_of_int_rat @ N3 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_int_ceiling_cancel
% 5.52/5.86 thf(fact_7220_of__int__ceiling__cancel,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) )
% 5.52/5.86 = X2 )
% 5.52/5.86 = ( ? [N3: int] :
% 5.52/5.86 ( X2
% 5.52/5.86 = ( ring_1_of_int_real @ N3 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_int_ceiling_cancel
% 5.52/5.86 thf(fact_7221_heigt__uplog__rel,axiom,
% 5.52/5.86 ! [T: vEBT_VEBT,N: nat] :
% 5.52/5.86 ( ( vEBT_invar_vebt @ T @ N )
% 5.52/5.86 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ T ) )
% 5.52/5.86 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % heigt_uplog_rel
% 5.52/5.86 thf(fact_7222_lessThan__subset__iff,axiom,
% 5.52/5.86 ! [X2: rat,Y2: rat] :
% 5.52/5.86 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X2 ) @ ( set_ord_lessThan_rat @ Y2 ) )
% 5.52/5.86 = ( ord_less_eq_rat @ X2 @ Y2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_subset_iff
% 5.52/5.86 thf(fact_7223_lessThan__subset__iff,axiom,
% 5.52/5.86 ! [X2: num,Y2: num] :
% 5.52/5.86 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X2 ) @ ( set_ord_lessThan_num @ Y2 ) )
% 5.52/5.86 = ( ord_less_eq_num @ X2 @ Y2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_subset_iff
% 5.52/5.86 thf(fact_7224_lessThan__subset__iff,axiom,
% 5.52/5.86 ! [X2: int,Y2: int] :
% 5.52/5.86 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X2 ) @ ( set_ord_lessThan_int @ Y2 ) )
% 5.52/5.86 = ( ord_less_eq_int @ X2 @ Y2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_subset_iff
% 5.52/5.86 thf(fact_7225_lessThan__subset__iff,axiom,
% 5.52/5.86 ! [X2: nat,Y2: nat] :
% 5.52/5.86 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X2 ) @ ( set_ord_lessThan_nat @ Y2 ) )
% 5.52/5.86 = ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_subset_iff
% 5.52/5.86 thf(fact_7226_lessThan__subset__iff,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X2 ) @ ( set_or5984915006950818249n_real @ Y2 ) )
% 5.52/5.86 = ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_subset_iff
% 5.52/5.86 thf(fact_7227_ceiling__numeral,axiom,
% 5.52/5.86 ! [V: num] :
% 5.52/5.86 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 5.52/5.86 = ( numeral_numeral_int @ V ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_numeral
% 5.52/5.86 thf(fact_7228_ceiling__numeral,axiom,
% 5.52/5.86 ! [V: num] :
% 5.52/5.86 ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 5.52/5.86 = ( numeral_numeral_int @ V ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_numeral
% 5.52/5.86 thf(fact_7229_ceiling__one,axiom,
% 5.52/5.86 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 5.52/5.86 = one_one_int ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_one
% 5.52/5.86 thf(fact_7230_ceiling__one,axiom,
% 5.52/5.86 ( ( archim7802044766580827645g_real @ one_one_real )
% 5.52/5.86 = one_one_int ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_one
% 5.52/5.86 thf(fact_7231_sum_OlessThan__Suc,axiom,
% 5.52/5.86 ! [G: nat > rat,N: nat] :
% 5.52/5.86 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.86 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.lessThan_Suc
% 5.52/5.86 thf(fact_7232_sum_OlessThan__Suc,axiom,
% 5.52/5.86 ! [G: nat > int,N: nat] :
% 5.52/5.86 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.86 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.lessThan_Suc
% 5.52/5.86 thf(fact_7233_sum_OlessThan__Suc,axiom,
% 5.52/5.86 ! [G: nat > complex,N: nat] :
% 5.52/5.86 ( ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.86 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.lessThan_Suc
% 5.52/5.86 thf(fact_7234_sum_OlessThan__Suc,axiom,
% 5.52/5.86 ! [G: nat > nat,N: nat] :
% 5.52/5.86 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.86 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.lessThan_Suc
% 5.52/5.86 thf(fact_7235_sum_OlessThan__Suc,axiom,
% 5.52/5.86 ! [G: nat > real,N: nat] :
% 5.52/5.86 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.86 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.lessThan_Suc
% 5.52/5.86 thf(fact_7236_ceiling__add__of__int,axiom,
% 5.52/5.86 ! [X2: rat,Z: int] :
% 5.52/5.86 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.52/5.86 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_add_of_int
% 5.52/5.86 thf(fact_7237_ceiling__add__of__int,axiom,
% 5.52/5.86 ! [X2: real,Z: int] :
% 5.52/5.86 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) )
% 5.52/5.86 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ Z ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_add_of_int
% 5.52/5.86 thf(fact_7238_ceiling__le__zero,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ zero_zero_int )
% 5.52/5.86 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_le_zero
% 5.52/5.86 thf(fact_7239_ceiling__le__zero,axiom,
% 5.52/5.86 ! [X2: rat] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 5.52/5.86 = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_le_zero
% 5.52/5.86 thf(fact_7240_zero__less__ceiling,axiom,
% 5.52/5.86 ! [X2: rat] :
% 5.52/5.86 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.52/5.86 = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % zero_less_ceiling
% 5.52/5.86 thf(fact_7241_zero__less__ceiling,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.52/5.86 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % zero_less_ceiling
% 5.52/5.86 thf(fact_7242_ceiling__le__numeral,axiom,
% 5.52/5.86 ! [X2: real,V: num] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.86 = ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_le_numeral
% 5.52/5.86 thf(fact_7243_ceiling__le__numeral,axiom,
% 5.52/5.86 ! [X2: rat,V: num] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.86 = ( ord_less_eq_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_le_numeral
% 5.52/5.86 thf(fact_7244_ceiling__less__one,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int )
% 5.52/5.86 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_less_one
% 5.52/5.86 thf(fact_7245_ceiling__less__one,axiom,
% 5.52/5.86 ! [X2: rat] :
% 5.52/5.86 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 5.52/5.86 = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_less_one
% 5.52/5.86 thf(fact_7246_numeral__less__ceiling,axiom,
% 5.52/5.86 ! [V: num,X2: real] :
% 5.52/5.86 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.52/5.86 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % numeral_less_ceiling
% 5.52/5.86 thf(fact_7247_numeral__less__ceiling,axiom,
% 5.52/5.86 ! [V: num,X2: rat] :
% 5.52/5.86 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.52/5.86 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % numeral_less_ceiling
% 5.52/5.86 thf(fact_7248_one__le__ceiling,axiom,
% 5.52/5.86 ! [X2: rat] :
% 5.52/5.86 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.52/5.86 = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % one_le_ceiling
% 5.52/5.86 thf(fact_7249_one__le__ceiling,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.52/5.86 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % one_le_ceiling
% 5.52/5.86 thf(fact_7250_ceiling__le__one,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int )
% 5.52/5.86 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_le_one
% 5.52/5.86 thf(fact_7251_ceiling__le__one,axiom,
% 5.52/5.86 ! [X2: rat] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 5.52/5.86 = ( ord_less_eq_rat @ X2 @ one_one_rat ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_le_one
% 5.52/5.86 thf(fact_7252_one__less__ceiling,axiom,
% 5.52/5.86 ! [X2: rat] :
% 5.52/5.86 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.52/5.86 = ( ord_less_rat @ one_one_rat @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % one_less_ceiling
% 5.52/5.86 thf(fact_7253_one__less__ceiling,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.52/5.86 = ( ord_less_real @ one_one_real @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % one_less_ceiling
% 5.52/5.86 thf(fact_7254_ceiling__add__numeral,axiom,
% 5.52/5.86 ! [X2: real,V: num] :
% 5.52/5.86 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.86 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_add_numeral
% 5.52/5.86 thf(fact_7255_ceiling__add__numeral,axiom,
% 5.52/5.86 ! [X2: rat,V: num] :
% 5.52/5.86 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.86 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_add_numeral
% 5.52/5.86 thf(fact_7256_ceiling__neg__numeral,axiom,
% 5.52/5.86 ! [V: num] :
% 5.52/5.86 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.86 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_neg_numeral
% 5.52/5.86 thf(fact_7257_ceiling__neg__numeral,axiom,
% 5.52/5.86 ! [V: num] :
% 5.52/5.86 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.86 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_neg_numeral
% 5.52/5.86 thf(fact_7258_ceiling__add__one,axiom,
% 5.52/5.86 ! [X2: rat] :
% 5.52/5.86 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) )
% 5.52/5.86 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_add_one
% 5.52/5.86 thf(fact_7259_ceiling__add__one,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ one_one_real ) )
% 5.52/5.86 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_add_one
% 5.52/5.86 thf(fact_7260_ceiling__diff__numeral,axiom,
% 5.52/5.86 ! [X2: real,V: num] :
% 5.52/5.86 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.86 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_diff_numeral
% 5.52/5.86 thf(fact_7261_ceiling__diff__numeral,axiom,
% 5.52/5.86 ! [X2: rat,V: num] :
% 5.52/5.86 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.86 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_diff_numeral
% 5.52/5.86 thf(fact_7262_ceiling__diff__one,axiom,
% 5.52/5.86 ! [X2: rat] :
% 5.52/5.86 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 5.52/5.86 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_diff_one
% 5.52/5.86 thf(fact_7263_ceiling__diff__one,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ one_one_real ) )
% 5.52/5.86 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_diff_one
% 5.52/5.86 thf(fact_7264_ceiling__numeral__power,axiom,
% 5.52/5.86 ! [X2: num,N: nat] :
% 5.52/5.86 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.52/5.86 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_numeral_power
% 5.52/5.86 thf(fact_7265_ceiling__numeral__power,axiom,
% 5.52/5.86 ! [X2: num,N: nat] :
% 5.52/5.86 ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.52/5.86 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_numeral_power
% 5.52/5.86 thf(fact_7266_powser__zero,axiom,
% 5.52/5.86 ! [F: nat > complex] :
% 5.52/5.86 ( ( suminf_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) )
% 5.52/5.86 = ( F @ zero_zero_nat ) ) ).
% 5.52/5.86
% 5.52/5.86 % powser_zero
% 5.52/5.86 thf(fact_7267_powser__zero,axiom,
% 5.52/5.86 ! [F: nat > real] :
% 5.52/5.86 ( ( suminf_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) )
% 5.52/5.86 = ( F @ zero_zero_nat ) ) ).
% 5.52/5.86
% 5.52/5.86 % powser_zero
% 5.52/5.86 thf(fact_7268_ceiling__less__zero,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ zero_zero_int )
% 5.52/5.86 = ( ord_less_eq_real @ X2 @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_less_zero
% 5.52/5.86 thf(fact_7269_ceiling__less__zero,axiom,
% 5.52/5.86 ! [X2: rat] :
% 5.52/5.86 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 5.52/5.86 = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_less_zero
% 5.52/5.86 thf(fact_7270_zero__le__ceiling,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.52/5.86 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % zero_le_ceiling
% 5.52/5.86 thf(fact_7271_zero__le__ceiling,axiom,
% 5.52/5.86 ! [X2: rat] :
% 5.52/5.86 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.52/5.86 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % zero_le_ceiling
% 5.52/5.86 thf(fact_7272_ceiling__divide__eq__div__numeral,axiom,
% 5.52/5.86 ! [A: num,B: num] :
% 5.52/5.86 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.52/5.86 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_divide_eq_div_numeral
% 5.52/5.86 thf(fact_7273_ceiling__less__numeral,axiom,
% 5.52/5.86 ! [X2: real,V: num] :
% 5.52/5.86 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.86 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_less_numeral
% 5.52/5.86 thf(fact_7274_ceiling__less__numeral,axiom,
% 5.52/5.86 ! [X2: rat,V: num] :
% 5.52/5.86 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.86 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_less_numeral
% 5.52/5.86 thf(fact_7275_numeral__le__ceiling,axiom,
% 5.52/5.86 ! [V: num,X2: real] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.52/5.86 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % numeral_le_ceiling
% 5.52/5.86 thf(fact_7276_numeral__le__ceiling,axiom,
% 5.52/5.86 ! [V: num,X2: rat] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.52/5.86 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % numeral_le_ceiling
% 5.52/5.86 thf(fact_7277_ceiling__le__neg__numeral,axiom,
% 5.52/5.86 ! [X2: real,V: num] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.86 = ( ord_less_eq_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_le_neg_numeral
% 5.52/5.86 thf(fact_7278_ceiling__le__neg__numeral,axiom,
% 5.52/5.86 ! [X2: rat,V: num] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.86 = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_le_neg_numeral
% 5.52/5.86 thf(fact_7279_neg__numeral__less__ceiling,axiom,
% 5.52/5.86 ! [V: num,X2: real] :
% 5.52/5.86 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.52/5.86 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % neg_numeral_less_ceiling
% 5.52/5.86 thf(fact_7280_neg__numeral__less__ceiling,axiom,
% 5.52/5.86 ! [V: num,X2: rat] :
% 5.52/5.86 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.52/5.86 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % neg_numeral_less_ceiling
% 5.52/5.86 thf(fact_7281_set__encode__insert,axiom,
% 5.52/5.86 ! [A2: set_nat,N: nat] :
% 5.52/5.86 ( ( finite_finite_nat @ A2 )
% 5.52/5.86 => ( ~ ( member_nat @ N @ A2 )
% 5.52/5.86 => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 5.52/5.86 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % set_encode_insert
% 5.52/5.86 thf(fact_7282_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.52/5.86 ! [A: num,B: num] :
% 5.52/5.86 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.52/5.86 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_minus_divide_eq_div_numeral
% 5.52/5.86 thf(fact_7283_ceiling__less__neg__numeral,axiom,
% 5.52/5.86 ! [X2: real,V: num] :
% 5.52/5.86 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.86 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_less_neg_numeral
% 5.52/5.86 thf(fact_7284_ceiling__less__neg__numeral,axiom,
% 5.52/5.86 ! [X2: rat,V: num] :
% 5.52/5.86 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.86 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_less_neg_numeral
% 5.52/5.86 thf(fact_7285_neg__numeral__le__ceiling,axiom,
% 5.52/5.86 ! [V: num,X2: real] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.52/5.86 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % neg_numeral_le_ceiling
% 5.52/5.86 thf(fact_7286_neg__numeral__le__ceiling,axiom,
% 5.52/5.86 ! [V: num,X2: rat] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.52/5.86 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % neg_numeral_le_ceiling
% 5.52/5.86 thf(fact_7287_lessThan__nat__numeral,axiom,
% 5.52/5.86 ! [K: num] :
% 5.52/5.86 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.52/5.86 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_nat_numeral
% 5.52/5.86 thf(fact_7288_lessThan__def,axiom,
% 5.52/5.86 ( set_or6234697943151750426at_rat
% 5.52/5.86 = ( ^ [U2: set_nat_rat] :
% 5.52/5.86 ( collect_set_nat_rat
% 5.52/5.86 @ ^ [X: set_nat_rat] : ( ord_less_set_nat_rat @ X @ U2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_def
% 5.52/5.86 thf(fact_7289_lessThan__def,axiom,
% 5.52/5.86 ( set_or6855495488841395556at_rat
% 5.52/5.86 = ( ^ [U2: nat > rat] :
% 5.52/5.86 ( collect_nat_rat
% 5.52/5.86 @ ^ [X: nat > rat] : ( ord_less_nat_rat @ X @ U2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_def
% 5.52/5.86 thf(fact_7290_lessThan__def,axiom,
% 5.52/5.86 ( set_ord_lessThan_rat
% 5.52/5.86 = ( ^ [U2: rat] :
% 5.52/5.86 ( collect_rat
% 5.52/5.86 @ ^ [X: rat] : ( ord_less_rat @ X @ U2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_def
% 5.52/5.86 thf(fact_7291_lessThan__def,axiom,
% 5.52/5.86 ( set_ord_lessThan_num
% 5.52/5.86 = ( ^ [U2: num] :
% 5.52/5.86 ( collect_num
% 5.52/5.86 @ ^ [X: num] : ( ord_less_num @ X @ U2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_def
% 5.52/5.86 thf(fact_7292_lessThan__def,axiom,
% 5.52/5.86 ( set_ord_lessThan_int
% 5.52/5.86 = ( ^ [U2: int] :
% 5.52/5.86 ( collect_int
% 5.52/5.86 @ ^ [X: int] : ( ord_less_int @ X @ U2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_def
% 5.52/5.86 thf(fact_7293_lessThan__def,axiom,
% 5.52/5.86 ( set_ord_lessThan_nat
% 5.52/5.86 = ( ^ [U2: nat] :
% 5.52/5.86 ( collect_nat
% 5.52/5.86 @ ^ [X: nat] : ( ord_less_nat @ X @ U2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_def
% 5.52/5.86 thf(fact_7294_lessThan__def,axiom,
% 5.52/5.86 ( set_or5984915006950818249n_real
% 5.52/5.86 = ( ^ [U2: real] :
% 5.52/5.86 ( collect_real
% 5.52/5.86 @ ^ [X: real] : ( ord_less_real @ X @ U2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_def
% 5.52/5.86 thf(fact_7295_not__bit__Suc__0__Suc,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % not_bit_Suc_0_Suc
% 5.52/5.86 thf(fact_7296_bit__Suc__0__iff,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.52/5.86 = ( N = zero_zero_nat ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_Suc_0_iff
% 5.52/5.86 thf(fact_7297_ceiling__mono,axiom,
% 5.52/5.86 ! [Y2: real,X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ Y2 @ X2 )
% 5.52/5.86 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y2 ) @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_mono
% 5.52/5.86 thf(fact_7298_ceiling__mono,axiom,
% 5.52/5.86 ! [Y2: rat,X2: rat] :
% 5.52/5.86 ( ( ord_less_eq_rat @ Y2 @ X2 )
% 5.52/5.86 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y2 ) @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_mono
% 5.52/5.86 thf(fact_7299_le__of__int__ceiling,axiom,
% 5.52/5.86 ! [X2: real] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % le_of_int_ceiling
% 5.52/5.86 thf(fact_7300_le__of__int__ceiling,axiom,
% 5.52/5.86 ! [X2: rat] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % le_of_int_ceiling
% 5.52/5.86 thf(fact_7301_ceiling__less__cancel,axiom,
% 5.52/5.86 ! [X2: rat,Y2: rat] :
% 5.52/5.86 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y2 ) )
% 5.52/5.86 => ( ord_less_rat @ X2 @ Y2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_less_cancel
% 5.52/5.86 thf(fact_7302_ceiling__less__cancel,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim7802044766580827645g_real @ Y2 ) )
% 5.52/5.86 => ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_less_cancel
% 5.52/5.86 thf(fact_7303_lessThan__strict__subset__iff,axiom,
% 5.52/5.86 ! [M: rat,N: rat] :
% 5.52/5.86 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 5.52/5.86 = ( ord_less_rat @ M @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_strict_subset_iff
% 5.52/5.86 thf(fact_7304_lessThan__strict__subset__iff,axiom,
% 5.52/5.86 ! [M: num,N: num] :
% 5.52/5.86 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 5.52/5.86 = ( ord_less_num @ M @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_strict_subset_iff
% 5.52/5.86 thf(fact_7305_lessThan__strict__subset__iff,axiom,
% 5.52/5.86 ! [M: int,N: int] :
% 5.52/5.86 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 5.52/5.86 = ( ord_less_int @ M @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_strict_subset_iff
% 5.52/5.86 thf(fact_7306_lessThan__strict__subset__iff,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_strict_subset_iff
% 5.52/5.86 thf(fact_7307_lessThan__strict__subset__iff,axiom,
% 5.52/5.86 ! [M: real,N: real] :
% 5.52/5.86 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 5.52/5.86 = ( ord_less_real @ M @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % lessThan_strict_subset_iff
% 5.52/5.86 thf(fact_7308_not__bit__Suc__0__numeral,axiom,
% 5.52/5.86 ! [N: num] :
% 5.52/5.86 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % not_bit_Suc_0_numeral
% 5.52/5.86 thf(fact_7309_ceiling__le,axiom,
% 5.52/5.86 ! [X2: real,A: int] :
% 5.52/5.86 ( ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ A ) )
% 5.52/5.86 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ A ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_le
% 5.52/5.86 thf(fact_7310_ceiling__le,axiom,
% 5.52/5.86 ! [X2: rat,A: int] :
% 5.52/5.86 ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A ) )
% 5.52/5.86 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ A ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_le
% 5.52/5.86 thf(fact_7311_ceiling__le__iff,axiom,
% 5.52/5.86 ! [X2: real,Z: int] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ Z )
% 5.52/5.86 = ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_le_iff
% 5.52/5.86 thf(fact_7312_ceiling__le__iff,axiom,
% 5.52/5.86 ! [X2: rat,Z: int] :
% 5.52/5.86 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z )
% 5.52/5.86 = ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_le_iff
% 5.52/5.86 thf(fact_7313_less__ceiling__iff,axiom,
% 5.52/5.86 ! [Z: int,X2: rat] :
% 5.52/5.86 ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.52/5.86 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % less_ceiling_iff
% 5.52/5.86 thf(fact_7314_less__ceiling__iff,axiom,
% 5.52/5.86 ! [Z: int,X2: real] :
% 5.52/5.86 ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X2 ) )
% 5.52/5.86 = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % less_ceiling_iff
% 5.52/5.86 thf(fact_7315_ceiling__add__le,axiom,
% 5.52/5.86 ! [X2: rat,Y2: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ Y2 ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_add_le
% 5.52/5.86 thf(fact_7316_ceiling__add__le,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim7802044766580827645g_real @ Y2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_add_le
% 5.52/5.86 thf(fact_7317_Icc__eq__insert__lb__nat,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.86 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 5.52/5.86 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Icc_eq_insert_lb_nat
% 5.52/5.86 thf(fact_7318_atLeastAtMostSuc__conv,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.86 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 5.52/5.86 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % atLeastAtMostSuc_conv
% 5.52/5.86 thf(fact_7319_atLeastAtMost__insertL,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.86 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.52/5.86 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % atLeastAtMost_insertL
% 5.52/5.86 thf(fact_7320_sum__diff__distrib,axiom,
% 5.52/5.86 ! [Q: real > nat,P: real > nat,N: real] :
% 5.52/5.86 ( ! [X4: real] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 5.52/5.86 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 5.52/5.86 = ( groups1935376822645274424al_nat
% 5.52/5.86 @ ^ [X: real] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.52/5.86 @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_diff_distrib
% 5.52/5.86 thf(fact_7321_sum__diff__distrib,axiom,
% 5.52/5.86 ! [Q: nat > nat,P: nat > nat,N: nat] :
% 5.52/5.86 ( ! [X4: nat] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 5.52/5.86 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 5.52/5.86 = ( groups3542108847815614940at_nat
% 5.52/5.86 @ ^ [X: nat] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_diff_distrib
% 5.52/5.86 thf(fact_7322_of__int__ceiling__le__add__one,axiom,
% 5.52/5.86 ! [R: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R ) ) @ ( plus_plus_real @ R @ one_one_real ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_int_ceiling_le_add_one
% 5.52/5.86 thf(fact_7323_of__int__ceiling__le__add__one,axiom,
% 5.52/5.86 ! [R: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R ) ) @ ( plus_plus_rat @ R @ one_one_rat ) ) ).
% 5.52/5.86
% 5.52/5.86 % of_int_ceiling_le_add_one
% 5.52/5.86 thf(fact_7324_of__int__ceiling__diff__one__le,axiom,
% 5.52/5.86 ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R ) ) @ one_one_real ) @ R ) ).
% 5.52/5.86
% 5.52/5.86 % of_int_ceiling_diff_one_le
% 5.52/5.86 thf(fact_7325_of__int__ceiling__diff__one__le,axiom,
% 5.52/5.86 ! [R: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R ) ) @ one_one_rat ) @ R ) ).
% 5.52/5.86
% 5.52/5.86 % of_int_ceiling_diff_one_le
% 5.52/5.86 thf(fact_7326_ceiling__divide__eq__div,axiom,
% 5.52/5.86 ! [A: int,B: int] :
% 5.52/5.86 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 5.52/5.86 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_divide_eq_div
% 5.52/5.86 thf(fact_7327_ceiling__divide__eq__div,axiom,
% 5.52/5.86 ! [A: int,B: int] :
% 5.52/5.86 ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 5.52/5.86 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_divide_eq_div
% 5.52/5.86 thf(fact_7328_sum_OlessThan__Suc__shift,axiom,
% 5.52/5.86 ! [G: nat > rat,N: nat] :
% 5.52/5.86 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.86 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.52/5.86 @ ( groups2906978787729119204at_rat
% 5.52/5.86 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.lessThan_Suc_shift
% 5.52/5.86 thf(fact_7329_sum_OlessThan__Suc__shift,axiom,
% 5.52/5.86 ! [G: nat > int,N: nat] :
% 5.52/5.86 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.86 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.52/5.86 @ ( groups3539618377306564664at_int
% 5.52/5.86 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.lessThan_Suc_shift
% 5.52/5.86 thf(fact_7330_sum_OlessThan__Suc__shift,axiom,
% 5.52/5.86 ! [G: nat > complex,N: nat] :
% 5.52/5.86 ( ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.86 = ( plus_plus_complex @ ( G @ zero_zero_nat )
% 5.52/5.86 @ ( groups2073611262835488442omplex
% 5.52/5.86 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.lessThan_Suc_shift
% 5.52/5.86 thf(fact_7331_sum_OlessThan__Suc__shift,axiom,
% 5.52/5.86 ! [G: nat > nat,N: nat] :
% 5.52/5.86 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.86 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.52/5.86 @ ( groups3542108847815614940at_nat
% 5.52/5.86 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.lessThan_Suc_shift
% 5.52/5.86 thf(fact_7332_sum_OlessThan__Suc__shift,axiom,
% 5.52/5.86 ! [G: nat > real,N: nat] :
% 5.52/5.86 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.86 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum.lessThan_Suc_shift
% 5.52/5.86 thf(fact_7333_sumr__diff__mult__const2,axiom,
% 5.52/5.86 ! [F: nat > complex,N: nat,R: complex] :
% 5.52/5.86 ( ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ R ) )
% 5.52/5.86 = ( groups2073611262835488442omplex
% 5.52/5.86 @ ^ [I4: nat] : ( minus_minus_complex @ ( F @ I4 ) @ R )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sumr_diff_mult_const2
% 5.52/5.86 thf(fact_7334_sumr__diff__mult__const2,axiom,
% 5.52/5.86 ! [F: nat > int,N: nat,R: int] :
% 5.52/5.86 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R ) )
% 5.52/5.86 = ( groups3539618377306564664at_int
% 5.52/5.86 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ I4 ) @ R )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sumr_diff_mult_const2
% 5.52/5.86 thf(fact_7335_sumr__diff__mult__const2,axiom,
% 5.52/5.86 ! [F: nat > rat,N: nat,R: rat] :
% 5.52/5.86 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R ) )
% 5.52/5.86 = ( groups2906978787729119204at_rat
% 5.52/5.86 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ I4 ) @ R )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sumr_diff_mult_const2
% 5.52/5.86 thf(fact_7336_sumr__diff__mult__const2,axiom,
% 5.52/5.86 ! [F: nat > real,N: nat,R: real] :
% 5.52/5.86 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R ) )
% 5.52/5.86 = ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ I4 ) @ R )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sumr_diff_mult_const2
% 5.52/5.86 thf(fact_7337_ceiling__split,axiom,
% 5.52/5.86 ! [P: int > $o,T: real] :
% 5.52/5.86 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 5.52/5.86 = ( ! [I4: int] :
% 5.52/5.86 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) @ T )
% 5.52/5.86 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I4 ) ) )
% 5.52/5.86 => ( P @ I4 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_split
% 5.52/5.86 thf(fact_7338_ceiling__split,axiom,
% 5.52/5.86 ! [P: int > $o,T: rat] :
% 5.52/5.86 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 5.52/5.86 = ( ! [I4: int] :
% 5.52/5.86 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) @ T )
% 5.52/5.86 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I4 ) ) )
% 5.52/5.86 => ( P @ I4 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_split
% 5.52/5.86 thf(fact_7339_ceiling__eq__iff,axiom,
% 5.52/5.86 ! [X2: real,A: int] :
% 5.52/5.86 ( ( ( archim7802044766580827645g_real @ X2 )
% 5.52/5.86 = A )
% 5.52/5.86 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X2 )
% 5.52/5.86 & ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_eq_iff
% 5.52/5.86 thf(fact_7340_ceiling__eq__iff,axiom,
% 5.52/5.86 ! [X2: rat,A: int] :
% 5.52/5.86 ( ( ( archim2889992004027027881ng_rat @ X2 )
% 5.52/5.86 = A )
% 5.52/5.86 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X2 )
% 5.52/5.86 & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_eq_iff
% 5.52/5.86 thf(fact_7341_ceiling__unique,axiom,
% 5.52/5.86 ! [Z: int,X2: real] :
% 5.52/5.86 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z ) )
% 5.52/5.86 => ( ( archim7802044766580827645g_real @ X2 )
% 5.52/5.86 = Z ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_unique
% 5.52/5.86 thf(fact_7342_ceiling__unique,axiom,
% 5.52/5.86 ! [Z: int,X2: rat] :
% 5.52/5.86 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z ) )
% 5.52/5.86 => ( ( archim2889992004027027881ng_rat @ X2 )
% 5.52/5.86 = Z ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_unique
% 5.52/5.86 thf(fact_7343_ceiling__correct,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) @ one_one_real ) @ X2 )
% 5.52/5.86 & ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_correct
% 5.52/5.86 thf(fact_7344_ceiling__correct,axiom,
% 5.52/5.86 ! [X2: rat] :
% 5.52/5.86 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) @ one_one_rat ) @ X2 )
% 5.52/5.86 & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_correct
% 5.52/5.86 thf(fact_7345_mult__ceiling__le,axiom,
% 5.52/5.86 ! [A: real,B: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.86 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.86 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % mult_ceiling_le
% 5.52/5.86 thf(fact_7346_mult__ceiling__le,axiom,
% 5.52/5.86 ! [A: rat,B: rat] :
% 5.52/5.86 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.86 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.86 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % mult_ceiling_le
% 5.52/5.86 thf(fact_7347_ceiling__less__iff,axiom,
% 5.52/5.86 ! [X2: real,Z: int] :
% 5.52/5.86 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ Z )
% 5.52/5.86 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_less_iff
% 5.52/5.86 thf(fact_7348_ceiling__less__iff,axiom,
% 5.52/5.86 ! [X2: rat,Z: int] :
% 5.52/5.86 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z )
% 5.52/5.86 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_less_iff
% 5.52/5.86 thf(fact_7349_le__ceiling__iff,axiom,
% 5.52/5.86 ! [Z: int,X2: rat] :
% 5.52/5.86 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.52/5.86 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % le_ceiling_iff
% 5.52/5.86 thf(fact_7350_le__ceiling__iff,axiom,
% 5.52/5.86 ! [Z: int,X2: real] :
% 5.52/5.86 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X2 ) )
% 5.52/5.86 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % le_ceiling_iff
% 5.52/5.86 thf(fact_7351_one__diff__power__eq,axiom,
% 5.52/5.86 ! [X2: complex,N: nat] :
% 5.52/5.86 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) )
% 5.52/5.86 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % one_diff_power_eq
% 5.52/5.86 thf(fact_7352_one__diff__power__eq,axiom,
% 5.52/5.86 ! [X2: rat,N: nat] :
% 5.52/5.86 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) )
% 5.52/5.86 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % one_diff_power_eq
% 5.52/5.86 thf(fact_7353_one__diff__power__eq,axiom,
% 5.52/5.86 ! [X2: int,N: nat] :
% 5.52/5.86 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ N ) )
% 5.52/5.86 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % one_diff_power_eq
% 5.52/5.86 thf(fact_7354_one__diff__power__eq,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) )
% 5.52/5.86 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % one_diff_power_eq
% 5.52/5.86 thf(fact_7355_power__diff__1__eq,axiom,
% 5.52/5.86 ! [X2: complex,N: nat] :
% 5.52/5.86 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ one_one_complex )
% 5.52/5.86 = ( times_times_complex @ ( minus_minus_complex @ X2 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % power_diff_1_eq
% 5.52/5.86 thf(fact_7356_power__diff__1__eq,axiom,
% 5.52/5.86 ! [X2: rat,N: nat] :
% 5.52/5.86 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ one_one_rat )
% 5.52/5.86 = ( times_times_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % power_diff_1_eq
% 5.52/5.86 thf(fact_7357_power__diff__1__eq,axiom,
% 5.52/5.86 ! [X2: int,N: nat] :
% 5.52/5.86 ( ( minus_minus_int @ ( power_power_int @ X2 @ N ) @ one_one_int )
% 5.52/5.86 = ( times_times_int @ ( minus_minus_int @ X2 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % power_diff_1_eq
% 5.52/5.86 thf(fact_7358_power__diff__1__eq,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ one_one_real )
% 5.52/5.86 = ( times_times_real @ ( minus_minus_real @ X2 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % power_diff_1_eq
% 5.52/5.86 thf(fact_7359_geometric__sum,axiom,
% 5.52/5.86 ! [X2: complex,N: nat] :
% 5.52/5.86 ( ( X2 != one_one_complex )
% 5.52/5.86 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X2 @ one_one_complex ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % geometric_sum
% 5.52/5.86 thf(fact_7360_geometric__sum,axiom,
% 5.52/5.86 ! [X2: rat,N: nat] :
% 5.52/5.86 ( ( X2 != one_one_rat )
% 5.52/5.86 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % geometric_sum
% 5.52/5.86 thf(fact_7361_geometric__sum,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( X2 != one_one_real )
% 5.52/5.86 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % geometric_sum
% 5.52/5.86 thf(fact_7362_ceiling__divide__upper,axiom,
% 5.52/5.86 ! [Q2: real,P6: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.52/5.86 => ( ord_less_eq_real @ P6 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_divide_upper
% 5.52/5.86 thf(fact_7363_ceiling__divide__upper,axiom,
% 5.52/5.86 ! [Q2: rat,P6: rat] :
% 5.52/5.86 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.52/5.86 => ( ord_less_eq_rat @ P6 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_divide_upper
% 5.52/5.86 thf(fact_7364_bit__nat__def,axiom,
% 5.52/5.86 ( bit_se1148574629649215175it_nat
% 5.52/5.86 = ( ^ [M3: nat,N3: nat] :
% 5.52/5.86 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % bit_nat_def
% 5.52/5.86 thf(fact_7365_monoseq__realpow,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.52/5.86 => ( topolo6980174941875973593q_real @ ( power_power_real @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % monoseq_realpow
% 5.52/5.86 thf(fact_7366_sum__gp__strict,axiom,
% 5.52/5.86 ! [X2: complex,N: nat] :
% 5.52/5.86 ( ( ( X2 = one_one_complex )
% 5.52/5.86 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( semiri8010041392384452111omplex @ N ) ) )
% 5.52/5.86 & ( ( X2 != one_one_complex )
% 5.52/5.86 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_gp_strict
% 5.52/5.86 thf(fact_7367_sum__gp__strict,axiom,
% 5.52/5.86 ! [X2: rat,N: nat] :
% 5.52/5.86 ( ( ( X2 = one_one_rat )
% 5.52/5.86 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( semiri681578069525770553at_rat @ N ) ) )
% 5.52/5.86 & ( ( X2 != one_one_rat )
% 5.52/5.86 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_gp_strict
% 5.52/5.86 thf(fact_7368_sum__gp__strict,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( ( X2 = one_one_real )
% 5.52/5.86 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( semiri5074537144036343181t_real @ N ) ) )
% 5.52/5.86 & ( ( X2 != one_one_real )
% 5.52/5.86 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_gp_strict
% 5.52/5.86 thf(fact_7369_lemma__termdiff1,axiom,
% 5.52/5.86 ! [Z: complex,H2: complex,M: nat] :
% 5.52/5.86 ( ( groups2073611262835488442omplex
% 5.52/5.86 @ ^ [P4: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_complex @ Z @ P4 ) ) @ ( power_power_complex @ Z @ M ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ M ) )
% 5.52/5.86 = ( groups2073611262835488442omplex
% 5.52/5.86 @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P4 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lemma_termdiff1
% 5.52/5.86 thf(fact_7370_lemma__termdiff1,axiom,
% 5.52/5.86 ! [Z: rat,H2: rat,M: nat] :
% 5.52/5.86 ( ( groups2906978787729119204at_rat
% 5.52/5.86 @ ^ [P4: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_rat @ Z @ P4 ) ) @ ( power_power_rat @ Z @ M ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ M ) )
% 5.52/5.86 = ( groups2906978787729119204at_rat
% 5.52/5.86 @ ^ [P4: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P4 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lemma_termdiff1
% 5.52/5.86 thf(fact_7371_lemma__termdiff1,axiom,
% 5.52/5.86 ! [Z: int,H2: int,M: nat] :
% 5.52/5.86 ( ( groups3539618377306564664at_int
% 5.52/5.86 @ ^ [P4: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_int @ Z @ P4 ) ) @ ( power_power_int @ Z @ M ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ M ) )
% 5.52/5.86 = ( groups3539618377306564664at_int
% 5.52/5.86 @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ Z @ P4 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lemma_termdiff1
% 5.52/5.86 thf(fact_7372_lemma__termdiff1,axiom,
% 5.52/5.86 ! [Z: real,H2: real,M: nat] :
% 5.52/5.86 ( ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [P4: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_real @ Z @ P4 ) ) @ ( power_power_real @ Z @ M ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ M ) )
% 5.52/5.86 = ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ Z @ P4 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % lemma_termdiff1
% 5.52/5.86 thf(fact_7373_power__diff__sumr2,axiom,
% 5.52/5.86 ! [X2: complex,N: nat,Y2: complex] :
% 5.52/5.86 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y2 @ N ) )
% 5.52/5.86 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y2 )
% 5.52/5.86 @ ( groups2073611262835488442omplex
% 5.52/5.86 @ ^ [I4: nat] : ( times_times_complex @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % power_diff_sumr2
% 5.52/5.86 thf(fact_7374_power__diff__sumr2,axiom,
% 5.52/5.86 ! [X2: rat,N: nat,Y2: rat] :
% 5.52/5.86 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ Y2 @ N ) )
% 5.52/5.86 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y2 )
% 5.52/5.86 @ ( groups2906978787729119204at_rat
% 5.52/5.86 @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_rat @ X2 @ I4 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % power_diff_sumr2
% 5.52/5.86 thf(fact_7375_power__diff__sumr2,axiom,
% 5.52/5.86 ! [X2: int,N: nat,Y2: int] :
% 5.52/5.86 ( ( minus_minus_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y2 @ N ) )
% 5.52/5.86 = ( times_times_int @ ( minus_minus_int @ X2 @ Y2 )
% 5.52/5.86 @ ( groups3539618377306564664at_int
% 5.52/5.86 @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_int @ X2 @ I4 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % power_diff_sumr2
% 5.52/5.86 thf(fact_7376_power__diff__sumr2,axiom,
% 5.52/5.86 ! [X2: real,N: nat,Y2: real] :
% 5.52/5.86 ( ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y2 @ N ) )
% 5.52/5.86 = ( times_times_real @ ( minus_minus_real @ X2 @ Y2 )
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_real @ X2 @ I4 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % power_diff_sumr2
% 5.52/5.86 thf(fact_7377_diff__power__eq__sum,axiom,
% 5.52/5.86 ! [X2: complex,N: nat,Y2: complex] :
% 5.52/5.86 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ ( suc @ N ) ) @ ( power_power_complex @ Y2 @ ( suc @ N ) ) )
% 5.52/5.86 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y2 )
% 5.52/5.86 @ ( groups2073611262835488442omplex
% 5.52/5.86 @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ X2 @ P4 ) @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % diff_power_eq_sum
% 5.52/5.86 thf(fact_7378_diff__power__eq__sum,axiom,
% 5.52/5.86 ! [X2: rat,N: nat,Y2: rat] :
% 5.52/5.86 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ ( suc @ N ) ) @ ( power_power_rat @ Y2 @ ( suc @ N ) ) )
% 5.52/5.86 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y2 )
% 5.52/5.86 @ ( groups2906978787729119204at_rat
% 5.52/5.86 @ ^ [P4: nat] : ( times_times_rat @ ( power_power_rat @ X2 @ P4 ) @ ( power_power_rat @ Y2 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % diff_power_eq_sum
% 5.52/5.86 thf(fact_7379_diff__power__eq__sum,axiom,
% 5.52/5.86 ! [X2: int,N: nat,Y2: int] :
% 5.52/5.86 ( ( minus_minus_int @ ( power_power_int @ X2 @ ( suc @ N ) ) @ ( power_power_int @ Y2 @ ( suc @ N ) ) )
% 5.52/5.86 = ( times_times_int @ ( minus_minus_int @ X2 @ Y2 )
% 5.52/5.86 @ ( groups3539618377306564664at_int
% 5.52/5.86 @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ X2 @ P4 ) @ ( power_power_int @ Y2 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % diff_power_eq_sum
% 5.52/5.86 thf(fact_7380_diff__power__eq__sum,axiom,
% 5.52/5.86 ! [X2: real,N: nat,Y2: real] :
% 5.52/5.86 ( ( minus_minus_real @ ( power_power_real @ X2 @ ( suc @ N ) ) @ ( power_power_real @ Y2 @ ( suc @ N ) ) )
% 5.52/5.86 = ( times_times_real @ ( minus_minus_real @ X2 @ Y2 )
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ X2 @ P4 ) @ ( power_power_real @ Y2 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % diff_power_eq_sum
% 5.52/5.86 thf(fact_7381_set__decode__plus__power__2,axiom,
% 5.52/5.86 ! [N: nat,Z: nat] :
% 5.52/5.86 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 5.52/5.86 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 5.52/5.86 = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % set_decode_plus_power_2
% 5.52/5.86 thf(fact_7382_ceiling__divide__lower,axiom,
% 5.52/5.86 ! [Q2: real,P6: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.52/5.86 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) @ P6 ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_divide_lower
% 5.52/5.86 thf(fact_7383_ceiling__divide__lower,axiom,
% 5.52/5.86 ! [Q2: rat,P6: rat] :
% 5.52/5.86 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.52/5.86 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) @ P6 ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_divide_lower
% 5.52/5.86 thf(fact_7384_ceiling__eq,axiom,
% 5.52/5.86 ! [N: int,X2: real] :
% 5.52/5.86 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.52/5.86 => ( ( archim7802044766580827645g_real @ X2 )
% 5.52/5.86 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_eq
% 5.52/5.86 thf(fact_7385_ceiling__eq,axiom,
% 5.52/5.86 ! [N: int,X2: rat] :
% 5.52/5.86 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 5.52/5.86 => ( ( archim2889992004027027881ng_rat @ X2 )
% 5.52/5.86 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_eq
% 5.52/5.86 thf(fact_7386_real__sum__nat__ivl__bounded2,axiom,
% 5.52/5.86 ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 5.52/5.86 ( ! [P7: nat] :
% 5.52/5.86 ( ( ord_less_nat @ P7 @ N )
% 5.52/5.86 => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 5.52/5.86 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 5.52/5.86 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % real_sum_nat_ivl_bounded2
% 5.52/5.86 thf(fact_7387_real__sum__nat__ivl__bounded2,axiom,
% 5.52/5.86 ! [N: nat,F: nat > int,K5: int,K: nat] :
% 5.52/5.86 ( ! [P7: nat] :
% 5.52/5.86 ( ( ord_less_nat @ P7 @ N )
% 5.52/5.86 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 5.52/5.86 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.52/5.86 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % real_sum_nat_ivl_bounded2
% 5.52/5.86 thf(fact_7388_real__sum__nat__ivl__bounded2,axiom,
% 5.52/5.86 ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 5.52/5.86 ( ! [P7: nat] :
% 5.52/5.86 ( ( ord_less_nat @ P7 @ N )
% 5.52/5.86 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 5.52/5.86 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.52/5.86 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % real_sum_nat_ivl_bounded2
% 5.52/5.86 thf(fact_7389_real__sum__nat__ivl__bounded2,axiom,
% 5.52/5.86 ! [N: nat,F: nat > real,K5: real,K: nat] :
% 5.52/5.86 ( ! [P7: nat] :
% 5.52/5.86 ( ( ord_less_nat @ P7 @ N )
% 5.52/5.86 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 5.52/5.86 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.52/5.86 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % real_sum_nat_ivl_bounded2
% 5.52/5.86 thf(fact_7390_exp__bound__half,axiom,
% 5.52/5.86 ! [Z: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % exp_bound_half
% 5.52/5.86 thf(fact_7391_exp__bound__half,axiom,
% 5.52/5.86 ! [Z: complex] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % exp_bound_half
% 5.52/5.86 thf(fact_7392_one__diff__power__eq_H,axiom,
% 5.52/5.86 ! [X2: complex,N: nat] :
% 5.52/5.86 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) )
% 5.52/5.86 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 )
% 5.52/5.86 @ ( groups2073611262835488442omplex
% 5.52/5.86 @ ^ [I4: nat] : ( power_power_complex @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % one_diff_power_eq'
% 5.52/5.86 thf(fact_7393_one__diff__power__eq_H,axiom,
% 5.52/5.86 ! [X2: rat,N: nat] :
% 5.52/5.86 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) )
% 5.52/5.86 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 )
% 5.52/5.86 @ ( groups2906978787729119204at_rat
% 5.52/5.86 @ ^ [I4: nat] : ( power_power_rat @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % one_diff_power_eq'
% 5.52/5.86 thf(fact_7394_one__diff__power__eq_H,axiom,
% 5.52/5.86 ! [X2: int,N: nat] :
% 5.52/5.86 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ N ) )
% 5.52/5.86 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 )
% 5.52/5.86 @ ( groups3539618377306564664at_int
% 5.52/5.86 @ ^ [I4: nat] : ( power_power_int @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % one_diff_power_eq'
% 5.52/5.86 thf(fact_7395_one__diff__power__eq_H,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) )
% 5.52/5.86 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 )
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [I4: nat] : ( power_power_real @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % one_diff_power_eq'
% 5.52/5.86 thf(fact_7396_sum__split__even__odd,axiom,
% 5.52/5.86 ! [F: nat > real,G: nat > real,N: nat] :
% 5.52/5.86 ( ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( F @ I4 ) @ ( G @ I4 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.86 = ( plus_plus_real
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [I4: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ one_one_nat ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_split_even_odd
% 5.52/5.86 thf(fact_7397_exp__bound__lemma,axiom,
% 5.52/5.86 ! [Z: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % exp_bound_lemma
% 5.52/5.86 thf(fact_7398_exp__bound__lemma,axiom,
% 5.52/5.86 ! [Z: complex] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % exp_bound_lemma
% 5.52/5.86 thf(fact_7399_ceiling__log__nat__eq__if,axiom,
% 5.52/5.86 ! [B: nat,N: nat,K: nat] :
% 5.52/5.86 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.52/5.86 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.52/5.86 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.52/5.86 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.52/5.86 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_log_nat_eq_if
% 5.52/5.86 thf(fact_7400_ceiling__log__nat__eq__powr__iff,axiom,
% 5.52/5.86 ! [B: nat,K: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.52/5.86 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.86 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.52/5.86 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.52/5.86 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.52/5.86 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_log_nat_eq_powr_iff
% 5.52/5.86 thf(fact_7401_ceiling__log2__div2,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.86 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.52/5.86 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % ceiling_log2_div2
% 5.52/5.86 thf(fact_7402_arctan__series,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.52/5.86 => ( ( arctan @ X2 )
% 5.52/5.86 = ( suminf_real
% 5.52/5.86 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % arctan_series
% 5.52/5.86 thf(fact_7403_norm__divide__numeral,axiom,
% 5.52/5.86 ! [A: real,W: num] :
% 5.52/5.86 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.52/5.86 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_divide_numeral
% 5.52/5.86 thf(fact_7404_norm__divide__numeral,axiom,
% 5.52/5.86 ! [A: complex,W: num] :
% 5.52/5.86 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.52/5.86 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_divide_numeral
% 5.52/5.86 thf(fact_7405_norm__mult__numeral1,axiom,
% 5.52/5.86 ! [W: num,A: real] :
% 5.52/5.86 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.52/5.86 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_mult_numeral1
% 5.52/5.86 thf(fact_7406_norm__mult__numeral1,axiom,
% 5.52/5.86 ! [W: num,A: complex] :
% 5.52/5.86 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.52/5.86 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_mult_numeral1
% 5.52/5.86 thf(fact_7407_norm__mult__numeral2,axiom,
% 5.52/5.86 ! [A: real,W: num] :
% 5.52/5.86 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.52/5.86 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_mult_numeral2
% 5.52/5.86 thf(fact_7408_norm__mult__numeral2,axiom,
% 5.52/5.86 ! [A: complex,W: num] :
% 5.52/5.86 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.52/5.86 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_mult_numeral2
% 5.52/5.86 thf(fact_7409_norm__neg__numeral,axiom,
% 5.52/5.86 ! [W: num] :
% 5.52/5.86 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.52/5.86 = ( numeral_numeral_real @ W ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_neg_numeral
% 5.52/5.86 thf(fact_7410_norm__neg__numeral,axiom,
% 5.52/5.86 ! [W: num] :
% 5.52/5.86 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.52/5.86 = ( numeral_numeral_real @ W ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_neg_numeral
% 5.52/5.86 thf(fact_7411_zero__less__norm__iff,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.52/5.86 = ( X2 != zero_zero_real ) ) ).
% 5.52/5.86
% 5.52/5.86 % zero_less_norm_iff
% 5.52/5.86 thf(fact_7412_zero__less__norm__iff,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.52/5.86 = ( X2 != zero_zero_complex ) ) ).
% 5.52/5.86
% 5.52/5.86 % zero_less_norm_iff
% 5.52/5.86 thf(fact_7413_norm__one,axiom,
% 5.52/5.86 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % norm_one
% 5.52/5.86 thf(fact_7414_norm__one,axiom,
% 5.52/5.86 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % norm_one
% 5.52/5.86 thf(fact_7415_norm__numeral,axiom,
% 5.52/5.86 ! [W: num] :
% 5.52/5.86 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.52/5.86 = ( numeral_numeral_real @ W ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_numeral
% 5.52/5.86 thf(fact_7416_norm__numeral,axiom,
% 5.52/5.86 ! [W: num] :
% 5.52/5.86 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.52/5.86 = ( numeral_numeral_real @ W ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_numeral
% 5.52/5.86 thf(fact_7417_norm__not__less__zero,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ zero_zero_real ) ).
% 5.52/5.86
% 5.52/5.86 % norm_not_less_zero
% 5.52/5.86 thf(fact_7418_norm__mult,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y2 ) )
% 5.52/5.86 = ( times_times_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_mult
% 5.52/5.86 thf(fact_7419_norm__mult,axiom,
% 5.52/5.86 ! [X2: complex,Y2: complex] :
% 5.52/5.86 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y2 ) )
% 5.52/5.86 = ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_mult
% 5.52/5.86 thf(fact_7420_norm__divide,axiom,
% 5.52/5.86 ! [A: real,B: real] :
% 5.52/5.86 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.52/5.86 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_divide
% 5.52/5.86 thf(fact_7421_norm__divide,axiom,
% 5.52/5.86 ! [A: complex,B: complex] :
% 5.52/5.86 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.52/5.86 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_divide
% 5.52/5.86 thf(fact_7422_norm__power,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N ) )
% 5.52/5.86 = ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_power
% 5.52/5.86 thf(fact_7423_norm__power,axiom,
% 5.52/5.86 ! [X2: complex,N: nat] :
% 5.52/5.86 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N ) )
% 5.52/5.86 = ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_power
% 5.52/5.86 thf(fact_7424_norm__uminus__minus,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ Y2 ) )
% 5.52/5.86 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_uminus_minus
% 5.52/5.86 thf(fact_7425_norm__uminus__minus,axiom,
% 5.52/5.86 ! [X2: complex,Y2: complex] :
% 5.52/5.86 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ Y2 ) )
% 5.52/5.86 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_uminus_minus
% 5.52/5.86 thf(fact_7426_nonzero__norm__divide,axiom,
% 5.52/5.86 ! [B: real,A: real] :
% 5.52/5.86 ( ( B != zero_zero_real )
% 5.52/5.86 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.52/5.86 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % nonzero_norm_divide
% 5.52/5.86 thf(fact_7427_nonzero__norm__divide,axiom,
% 5.52/5.86 ! [B: complex,A: complex] :
% 5.52/5.86 ( ( B != zero_zero_complex )
% 5.52/5.86 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.52/5.86 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % nonzero_norm_divide
% 5.52/5.86 thf(fact_7428_power__eq__imp__eq__norm,axiom,
% 5.52/5.86 ! [W: real,N: nat,Z: real] :
% 5.52/5.86 ( ( ( power_power_real @ W @ N )
% 5.52/5.86 = ( power_power_real @ Z @ N ) )
% 5.52/5.86 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ( real_V7735802525324610683m_real @ W )
% 5.52/5.86 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % power_eq_imp_eq_norm
% 5.52/5.86 thf(fact_7429_power__eq__imp__eq__norm,axiom,
% 5.52/5.86 ! [W: complex,N: nat,Z: complex] :
% 5.52/5.86 ( ( ( power_power_complex @ W @ N )
% 5.52/5.86 = ( power_power_complex @ Z @ N ) )
% 5.52/5.86 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ( real_V1022390504157884413omplex @ W )
% 5.52/5.86 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % power_eq_imp_eq_norm
% 5.52/5.86 thf(fact_7430_norm__mult__less,axiom,
% 5.52/5.86 ! [X2: real,R: real,Y2: real,S: real] :
% 5.52/5.86 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R )
% 5.52/5.86 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y2 ) @ S )
% 5.52/5.86 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y2 ) ) @ ( times_times_real @ R @ S ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_mult_less
% 5.52/5.86 thf(fact_7431_norm__mult__less,axiom,
% 5.52/5.86 ! [X2: complex,R: real,Y2: complex,S: real] :
% 5.52/5.86 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R )
% 5.52/5.86 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y2 ) @ S )
% 5.52/5.86 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y2 ) ) @ ( times_times_real @ R @ S ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_mult_less
% 5.52/5.86 thf(fact_7432_norm__mult__ineq,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y2 ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_mult_ineq
% 5.52/5.86 thf(fact_7433_norm__mult__ineq,axiom,
% 5.52/5.86 ! [X2: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y2 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_mult_ineq
% 5.52/5.86 thf(fact_7434_norm__add__less,axiom,
% 5.52/5.86 ! [X2: real,R: real,Y2: real,S: real] :
% 5.52/5.86 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R )
% 5.52/5.86 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y2 ) @ S )
% 5.52/5.86 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_add_less
% 5.52/5.86 thf(fact_7435_norm__add__less,axiom,
% 5.52/5.86 ! [X2: complex,R: real,Y2: complex,S: real] :
% 5.52/5.86 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R )
% 5.52/5.86 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y2 ) @ S )
% 5.52/5.86 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y2 ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_add_less
% 5.52/5.86 thf(fact_7436_norm__triangle__lt,axiom,
% 5.52/5.86 ! [X2: real,Y2: real,E: real] :
% 5.52/5.86 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y2 ) ) @ E )
% 5.52/5.86 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ E ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_triangle_lt
% 5.52/5.86 thf(fact_7437_norm__triangle__lt,axiom,
% 5.52/5.86 ! [X2: complex,Y2: complex,E: real] :
% 5.52/5.86 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 5.52/5.86 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y2 ) ) @ E ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_triangle_lt
% 5.52/5.86 thf(fact_7438_norm__add__leD,axiom,
% 5.52/5.86 ! [A: real,B: real,C: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_add_leD
% 5.52/5.86 thf(fact_7439_norm__add__leD,axiom,
% 5.52/5.86 ! [A: complex,B: complex,C: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_add_leD
% 5.52/5.86 thf(fact_7440_norm__triangle__le,axiom,
% 5.52/5.86 ! [X2: real,Y2: real,E: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y2 ) ) @ E )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ E ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_triangle_le
% 5.52/5.86 thf(fact_7441_norm__triangle__le,axiom,
% 5.52/5.86 ! [X2: complex,Y2: complex,E: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y2 ) ) @ E ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_triangle_le
% 5.52/5.86 thf(fact_7442_norm__triangle__ineq,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_triangle_ineq
% 5.52/5.86 thf(fact_7443_norm__triangle__ineq,axiom,
% 5.52/5.86 ! [X2: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y2 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_triangle_ineq
% 5.52/5.86 thf(fact_7444_norm__triangle__mono,axiom,
% 5.52/5.86 ! [A: real,R: real,B: real,S: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R )
% 5.52/5.86 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_triangle_mono
% 5.52/5.86 thf(fact_7445_norm__triangle__mono,axiom,
% 5.52/5.86 ! [A: complex,R: real,B: complex,S: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R )
% 5.52/5.86 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_triangle_mono
% 5.52/5.86 thf(fact_7446_norm__power__ineq,axiom,
% 5.52/5.86 ! [X2: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_power_ineq
% 5.52/5.86 thf(fact_7447_norm__power__ineq,axiom,
% 5.52/5.86 ! [X2: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_power_ineq
% 5.52/5.86 thf(fact_7448_norm__diff__triangle__less,axiom,
% 5.52/5.86 ! [X2: real,Y2: real,E1: real,Z: real,E22: real] :
% 5.52/5.86 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y2 ) ) @ E1 )
% 5.52/5.86 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y2 @ Z ) ) @ E22 )
% 5.52/5.86 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_diff_triangle_less
% 5.52/5.86 thf(fact_7449_norm__diff__triangle__less,axiom,
% 5.52/5.86 ! [X2: complex,Y2: complex,E1: real,Z: complex,E22: real] :
% 5.52/5.86 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y2 ) ) @ E1 )
% 5.52/5.86 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y2 @ Z ) ) @ E22 )
% 5.52/5.86 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_diff_triangle_less
% 5.52/5.86 thf(fact_7450_norm__diff__ineq,axiom,
% 5.52/5.86 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_diff_ineq
% 5.52/5.86 thf(fact_7451_norm__diff__ineq,axiom,
% 5.52/5.86 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_diff_ineq
% 5.52/5.86 thf(fact_7452_power__eq__1__iff,axiom,
% 5.52/5.86 ! [W: real,N: nat] :
% 5.52/5.86 ( ( ( power_power_real @ W @ N )
% 5.52/5.86 = one_one_real )
% 5.52/5.86 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.52/5.86 = one_one_real )
% 5.52/5.86 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % power_eq_1_iff
% 5.52/5.86 thf(fact_7453_power__eq__1__iff,axiom,
% 5.52/5.86 ! [W: complex,N: nat] :
% 5.52/5.86 ( ( ( power_power_complex @ W @ N )
% 5.52/5.86 = one_one_complex )
% 5.52/5.86 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.52/5.86 = one_one_real )
% 5.52/5.86 | ( N = zero_zero_nat ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % power_eq_1_iff
% 5.52/5.86 thf(fact_7454_norm__diff__triangle__ineq,axiom,
% 5.52/5.86 ! [A: real,B: real,C: real,D2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D2 ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_diff_triangle_ineq
% 5.52/5.86 thf(fact_7455_norm__diff__triangle__ineq,axiom,
% 5.52/5.86 ! [A: complex,B: complex,C: complex,D2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D2 ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_diff_triangle_ineq
% 5.52/5.86 thf(fact_7456_square__norm__one,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.86 = one_one_real )
% 5.52/5.86 => ( ( real_V7735802525324610683m_real @ X2 )
% 5.52/5.86 = one_one_real ) ) ).
% 5.52/5.86
% 5.52/5.86 % square_norm_one
% 5.52/5.86 thf(fact_7457_square__norm__one,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ( ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.86 = one_one_complex )
% 5.52/5.86 => ( ( real_V1022390504157884413omplex @ X2 )
% 5.52/5.86 = one_one_real ) ) ).
% 5.52/5.86
% 5.52/5.86 % square_norm_one
% 5.52/5.86 thf(fact_7458_norm__power__diff,axiom,
% 5.52/5.86 ! [Z: real,W: real,M: nat] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.52/5.86 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z @ M ) @ ( power_power_real @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z @ W ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_power_diff
% 5.52/5.86 thf(fact_7459_norm__power__diff,axiom,
% 5.52/5.86 ! [Z: complex,W: complex,M: nat] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.52/5.86 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z @ M ) @ ( power_power_complex @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z @ W ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % norm_power_diff
% 5.52/5.86 thf(fact_7460_suminf__geometric,axiom,
% 5.52/5.86 ! [C: real] :
% 5.52/5.86 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.52/5.86 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.52/5.86 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_geometric
% 5.52/5.86 thf(fact_7461_suminf__geometric,axiom,
% 5.52/5.86 ! [C: complex] :
% 5.52/5.86 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.52/5.86 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.52/5.86 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_geometric
% 5.52/5.86 thf(fact_7462_sum__bounds__lt__plus1,axiom,
% 5.52/5.86 ! [F: nat > nat,Mm: nat] :
% 5.52/5.86 ( ( groups3542108847815614940at_nat
% 5.52/5.86 @ ^ [K2: nat] : ( F @ ( suc @ K2 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.52/5.86 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_bounds_lt_plus1
% 5.52/5.86 thf(fact_7463_sum__bounds__lt__plus1,axiom,
% 5.52/5.86 ! [F: nat > real,Mm: nat] :
% 5.52/5.86 ( ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [K2: nat] : ( F @ ( suc @ K2 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.52/5.86 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_bounds_lt_plus1
% 5.52/5.86 thf(fact_7464_sumr__cos__zero__one,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ zero_zero_real @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % sumr_cos_zero_one
% 5.52/5.86 thf(fact_7465_pi__series,axiom,
% 5.52/5.86 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = ( suminf_real
% 5.52/5.86 @ ^ [K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % pi_series
% 5.52/5.86 thf(fact_7466_summable__arctan__series,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_arctan_series
% 5.52/5.86 thf(fact_7467_summable__iff__shift,axiom,
% 5.52/5.86 ! [F: nat > real,K: nat] :
% 5.52/5.86 ( ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.52/5.86 = ( summable_real @ F ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_iff_shift
% 5.52/5.86 thf(fact_7468_summable__cmult__iff,axiom,
% 5.52/5.86 ! [C: real,F: nat > real] :
% 5.52/5.86 ( ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 5.52/5.86 = ( ( C = zero_zero_real )
% 5.52/5.86 | ( summable_real @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_cmult_iff
% 5.52/5.86 thf(fact_7469_summable__divide__iff,axiom,
% 5.52/5.86 ! [F: nat > complex,C: complex] :
% 5.52/5.86 ( ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C ) )
% 5.52/5.86 = ( ( C = zero_zero_complex )
% 5.52/5.86 | ( summable_complex @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_divide_iff
% 5.52/5.86 thf(fact_7470_summable__divide__iff,axiom,
% 5.52/5.86 ! [F: nat > real,C: real] :
% 5.52/5.86 ( ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C ) )
% 5.52/5.86 = ( ( C = zero_zero_real )
% 5.52/5.86 | ( summable_real @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_divide_iff
% 5.52/5.86 thf(fact_7471_summable__geometric__iff,axiom,
% 5.52/5.86 ! [C: real] :
% 5.52/5.86 ( ( summable_real @ ( power_power_real @ C ) )
% 5.52/5.86 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_geometric_iff
% 5.52/5.86 thf(fact_7472_summable__geometric__iff,axiom,
% 5.52/5.86 ! [C: complex] :
% 5.52/5.86 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.52/5.86 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_geometric_iff
% 5.52/5.86 thf(fact_7473_summable__divide,axiom,
% 5.52/5.86 ! [F: nat > complex,C: complex] :
% 5.52/5.86 ( ( summable_complex @ F )
% 5.52/5.86 => ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_divide
% 5.52/5.86 thf(fact_7474_summable__divide,axiom,
% 5.52/5.86 ! [F: nat > real,C: real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_divide
% 5.52/5.86 thf(fact_7475_summable__add,axiom,
% 5.52/5.86 ! [F: nat > real,G: nat > real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ( summable_real @ G )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( plus_plus_real @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_add
% 5.52/5.86 thf(fact_7476_summable__add,axiom,
% 5.52/5.86 ! [F: nat > nat,G: nat > nat] :
% 5.52/5.86 ( ( summable_nat @ F )
% 5.52/5.86 => ( ( summable_nat @ G )
% 5.52/5.86 => ( summable_nat
% 5.52/5.86 @ ^ [N3: nat] : ( plus_plus_nat @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_add
% 5.52/5.86 thf(fact_7477_summable__add,axiom,
% 5.52/5.86 ! [F: nat > int,G: nat > int] :
% 5.52/5.86 ( ( summable_int @ F )
% 5.52/5.86 => ( ( summable_int @ G )
% 5.52/5.86 => ( summable_int
% 5.52/5.86 @ ^ [N3: nat] : ( plus_plus_int @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_add
% 5.52/5.86 thf(fact_7478_summable__add,axiom,
% 5.52/5.86 ! [F: nat > complex,G: nat > complex] :
% 5.52/5.86 ( ( summable_complex @ F )
% 5.52/5.86 => ( ( summable_complex @ G )
% 5.52/5.86 => ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( plus_plus_complex @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_add
% 5.52/5.86 thf(fact_7479_summable__mult,axiom,
% 5.52/5.86 ! [F: nat > real,C: real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_mult
% 5.52/5.86 thf(fact_7480_summable__mult2,axiom,
% 5.52/5.86 ! [F: nat > real,C: real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ C ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_mult2
% 5.52/5.86 thf(fact_7481_summable__ignore__initial__segment,axiom,
% 5.52/5.86 ! [F: nat > real,K: nat] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_ignore_initial_segment
% 5.52/5.86 thf(fact_7482_summable__comparison__test,axiom,
% 5.52/5.86 ! [F: nat > real,G: nat > real] :
% 5.52/5.86 ( ? [N8: nat] :
% 5.52/5.86 ! [N2: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N8 @ N2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 5.52/5.86 => ( ( summable_real @ G )
% 5.52/5.86 => ( summable_real @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_comparison_test
% 5.52/5.86 thf(fact_7483_summable__comparison__test,axiom,
% 5.52/5.86 ! [F: nat > complex,G: nat > real] :
% 5.52/5.86 ( ? [N8: nat] :
% 5.52/5.86 ! [N2: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N8 @ N2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 5.52/5.86 => ( ( summable_real @ G )
% 5.52/5.86 => ( summable_complex @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_comparison_test
% 5.52/5.86 thf(fact_7484_summable__comparison__test_H,axiom,
% 5.52/5.86 ! [G: nat > real,N4: nat,F: nat > real] :
% 5.52/5.86 ( ( summable_real @ G )
% 5.52/5.86 => ( ! [N2: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N4 @ N2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 5.52/5.86 => ( summable_real @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_comparison_test'
% 5.52/5.86 thf(fact_7485_summable__comparison__test_H,axiom,
% 5.52/5.86 ! [G: nat > real,N4: nat,F: nat > complex] :
% 5.52/5.86 ( ( summable_real @ G )
% 5.52/5.86 => ( ! [N2: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N4 @ N2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 5.52/5.86 => ( summable_complex @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_comparison_test'
% 5.52/5.86 thf(fact_7486_suminf__le,axiom,
% 5.52/5.86 ! [F: nat > real,G: nat > real] :
% 5.52/5.86 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.52/5.86 => ( ( summable_real @ F )
% 5.52/5.86 => ( ( summable_real @ G )
% 5.52/5.86 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_le
% 5.52/5.86 thf(fact_7487_suminf__le,axiom,
% 5.52/5.86 ! [F: nat > nat,G: nat > nat] :
% 5.52/5.86 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.52/5.86 => ( ( summable_nat @ F )
% 5.52/5.86 => ( ( summable_nat @ G )
% 5.52/5.86 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_le
% 5.52/5.86 thf(fact_7488_suminf__le,axiom,
% 5.52/5.86 ! [F: nat > int,G: nat > int] :
% 5.52/5.86 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.52/5.86 => ( ( summable_int @ F )
% 5.52/5.86 => ( ( summable_int @ G )
% 5.52/5.86 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_le
% 5.52/5.86 thf(fact_7489_summable__mult__D,axiom,
% 5.52/5.86 ! [C: real,F: nat > real] :
% 5.52/5.86 ( ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 5.52/5.86 => ( ( C != zero_zero_real )
% 5.52/5.86 => ( summable_real @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_mult_D
% 5.52/5.86 thf(fact_7490_summable__zero__power,axiom,
% 5.52/5.86 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.52/5.86
% 5.52/5.86 % summable_zero_power
% 5.52/5.86 thf(fact_7491_summable__zero__power,axiom,
% 5.52/5.86 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.52/5.86
% 5.52/5.86 % summable_zero_power
% 5.52/5.86 thf(fact_7492_summable__zero__power,axiom,
% 5.52/5.86 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.52/5.86
% 5.52/5.86 % summable_zero_power
% 5.52/5.86 thf(fact_7493_suminf__mult2,axiom,
% 5.52/5.86 ! [F: nat > real,C: real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ( times_times_real @ ( suminf_real @ F ) @ C )
% 5.52/5.86 = ( suminf_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ C ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_mult2
% 5.52/5.86 thf(fact_7494_suminf__mult,axiom,
% 5.52/5.86 ! [F: nat > real,C: real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ( suminf_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 5.52/5.86 = ( times_times_real @ C @ ( suminf_real @ F ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_mult
% 5.52/5.86 thf(fact_7495_suminf__add,axiom,
% 5.52/5.86 ! [F: nat > real,G: nat > real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ( summable_real @ G )
% 5.52/5.86 => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.52/5.86 = ( suminf_real
% 5.52/5.86 @ ^ [N3: nat] : ( plus_plus_real @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_add
% 5.52/5.86 thf(fact_7496_suminf__add,axiom,
% 5.52/5.86 ! [F: nat > nat,G: nat > nat] :
% 5.52/5.86 ( ( summable_nat @ F )
% 5.52/5.86 => ( ( summable_nat @ G )
% 5.52/5.86 => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 5.52/5.86 = ( suminf_nat
% 5.52/5.86 @ ^ [N3: nat] : ( plus_plus_nat @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_add
% 5.52/5.86 thf(fact_7497_suminf__add,axiom,
% 5.52/5.86 ! [F: nat > int,G: nat > int] :
% 5.52/5.86 ( ( summable_int @ F )
% 5.52/5.86 => ( ( summable_int @ G )
% 5.52/5.86 => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 5.52/5.86 = ( suminf_int
% 5.52/5.86 @ ^ [N3: nat] : ( plus_plus_int @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_add
% 5.52/5.86 thf(fact_7498_suminf__add,axiom,
% 5.52/5.86 ! [F: nat > complex,G: nat > complex] :
% 5.52/5.86 ( ( summable_complex @ F )
% 5.52/5.86 => ( ( summable_complex @ G )
% 5.52/5.86 => ( ( plus_plus_complex @ ( suminf_complex @ F ) @ ( suminf_complex @ G ) )
% 5.52/5.86 = ( suminf_complex
% 5.52/5.86 @ ^ [N3: nat] : ( plus_plus_complex @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_add
% 5.52/5.86 thf(fact_7499_suminf__divide,axiom,
% 5.52/5.86 ! [F: nat > complex,C: complex] :
% 5.52/5.86 ( ( summable_complex @ F )
% 5.52/5.86 => ( ( suminf_complex
% 5.52/5.86 @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C ) )
% 5.52/5.86 = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_divide
% 5.52/5.86 thf(fact_7500_suminf__divide,axiom,
% 5.52/5.86 ! [F: nat > real,C: real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ( suminf_real
% 5.52/5.86 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C ) )
% 5.52/5.86 = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_divide
% 5.52/5.86 thf(fact_7501_powser__insidea,axiom,
% 5.52/5.86 ! [F: nat > real,X2: real,Z: real] :
% 5.52/5.86 ( ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X2 @ N3 ) ) )
% 5.52/5.86 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % powser_insidea
% 5.52/5.86 thf(fact_7502_powser__insidea,axiom,
% 5.52/5.86 ! [F: nat > complex,X2: complex,Z: complex] :
% 5.52/5.86 ( ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ X2 @ N3 ) ) )
% 5.52/5.86 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % powser_insidea
% 5.52/5.86 thf(fact_7503_suminf__nonneg,axiom,
% 5.52/5.86 ! [F: nat > real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 5.52/5.86 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_nonneg
% 5.52/5.86 thf(fact_7504_suminf__nonneg,axiom,
% 5.52/5.86 ! [F: nat > nat] :
% 5.52/5.86 ( ( summable_nat @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 5.52/5.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_nonneg
% 5.52/5.86 thf(fact_7505_suminf__nonneg,axiom,
% 5.52/5.86 ! [F: nat > int] :
% 5.52/5.86 ( ( summable_int @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 5.52/5.86 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_nonneg
% 5.52/5.86 thf(fact_7506_suminf__eq__zero__iff,axiom,
% 5.52/5.86 ! [F: nat > real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 5.52/5.86 => ( ( ( suminf_real @ F )
% 5.52/5.86 = zero_zero_real )
% 5.52/5.86 = ( ! [N3: nat] :
% 5.52/5.86 ( ( F @ N3 )
% 5.52/5.86 = zero_zero_real ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_eq_zero_iff
% 5.52/5.86 thf(fact_7507_suminf__eq__zero__iff,axiom,
% 5.52/5.86 ! [F: nat > nat] :
% 5.52/5.86 ( ( summable_nat @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 5.52/5.86 => ( ( ( suminf_nat @ F )
% 5.52/5.86 = zero_zero_nat )
% 5.52/5.86 = ( ! [N3: nat] :
% 5.52/5.86 ( ( F @ N3 )
% 5.52/5.86 = zero_zero_nat ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_eq_zero_iff
% 5.52/5.86 thf(fact_7508_suminf__eq__zero__iff,axiom,
% 5.52/5.86 ! [F: nat > int] :
% 5.52/5.86 ( ( summable_int @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 5.52/5.86 => ( ( ( suminf_int @ F )
% 5.52/5.86 = zero_zero_int )
% 5.52/5.86 = ( ! [N3: nat] :
% 5.52/5.86 ( ( F @ N3 )
% 5.52/5.86 = zero_zero_int ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_eq_zero_iff
% 5.52/5.86 thf(fact_7509_suminf__pos,axiom,
% 5.52/5.86 ! [F: nat > real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N2 ) )
% 5.52/5.86 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_pos
% 5.52/5.86 thf(fact_7510_suminf__pos,axiom,
% 5.52/5.86 ! [F: nat > nat] :
% 5.52/5.86 ( ( summable_nat @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N2 ) )
% 5.52/5.86 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_pos
% 5.52/5.86 thf(fact_7511_suminf__pos,axiom,
% 5.52/5.86 ! [F: nat > int] :
% 5.52/5.86 ( ( summable_int @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N2 ) )
% 5.52/5.86 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_pos
% 5.52/5.86 thf(fact_7512_summable__zero__power_H,axiom,
% 5.52/5.86 ! [F: nat > complex] :
% 5.52/5.86 ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_zero_power'
% 5.52/5.86 thf(fact_7513_summable__zero__power_H,axiom,
% 5.52/5.86 ! [F: nat > real] :
% 5.52/5.86 ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_zero_power'
% 5.52/5.86 thf(fact_7514_summable__zero__power_H,axiom,
% 5.52/5.86 ! [F: nat > int] :
% 5.52/5.86 ( summable_int
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_int @ ( F @ N3 ) @ ( power_power_int @ zero_zero_int @ N3 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_zero_power'
% 5.52/5.86 thf(fact_7515_summable__0__powser,axiom,
% 5.52/5.86 ! [F: nat > complex] :
% 5.52/5.86 ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_0_powser
% 5.52/5.86 thf(fact_7516_summable__0__powser,axiom,
% 5.52/5.86 ! [F: nat > real] :
% 5.52/5.86 ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_0_powser
% 5.52/5.86 thf(fact_7517_summable__powser__split__head,axiom,
% 5.52/5.86 ! [F: nat > complex,Z: complex] :
% 5.52/5.86 ( ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.52/5.86 = ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_powser_split_head
% 5.52/5.86 thf(fact_7518_summable__powser__split__head,axiom,
% 5.52/5.86 ! [F: nat > real,Z: real] :
% 5.52/5.86 ( ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.52/5.86 = ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_powser_split_head
% 5.52/5.86 thf(fact_7519_powser__split__head_I3_J,axiom,
% 5.52/5.86 ! [F: nat > complex,Z: complex] :
% 5.52/5.86 ( ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.52/5.86 => ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % powser_split_head(3)
% 5.52/5.86 thf(fact_7520_powser__split__head_I3_J,axiom,
% 5.52/5.86 ! [F: nat > real,Z: real] :
% 5.52/5.86 ( ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % powser_split_head(3)
% 5.52/5.86 thf(fact_7521_summable__powser__ignore__initial__segment,axiom,
% 5.52/5.86 ! [F: nat > complex,M: nat,Z: complex] :
% 5.52/5.86 ( ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N3 @ M ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.52/5.86 = ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_powser_ignore_initial_segment
% 5.52/5.86 thf(fact_7522_summable__powser__ignore__initial__segment,axiom,
% 5.52/5.86 ! [F: nat > real,M: nat,Z: real] :
% 5.52/5.86 ( ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N3 @ M ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.52/5.86 = ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_powser_ignore_initial_segment
% 5.52/5.86 thf(fact_7523_pi__not__less__zero,axiom,
% 5.52/5.86 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 5.52/5.86
% 5.52/5.86 % pi_not_less_zero
% 5.52/5.86 thf(fact_7524_pi__gt__zero,axiom,
% 5.52/5.86 ord_less_real @ zero_zero_real @ pi ).
% 5.52/5.86
% 5.52/5.86 % pi_gt_zero
% 5.52/5.86 thf(fact_7525_summable__norm__comparison__test,axiom,
% 5.52/5.86 ! [F: nat > complex,G: nat > real] :
% 5.52/5.86 ( ? [N8: nat] :
% 5.52/5.86 ! [N2: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N8 @ N2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 5.52/5.86 => ( ( summable_real @ G )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_norm_comparison_test
% 5.52/5.86 thf(fact_7526_summable__rabs__comparison__test,axiom,
% 5.52/5.86 ! [F: nat > real,G: nat > real] :
% 5.52/5.86 ( ? [N8: nat] :
% 5.52/5.86 ! [N2: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N8 @ N2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 5.52/5.86 => ( ( summable_real @ G )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( abs_abs_real @ ( F @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_rabs_comparison_test
% 5.52/5.86 thf(fact_7527_suminf__pos__iff,axiom,
% 5.52/5.86 ! [F: nat > real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 5.52/5.86 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.52/5.86 = ( ? [I4: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_pos_iff
% 5.52/5.86 thf(fact_7528_suminf__pos__iff,axiom,
% 5.52/5.86 ! [F: nat > nat] :
% 5.52/5.86 ( ( summable_nat @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 5.52/5.86 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.52/5.86 = ( ? [I4: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_pos_iff
% 5.52/5.86 thf(fact_7529_suminf__pos__iff,axiom,
% 5.52/5.86 ! [F: nat > int] :
% 5.52/5.86 ( ( summable_int @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 5.52/5.86 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.52/5.86 = ( ? [I4: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I4 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_pos_iff
% 5.52/5.86 thf(fact_7530_suminf__pos2,axiom,
% 5.52/5.86 ! [F: nat > real,I: nat] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 5.52/5.86 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.52/5.86 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_pos2
% 5.52/5.86 thf(fact_7531_suminf__pos2,axiom,
% 5.52/5.86 ! [F: nat > nat,I: nat] :
% 5.52/5.86 ( ( summable_nat @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 5.52/5.86 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.52/5.86 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_pos2
% 5.52/5.86 thf(fact_7532_suminf__pos2,axiom,
% 5.52/5.86 ! [F: nat > int,I: nat] :
% 5.52/5.86 ( ( summable_int @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 5.52/5.86 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.52/5.86 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_pos2
% 5.52/5.86 thf(fact_7533_suminf__le__const,axiom,
% 5.52/5.86 ! [F: nat > int,X2: int] :
% 5.52/5.86 ( ( summable_int @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X2 )
% 5.52/5.86 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_le_const
% 5.52/5.86 thf(fact_7534_suminf__le__const,axiom,
% 5.52/5.86 ! [F: nat > nat,X2: nat] :
% 5.52/5.86 ( ( summable_nat @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X2 )
% 5.52/5.86 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_le_const
% 5.52/5.86 thf(fact_7535_suminf__le__const,axiom,
% 5.52/5.86 ! [F: nat > real,X2: real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_le_const
% 5.52/5.86 thf(fact_7536_summableI__nonneg__bounded,axiom,
% 5.52/5.86 ! [F: nat > int,X2: int] :
% 5.52/5.86 ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X2 )
% 5.52/5.86 => ( summable_int @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summableI_nonneg_bounded
% 5.52/5.86 thf(fact_7537_summableI__nonneg__bounded,axiom,
% 5.52/5.86 ! [F: nat > nat,X2: nat] :
% 5.52/5.86 ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X2 )
% 5.52/5.86 => ( summable_nat @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summableI_nonneg_bounded
% 5.52/5.86 thf(fact_7538_summableI__nonneg__bounded,axiom,
% 5.52/5.86 ! [F: nat > real,X2: real] :
% 5.52/5.86 ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X2 )
% 5.52/5.86 => ( summable_real @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summableI_nonneg_bounded
% 5.52/5.86 thf(fact_7539_complete__algebra__summable__geometric,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ one_one_real )
% 5.52/5.86 => ( summable_real @ ( power_power_real @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % complete_algebra_summable_geometric
% 5.52/5.86 thf(fact_7540_complete__algebra__summable__geometric,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ one_one_real )
% 5.52/5.86 => ( summable_complex @ ( power_power_complex @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % complete_algebra_summable_geometric
% 5.52/5.86 thf(fact_7541_summable__geometric,axiom,
% 5.52/5.86 ! [C: real] :
% 5.52/5.86 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.52/5.86 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_geometric
% 5.52/5.86 thf(fact_7542_summable__geometric,axiom,
% 5.52/5.86 ! [C: complex] :
% 5.52/5.86 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.52/5.86 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_geometric
% 5.52/5.86 thf(fact_7543_sum__le__suminf,axiom,
% 5.52/5.86 ! [F: nat > int,I5: set_nat] :
% 5.52/5.86 ( ( summable_int @ F )
% 5.52/5.86 => ( ( finite_finite_nat @ I5 )
% 5.52/5.86 => ( ! [N2: nat] :
% 5.52/5.86 ( ( member_nat @ N2 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.52/5.86 => ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) ) )
% 5.52/5.86 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I5 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_le_suminf
% 5.52/5.86 thf(fact_7544_sum__le__suminf,axiom,
% 5.52/5.86 ! [F: nat > nat,I5: set_nat] :
% 5.52/5.86 ( ( summable_nat @ F )
% 5.52/5.86 => ( ( finite_finite_nat @ I5 )
% 5.52/5.86 => ( ! [N2: nat] :
% 5.52/5.86 ( ( member_nat @ N2 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.52/5.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) ) )
% 5.52/5.86 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I5 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_le_suminf
% 5.52/5.86 thf(fact_7545_sum__le__suminf,axiom,
% 5.52/5.86 ! [F: nat > real,I5: set_nat] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ( finite_finite_nat @ I5 )
% 5.52/5.86 => ( ! [N2: nat] :
% 5.52/5.86 ( ( member_nat @ N2 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.52/5.86 => ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) ) )
% 5.52/5.86 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I5 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_le_suminf
% 5.52/5.86 thf(fact_7546_suminf__split__initial__segment,axiom,
% 5.52/5.86 ! [F: nat > complex,K: nat] :
% 5.52/5.86 ( ( summable_complex @ F )
% 5.52/5.86 => ( ( suminf_complex @ F )
% 5.52/5.86 = ( plus_plus_complex
% 5.52/5.86 @ ( suminf_complex
% 5.52/5.86 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.52/5.86 @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_split_initial_segment
% 5.52/5.86 thf(fact_7547_suminf__split__initial__segment,axiom,
% 5.52/5.86 ! [F: nat > real,K: nat] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ( suminf_real @ F )
% 5.52/5.86 = ( plus_plus_real
% 5.52/5.86 @ ( suminf_real
% 5.52/5.86 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.52/5.86 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_split_initial_segment
% 5.52/5.86 thf(fact_7548_suminf__minus__initial__segment,axiom,
% 5.52/5.86 ! [F: nat > complex,K: nat] :
% 5.52/5.86 ( ( summable_complex @ F )
% 5.52/5.86 => ( ( suminf_complex
% 5.52/5.86 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.52/5.86 = ( minus_minus_complex @ ( suminf_complex @ F ) @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_minus_initial_segment
% 5.52/5.86 thf(fact_7549_suminf__minus__initial__segment,axiom,
% 5.52/5.86 ! [F: nat > real,K: nat] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ( suminf_real
% 5.52/5.86 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.52/5.86 = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_minus_initial_segment
% 5.52/5.86 thf(fact_7550_powser__inside,axiom,
% 5.52/5.86 ! [F: nat > real,X2: real,Z: real] :
% 5.52/5.86 ( ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X2 @ N3 ) ) )
% 5.52/5.86 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % powser_inside
% 5.52/5.86 thf(fact_7551_powser__inside,axiom,
% 5.52/5.86 ! [F: nat > complex,X2: complex,Z: complex] :
% 5.52/5.86 ( ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ X2 @ N3 ) ) )
% 5.52/5.86 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.52/5.86 => ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % powser_inside
% 5.52/5.86 thf(fact_7552_sum__less__suminf,axiom,
% 5.52/5.86 ! [F: nat > int,N: nat] :
% 5.52/5.86 ( ( summable_int @ F )
% 5.52/5.86 => ( ! [M4: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N @ M4 )
% 5.52/5.86 => ( ord_less_int @ zero_zero_int @ ( F @ M4 ) ) )
% 5.52/5.86 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_less_suminf
% 5.52/5.86 thf(fact_7553_sum__less__suminf,axiom,
% 5.52/5.86 ! [F: nat > nat,N: nat] :
% 5.52/5.86 ( ( summable_nat @ F )
% 5.52/5.86 => ( ! [M4: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N @ M4 )
% 5.52/5.86 => ( ord_less_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 5.52/5.86 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_less_suminf
% 5.52/5.86 thf(fact_7554_sum__less__suminf,axiom,
% 5.52/5.86 ! [F: nat > real,N: nat] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ! [M4: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N @ M4 )
% 5.52/5.86 => ( ord_less_real @ zero_zero_real @ ( F @ M4 ) ) )
% 5.52/5.86 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_less_suminf
% 5.52/5.86 thf(fact_7555_pi__less__4,axiom,
% 5.52/5.86 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % pi_less_4
% 5.52/5.86 thf(fact_7556_pi__ge__two,axiom,
% 5.52/5.86 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.52/5.86
% 5.52/5.86 % pi_ge_two
% 5.52/5.86 thf(fact_7557_pi__half__neq__two,axiom,
% 5.52/5.86 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.52/5.86 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % pi_half_neq_two
% 5.52/5.86 thf(fact_7558_powser__split__head_I1_J,axiom,
% 5.52/5.86 ! [F: nat > complex,Z: complex] :
% 5.52/5.86 ( ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.52/5.86 => ( ( suminf_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.52/5.86 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.52/5.86 @ ( times_times_complex
% 5.52/5.86 @ ( suminf_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.52/5.86 @ Z ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % powser_split_head(1)
% 5.52/5.86 thf(fact_7559_powser__split__head_I1_J,axiom,
% 5.52/5.86 ! [F: nat > real,Z: real] :
% 5.52/5.86 ( ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.52/5.86 => ( ( suminf_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.52/5.86 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.52/5.86 @ ( times_times_real
% 5.52/5.86 @ ( suminf_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.52/5.86 @ Z ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % powser_split_head(1)
% 5.52/5.86 thf(fact_7560_powser__split__head_I2_J,axiom,
% 5.52/5.86 ! [F: nat > complex,Z: complex] :
% 5.52/5.86 ( ( summable_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.52/5.86 => ( ( times_times_complex
% 5.52/5.86 @ ( suminf_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.52/5.86 @ Z )
% 5.52/5.86 = ( minus_minus_complex
% 5.52/5.86 @ ( suminf_complex
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.52/5.86 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % powser_split_head(2)
% 5.52/5.86 thf(fact_7561_powser__split__head_I2_J,axiom,
% 5.52/5.86 ! [F: nat > real,Z: real] :
% 5.52/5.86 ( ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.52/5.86 => ( ( times_times_real
% 5.52/5.86 @ ( suminf_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.52/5.86 @ Z )
% 5.52/5.86 = ( minus_minus_real
% 5.52/5.86 @ ( suminf_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.52/5.86 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % powser_split_head(2)
% 5.52/5.86 thf(fact_7562_summable__partial__sum__bound,axiom,
% 5.52/5.86 ! [F: nat > complex,E: real] :
% 5.52/5.86 ( ( summable_complex @ F )
% 5.52/5.86 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.52/5.86 => ~ ! [N9: nat] :
% 5.52/5.86 ~ ! [M2: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N9 @ M2 )
% 5.52/5.86 => ! [N7: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N7 ) ) ) @ E ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_partial_sum_bound
% 5.52/5.86 thf(fact_7563_summable__partial__sum__bound,axiom,
% 5.52/5.86 ! [F: nat > real,E: real] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.52/5.86 => ~ ! [N9: nat] :
% 5.52/5.86 ~ ! [M2: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N9 @ M2 )
% 5.52/5.86 => ! [N7: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N7 ) ) ) @ E ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_partial_sum_bound
% 5.52/5.86 thf(fact_7564_suminf__exist__split,axiom,
% 5.52/5.86 ! [R: real,F: nat > real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ R )
% 5.52/5.86 => ( ( summable_real @ F )
% 5.52/5.86 => ? [N9: nat] :
% 5.52/5.86 ! [N7: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N9 @ N7 )
% 5.52/5.86 => ( ord_less_real
% 5.52/5.86 @ ( real_V7735802525324610683m_real
% 5.52/5.86 @ ( suminf_real
% 5.52/5.86 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N7 ) ) ) )
% 5.52/5.86 @ R ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_exist_split
% 5.52/5.86 thf(fact_7565_suminf__exist__split,axiom,
% 5.52/5.86 ! [R: real,F: nat > complex] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ R )
% 5.52/5.86 => ( ( summable_complex @ F )
% 5.52/5.86 => ? [N9: nat] :
% 5.52/5.86 ! [N7: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N9 @ N7 )
% 5.52/5.86 => ( ord_less_real
% 5.52/5.86 @ ( real_V1022390504157884413omplex
% 5.52/5.86 @ ( suminf_complex
% 5.52/5.86 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N7 ) ) ) )
% 5.52/5.86 @ R ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % suminf_exist_split
% 5.52/5.86 thf(fact_7566_summable__power__series,axiom,
% 5.52/5.86 ! [F: nat > real,Z: real] :
% 5.52/5.86 ( ! [I2: nat] : ( ord_less_eq_real @ ( F @ I2 ) @ one_one_real )
% 5.52/5.86 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.52/5.86 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.52/5.86 => ( ( ord_less_real @ Z @ one_one_real )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [I4: nat] : ( times_times_real @ ( F @ I4 ) @ ( power_power_real @ Z @ I4 ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_power_series
% 5.52/5.86 thf(fact_7567_Abel__lemma,axiom,
% 5.52/5.86 ! [R: real,R0: real,A: nat > complex,M7: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ R )
% 5.52/5.86 => ( ( ord_less_real @ R @ R0 )
% 5.52/5.86 => ( ! [N2: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N2 ) ) @ ( power_power_real @ R0 @ N2 ) ) @ M7 )
% 5.52/5.86 => ( summable_real
% 5.52/5.86 @ ^ [N3: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R @ N3 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Abel_lemma
% 5.52/5.86 thf(fact_7568_summable__ratio__test,axiom,
% 5.52/5.86 ! [C: real,N4: nat,F: nat > real] :
% 5.52/5.86 ( ( ord_less_real @ C @ one_one_real )
% 5.52/5.86 => ( ! [N2: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N4 @ N2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N2 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) ) ) )
% 5.52/5.86 => ( summable_real @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_ratio_test
% 5.52/5.86 thf(fact_7569_summable__ratio__test,axiom,
% 5.52/5.86 ! [C: real,N4: nat,F: nat > complex] :
% 5.52/5.86 ( ( ord_less_real @ C @ one_one_real )
% 5.52/5.86 => ( ! [N2: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N4 @ N2 )
% 5.52/5.86 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N2 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) )
% 5.52/5.86 => ( summable_complex @ F ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % summable_ratio_test
% 5.52/5.86 thf(fact_7570_sum__less__suminf2,axiom,
% 5.52/5.86 ! [F: nat > int,N: nat,I: nat] :
% 5.52/5.86 ( ( summable_int @ F )
% 5.52/5.86 => ( ! [M4: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N @ M4 )
% 5.52/5.86 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M4 ) ) )
% 5.52/5.86 => ( ( ord_less_eq_nat @ N @ I )
% 5.52/5.86 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.52/5.86 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_less_suminf2
% 5.52/5.86 thf(fact_7571_sum__less__suminf2,axiom,
% 5.52/5.86 ! [F: nat > nat,N: nat,I: nat] :
% 5.52/5.86 ( ( summable_nat @ F )
% 5.52/5.86 => ( ! [M4: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N @ M4 )
% 5.52/5.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 5.52/5.86 => ( ( ord_less_eq_nat @ N @ I )
% 5.52/5.86 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.52/5.86 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_less_suminf2
% 5.52/5.86 thf(fact_7572_sum__less__suminf2,axiom,
% 5.52/5.86 ! [F: nat > real,N: nat,I: nat] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ! [M4: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N @ M4 )
% 5.52/5.86 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M4 ) ) )
% 5.52/5.86 => ( ( ord_less_eq_nat @ N @ I )
% 5.52/5.86 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.52/5.86 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_less_suminf2
% 5.52/5.86 thf(fact_7573_pi__half__neq__zero,axiom,
% 5.52/5.86 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.52/5.86 != zero_zero_real ) ).
% 5.52/5.86
% 5.52/5.86 % pi_half_neq_zero
% 5.52/5.86 thf(fact_7574_pi__half__less__two,axiom,
% 5.52/5.86 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.52/5.86
% 5.52/5.86 % pi_half_less_two
% 5.52/5.86 thf(fact_7575_pi__half__le__two,axiom,
% 5.52/5.86 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.52/5.86
% 5.52/5.86 % pi_half_le_two
% 5.52/5.86 thf(fact_7576_pi__half__gt__zero,axiom,
% 5.52/5.86 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % pi_half_gt_zero
% 5.52/5.86 thf(fact_7577_pi__half__ge__zero,axiom,
% 5.52/5.86 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % pi_half_ge_zero
% 5.52/5.86 thf(fact_7578_m2pi__less__pi,axiom,
% 5.52/5.86 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.52/5.86
% 5.52/5.86 % m2pi_less_pi
% 5.52/5.86 thf(fact_7579_arctan__ubound,axiom,
% 5.52/5.86 ! [Y2: real] : ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % arctan_ubound
% 5.52/5.86 thf(fact_7580_arctan__one,axiom,
% 5.52/5.86 ( ( arctan @ one_one_real )
% 5.52/5.86 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % arctan_one
% 5.52/5.86 thf(fact_7581_minus__pi__half__less__zero,axiom,
% 5.52/5.86 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.52/5.86
% 5.52/5.86 % minus_pi_half_less_zero
% 5.52/5.86 thf(fact_7582_arctan__lbound,axiom,
% 5.52/5.86 ! [Y2: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % arctan_lbound
% 5.52/5.86 thf(fact_7583_arctan__bounded,axiom,
% 5.52/5.86 ! [Y2: real] :
% 5.52/5.86 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) )
% 5.52/5.86 & ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % arctan_bounded
% 5.52/5.86 thf(fact_7584_machin__Euler,axiom,
% 5.52/5.86 ( ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.52/5.86 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % machin_Euler
% 5.52/5.86 thf(fact_7585_machin,axiom,
% 5.52/5.86 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % machin
% 5.52/5.86 thf(fact_7586_sum__pos__lt__pair,axiom,
% 5.52/5.86 ! [F: nat > real,K: nat] :
% 5.52/5.86 ( ( summable_real @ F )
% 5.52/5.86 => ( ! [D3: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) @ one_one_nat ) ) ) ) )
% 5.52/5.86 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sum_pos_lt_pair
% 5.52/5.86 thf(fact_7587_sin__cos__npi,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_cos_npi
% 5.52/5.86 thf(fact_7588_cos__pi__eq__zero,axiom,
% 5.52/5.86 ! [M: nat] :
% 5.52/5.86 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = zero_zero_real ) ).
% 5.52/5.86
% 5.52/5.86 % cos_pi_eq_zero
% 5.52/5.86 thf(fact_7589_and__int_Opelims,axiom,
% 5.52/5.86 ! [X2: int,Xa2: int,Y2: int] :
% 5.52/5.86 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa2 )
% 5.52/5.86 = Y2 )
% 5.52/5.86 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) )
% 5.52/5.86 => ~ ( ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.52/5.86 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.52/5.86 => ( Y2
% 5.52/5.86 = ( uminus_uminus_int
% 5.52/5.86 @ ( zero_n2684676970156552555ol_int
% 5.52/5.86 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.52/5.86 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.52/5.86 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.52/5.86 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.52/5.86 => ( Y2
% 5.52/5.86 = ( plus_plus_int
% 5.52/5.86 @ ( zero_n2684676970156552555ol_int
% 5.52/5.86 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.52/5.86 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.52/5.86 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.52/5.86 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % and_int.pelims
% 5.52/5.86 thf(fact_7590_and__int_Opsimps,axiom,
% 5.52/5.86 ! [K: int,L: int] :
% 5.52/5.86 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 5.52/5.86 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.52/5.86 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.52/5.86 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.52/5.86 = ( uminus_uminus_int
% 5.52/5.86 @ ( zero_n2684676970156552555ol_int
% 5.52/5.86 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.52/5.86 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 5.52/5.86 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.52/5.86 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.52/5.86 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.52/5.86 = ( plus_plus_int
% 5.52/5.86 @ ( zero_n2684676970156552555ol_int
% 5.52/5.86 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.52/5.86 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.52/5.86 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % and_int.psimps
% 5.52/5.86 thf(fact_7591_Maclaurin__exp__lt,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( X2 != zero_zero_real )
% 5.52/5.86 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ? [T4: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T4 ) )
% 5.52/5.86 & ( ord_less_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.52/5.86 & ( ( exp_real @ X2 )
% 5.52/5.86 = ( plus_plus_real
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_exp_lt
% 5.52/5.86 thf(fact_7592_cos__zero,axiom,
% 5.52/5.86 ( ( cos_complex @ zero_zero_complex )
% 5.52/5.86 = one_one_complex ) ).
% 5.52/5.86
% 5.52/5.86 % cos_zero
% 5.52/5.86 thf(fact_7593_cos__zero,axiom,
% 5.52/5.86 ( ( cos_real @ zero_zero_real )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % cos_zero
% 5.52/5.86 thf(fact_7594_fact__0,axiom,
% 5.52/5.86 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.52/5.86 = one_one_complex ) ).
% 5.52/5.86
% 5.52/5.86 % fact_0
% 5.52/5.86 thf(fact_7595_fact__0,axiom,
% 5.52/5.86 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.52/5.86 = one_one_rat ) ).
% 5.52/5.86
% 5.52/5.86 % fact_0
% 5.52/5.86 thf(fact_7596_fact__0,axiom,
% 5.52/5.86 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.52/5.86 = one_one_int ) ).
% 5.52/5.86
% 5.52/5.86 % fact_0
% 5.52/5.86 thf(fact_7597_fact__0,axiom,
% 5.52/5.86 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % fact_0
% 5.52/5.86 thf(fact_7598_fact__0,axiom,
% 5.52/5.86 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.52/5.86 = one_one_nat ) ).
% 5.52/5.86
% 5.52/5.86 % fact_0
% 5.52/5.86 thf(fact_7599_fact__1,axiom,
% 5.52/5.86 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.52/5.86 = one_one_complex ) ).
% 5.52/5.86
% 5.52/5.86 % fact_1
% 5.52/5.86 thf(fact_7600_fact__1,axiom,
% 5.52/5.86 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 5.52/5.86 = one_one_rat ) ).
% 5.52/5.86
% 5.52/5.86 % fact_1
% 5.52/5.86 thf(fact_7601_fact__1,axiom,
% 5.52/5.86 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.52/5.86 = one_one_int ) ).
% 5.52/5.86
% 5.52/5.86 % fact_1
% 5.52/5.86 thf(fact_7602_fact__1,axiom,
% 5.52/5.86 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % fact_1
% 5.52/5.86 thf(fact_7603_fact__1,axiom,
% 5.52/5.86 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.52/5.86 = one_one_nat ) ).
% 5.52/5.86
% 5.52/5.86 % fact_1
% 5.52/5.86 thf(fact_7604_fact__Suc__0,axiom,
% 5.52/5.86 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.52/5.86 = one_one_complex ) ).
% 5.52/5.86
% 5.52/5.86 % fact_Suc_0
% 5.52/5.86 thf(fact_7605_fact__Suc__0,axiom,
% 5.52/5.86 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.52/5.86 = one_one_rat ) ).
% 5.52/5.86
% 5.52/5.86 % fact_Suc_0
% 5.52/5.86 thf(fact_7606_fact__Suc__0,axiom,
% 5.52/5.86 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.52/5.86 = one_one_int ) ).
% 5.52/5.86
% 5.52/5.86 % fact_Suc_0
% 5.52/5.86 thf(fact_7607_fact__Suc__0,axiom,
% 5.52/5.86 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % fact_Suc_0
% 5.52/5.86 thf(fact_7608_fact__Suc__0,axiom,
% 5.52/5.86 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.52/5.86 = one_one_nat ) ).
% 5.52/5.86
% 5.52/5.86 % fact_Suc_0
% 5.52/5.86 thf(fact_7609_fact__Suc,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 5.52/5.86 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_Suc
% 5.52/5.86 thf(fact_7610_fact__Suc,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 5.52/5.86 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_Suc
% 5.52/5.86 thf(fact_7611_fact__Suc,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( semiri4449623510593786356d_enat @ ( suc @ N ) )
% 5.52/5.86 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ ( suc @ N ) ) @ ( semiri4449623510593786356d_enat @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_Suc
% 5.52/5.86 thf(fact_7612_fact__Suc,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 5.52/5.86 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_Suc
% 5.52/5.86 thf(fact_7613_fact__Suc,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 5.52/5.86 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_Suc
% 5.52/5.86 thf(fact_7614_fact__2,axiom,
% 5.52/5.86 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.86 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_2
% 5.52/5.86 thf(fact_7615_fact__2,axiom,
% 5.52/5.86 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.86 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_2
% 5.52/5.86 thf(fact_7616_fact__2,axiom,
% 5.52/5.86 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.86 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_2
% 5.52/5.86 thf(fact_7617_fact__2,axiom,
% 5.52/5.86 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.86 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_2
% 5.52/5.86 thf(fact_7618_fact__2,axiom,
% 5.52/5.86 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.86 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_2
% 5.52/5.86 thf(fact_7619_sin__cos__squared__add3,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ X2 ) ) @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( sin_complex @ X2 ) ) )
% 5.52/5.86 = one_one_complex ) ).
% 5.52/5.86
% 5.52/5.86 % sin_cos_squared_add3
% 5.52/5.86 thf(fact_7620_sin__cos__squared__add3,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ X2 ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ X2 ) ) )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % sin_cos_squared_add3
% 5.52/5.86 thf(fact_7621_cos__pi__half,axiom,
% 5.52/5.86 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = zero_zero_real ) ).
% 5.52/5.86
% 5.52/5.86 % cos_pi_half
% 5.52/5.86 thf(fact_7622_sin__two__pi,axiom,
% 5.52/5.86 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.52/5.86 = zero_zero_real ) ).
% 5.52/5.86
% 5.52/5.86 % sin_two_pi
% 5.52/5.86 thf(fact_7623_sin__pi__half,axiom,
% 5.52/5.86 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % sin_pi_half
% 5.52/5.86 thf(fact_7624_cos__two__pi,axiom,
% 5.52/5.86 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % cos_two_pi
% 5.52/5.86 thf(fact_7625_cos__periodic,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( cos_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.52/5.86 = ( cos_real @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_periodic
% 5.52/5.86 thf(fact_7626_sin__periodic,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( sin_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.52/5.86 = ( sin_real @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_periodic
% 5.52/5.86 thf(fact_7627_cos__2pi__minus,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X2 ) )
% 5.52/5.86 = ( cos_real @ X2 ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_2pi_minus
% 5.52/5.86 thf(fact_7628_cos__npi2,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.52/5.86 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_npi2
% 5.52/5.86 thf(fact_7629_cos__npi,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.52/5.86 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_npi
% 5.52/5.86 thf(fact_7630_sin__cos__squared__add2,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % sin_cos_squared_add2
% 5.52/5.86 thf(fact_7631_sin__cos__squared__add2,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = one_one_complex ) ).
% 5.52/5.86
% 5.52/5.86 % sin_cos_squared_add2
% 5.52/5.86 thf(fact_7632_sin__cos__squared__add,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % sin_cos_squared_add
% 5.52/5.86 thf(fact_7633_sin__cos__squared__add,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = one_one_complex ) ).
% 5.52/5.86
% 5.52/5.86 % sin_cos_squared_add
% 5.52/5.86 thf(fact_7634_sin__2npi,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.52/5.86 = zero_zero_real ) ).
% 5.52/5.86
% 5.52/5.86 % sin_2npi
% 5.52/5.86 thf(fact_7635_cos__2npi,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % cos_2npi
% 5.52/5.86 thf(fact_7636_sin__2pi__minus,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X2 ) )
% 5.52/5.86 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_2pi_minus
% 5.52/5.86 thf(fact_7637_sin__int__2pin,axiom,
% 5.52/5.86 ! [N: int] :
% 5.52/5.86 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.52/5.86 = zero_zero_real ) ).
% 5.52/5.86
% 5.52/5.86 % sin_int_2pin
% 5.52/5.86 thf(fact_7638_cos__int__2pin,axiom,
% 5.52/5.86 ! [N: int] :
% 5.52/5.86 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.52/5.86 = one_one_real ) ).
% 5.52/5.86
% 5.52/5.86 % cos_int_2pin
% 5.52/5.86 thf(fact_7639_cos__3over2__pi,axiom,
% 5.52/5.86 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.52/5.86 = zero_zero_real ) ).
% 5.52/5.86
% 5.52/5.86 % cos_3over2_pi
% 5.52/5.86 thf(fact_7640_sin__3over2__pi,axiom,
% 5.52/5.86 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.52/5.86 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_3over2_pi
% 5.52/5.86 thf(fact_7641_cos__npi__int,axiom,
% 5.52/5.86 ! [N: int] :
% 5.52/5.86 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.52/5.86 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.52/5.86 = one_one_real ) )
% 5.52/5.86 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.52/5.86 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.52/5.86 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_npi_int
% 5.52/5.86 thf(fact_7642_sin__diff,axiom,
% 5.52/5.86 ! [X2: complex,Y2: complex] :
% 5.52/5.86 ( ( sin_complex @ ( minus_minus_complex @ X2 @ Y2 ) )
% 5.52/5.86 = ( minus_minus_complex @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( cos_complex @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( sin_complex @ Y2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_diff
% 5.52/5.86 thf(fact_7643_sin__diff,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( sin_real @ ( minus_minus_real @ X2 @ Y2 ) )
% 5.52/5.86 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( sin_real @ Y2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_diff
% 5.52/5.86 thf(fact_7644_sin__add,axiom,
% 5.52/5.86 ! [X2: complex,Y2: complex] :
% 5.52/5.86 ( ( sin_complex @ ( plus_plus_complex @ X2 @ Y2 ) )
% 5.52/5.86 = ( plus_plus_complex @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( cos_complex @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( sin_complex @ Y2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_add
% 5.52/5.86 thf(fact_7645_sin__add,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( sin_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.52/5.86 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( sin_real @ Y2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_add
% 5.52/5.86 thf(fact_7646_cos__one__sin__zero,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ( ( ( cos_complex @ X2 )
% 5.52/5.86 = one_one_complex )
% 5.52/5.86 => ( ( sin_complex @ X2 )
% 5.52/5.86 = zero_zero_complex ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_one_sin_zero
% 5.52/5.86 thf(fact_7647_cos__one__sin__zero,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ( cos_real @ X2 )
% 5.52/5.86 = one_one_real )
% 5.52/5.86 => ( ( sin_real @ X2 )
% 5.52/5.86 = zero_zero_real ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_one_sin_zero
% 5.52/5.86 thf(fact_7648_cos__add,axiom,
% 5.52/5.86 ! [X2: complex,Y2: complex] :
% 5.52/5.86 ( ( cos_complex @ ( plus_plus_complex @ X2 @ Y2 ) )
% 5.52/5.86 = ( minus_minus_complex @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y2 ) ) @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( sin_complex @ Y2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_add
% 5.52/5.86 thf(fact_7649_cos__add,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( cos_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.52/5.86 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_add
% 5.52/5.86 thf(fact_7650_cos__diff,axiom,
% 5.52/5.86 ! [X2: complex,Y2: complex] :
% 5.52/5.86 ( ( cos_complex @ ( minus_minus_complex @ X2 @ Y2 ) )
% 5.52/5.86 = ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y2 ) ) @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( sin_complex @ Y2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_diff
% 5.52/5.86 thf(fact_7651_cos__diff,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( cos_real @ ( minus_minus_real @ X2 @ Y2 ) )
% 5.52/5.86 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_diff
% 5.52/5.86 thf(fact_7652_sin__double,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.52/5.86 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X2 ) ) @ ( cos_complex @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_double
% 5.52/5.86 thf(fact_7653_sin__double,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.52/5.86 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X2 ) ) @ ( cos_real @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_double
% 5.52/5.86 thf(fact_7654_sincos__principal__value,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ? [Y3: real] :
% 5.52/5.86 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.52/5.86 & ( ord_less_eq_real @ Y3 @ pi )
% 5.52/5.86 & ( ( sin_real @ Y3 )
% 5.52/5.86 = ( sin_real @ X2 ) )
% 5.52/5.86 & ( ( cos_real @ Y3 )
% 5.52/5.86 = ( cos_real @ X2 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sincos_principal_value
% 5.52/5.86 thf(fact_7655_fact__ge__zero,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_ge_zero
% 5.52/5.86 thf(fact_7656_fact__ge__zero,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_ge_zero
% 5.52/5.86 thf(fact_7657_fact__ge__zero,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_ge_zero
% 5.52/5.86 thf(fact_7658_fact__ge__zero,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_ge_zero
% 5.52/5.86 thf(fact_7659_fact__gt__zero,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_gt_zero
% 5.52/5.86 thf(fact_7660_fact__gt__zero,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_gt_zero
% 5.52/5.86 thf(fact_7661_fact__gt__zero,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_gt_zero
% 5.52/5.86 thf(fact_7662_fact__gt__zero,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_gt_zero
% 5.52/5.86 thf(fact_7663_fact__not__neg,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 5.52/5.86
% 5.52/5.86 % fact_not_neg
% 5.52/5.86 thf(fact_7664_fact__not__neg,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 5.52/5.86
% 5.52/5.86 % fact_not_neg
% 5.52/5.86 thf(fact_7665_fact__not__neg,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 5.52/5.86
% 5.52/5.86 % fact_not_neg
% 5.52/5.86 thf(fact_7666_fact__not__neg,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 5.52/5.86
% 5.52/5.86 % fact_not_neg
% 5.52/5.86 thf(fact_7667_fact__ge__1,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_ge_1
% 5.52/5.86 thf(fact_7668_fact__ge__1,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_ge_1
% 5.52/5.86 thf(fact_7669_fact__ge__1,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_ge_1
% 5.52/5.86 thf(fact_7670_fact__ge__1,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_ge_1
% 5.52/5.86 thf(fact_7671_fact__mono,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.86 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_mono
% 5.52/5.86 thf(fact_7672_fact__mono,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.86 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_mono
% 5.52/5.86 thf(fact_7673_fact__mono,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.86 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_mono
% 5.52/5.86 thf(fact_7674_fact__mono,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.86 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_mono
% 5.52/5.86 thf(fact_7675_fact__dvd,axiom,
% 5.52/5.86 ! [N: nat,M: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.86 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_dvd
% 5.52/5.86 thf(fact_7676_fact__dvd,axiom,
% 5.52/5.86 ! [N: nat,M: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.86 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_dvd
% 5.52/5.86 thf(fact_7677_fact__dvd,axiom,
% 5.52/5.86 ! [N: nat,M: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.86 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_dvd
% 5.52/5.86 thf(fact_7678_fact__dvd,axiom,
% 5.52/5.86 ! [N: nat,M: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.86 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_dvd
% 5.52/5.86 thf(fact_7679_sin__squared__eq,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ( ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.86 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_squared_eq
% 5.52/5.86 thf(fact_7680_sin__squared__eq,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.86 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_squared_eq
% 5.52/5.86 thf(fact_7681_cos__squared__eq,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ( ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.86 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_squared_eq
% 5.52/5.86 thf(fact_7682_cos__squared__eq,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.86 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_squared_eq
% 5.52/5.86 thf(fact_7683_sin__gt__zero,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ X2 @ pi )
% 5.52/5.86 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_gt_zero
% 5.52/5.86 thf(fact_7684_fact__less__mono,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.86 => ( ( ord_less_nat @ M @ N )
% 5.52/5.86 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_less_mono
% 5.52/5.86 thf(fact_7685_fact__less__mono,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.86 => ( ( ord_less_nat @ M @ N )
% 5.52/5.86 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_less_mono
% 5.52/5.86 thf(fact_7686_fact__less__mono,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.86 => ( ( ord_less_nat @ M @ N )
% 5.52/5.86 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_less_mono
% 5.52/5.86 thf(fact_7687_fact__less__mono,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.86 => ( ( ord_less_nat @ M @ N )
% 5.52/5.86 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_less_mono
% 5.52/5.86 thf(fact_7688_sin__times__sin,axiom,
% 5.52/5.86 ! [W: complex,Z: complex] :
% 5.52/5.86 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.52/5.86 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_times_sin
% 5.52/5.86 thf(fact_7689_sin__times__sin,axiom,
% 5.52/5.86 ! [W: real,Z: real] :
% 5.52/5.86 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.52/5.86 = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_times_sin
% 5.52/5.86 thf(fact_7690_sin__times__cos,axiom,
% 5.52/5.86 ! [W: complex,Z: complex] :
% 5.52/5.86 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.52/5.86 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_times_cos
% 5.52/5.86 thf(fact_7691_sin__times__cos,axiom,
% 5.52/5.86 ! [W: real,Z: real] :
% 5.52/5.86 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.52/5.86 = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_times_cos
% 5.52/5.86 thf(fact_7692_cos__times__sin,axiom,
% 5.52/5.86 ! [W: complex,Z: complex] :
% 5.52/5.86 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.52/5.86 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_times_sin
% 5.52/5.86 thf(fact_7693_cos__times__sin,axiom,
% 5.52/5.86 ! [W: real,Z: real] :
% 5.52/5.86 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.52/5.86 = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_times_sin
% 5.52/5.86 thf(fact_7694_sin__plus__sin,axiom,
% 5.52/5.86 ! [W: complex,Z: complex] :
% 5.52/5.86 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.52/5.86 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_plus_sin
% 5.52/5.86 thf(fact_7695_sin__plus__sin,axiom,
% 5.52/5.86 ! [W: real,Z: real] :
% 5.52/5.86 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.52/5.86 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_plus_sin
% 5.52/5.86 thf(fact_7696_sin__diff__sin,axiom,
% 5.52/5.86 ! [W: complex,Z: complex] :
% 5.52/5.86 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.52/5.86 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_diff_sin
% 5.52/5.86 thf(fact_7697_sin__diff__sin,axiom,
% 5.52/5.86 ! [W: real,Z: real] :
% 5.52/5.86 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.52/5.86 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_diff_sin
% 5.52/5.86 thf(fact_7698_cos__diff__cos,axiom,
% 5.52/5.86 ! [W: complex,Z: complex] :
% 5.52/5.86 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.52/5.86 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z @ W ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_diff_cos
% 5.52/5.86 thf(fact_7699_cos__diff__cos,axiom,
% 5.52/5.86 ! [W: real,Z: real] :
% 5.52/5.86 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.52/5.86 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z @ W ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_diff_cos
% 5.52/5.86 thf(fact_7700_fact__fact__dvd__fact,axiom,
% 5.52/5.86 ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_fact_dvd_fact
% 5.52/5.86 thf(fact_7701_fact__fact__dvd__fact,axiom,
% 5.52/5.86 ! [K: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_fact_dvd_fact
% 5.52/5.86 thf(fact_7702_fact__fact__dvd__fact,axiom,
% 5.52/5.86 ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_fact_dvd_fact
% 5.52/5.86 thf(fact_7703_fact__fact__dvd__fact,axiom,
% 5.52/5.86 ! [K: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_fact_dvd_fact
% 5.52/5.86 thf(fact_7704_fact__fact__dvd__fact,axiom,
% 5.52/5.86 ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_fact_dvd_fact
% 5.52/5.86 thf(fact_7705_fact__mod,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.86 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.52/5.86 = zero_zero_int ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_mod
% 5.52/5.86 thf(fact_7706_fact__mod,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.86 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.52/5.86 = zero_zero_nat ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_mod
% 5.52/5.86 thf(fact_7707_cos__double,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.52/5.86 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_double
% 5.52/5.86 thf(fact_7708_cos__double,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.52/5.86 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_double
% 5.52/5.86 thf(fact_7709_fact__le__power,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_le_power
% 5.52/5.86 thf(fact_7710_fact__le__power,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_le_power
% 5.52/5.86 thf(fact_7711_fact__le__power,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_le_power
% 5.52/5.86 thf(fact_7712_fact__le__power,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_le_power
% 5.52/5.86 thf(fact_7713_cos__double__sin,axiom,
% 5.52/5.86 ! [W: complex] :
% 5.52/5.86 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.52/5.86 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_double_sin
% 5.52/5.86 thf(fact_7714_cos__double__sin,axiom,
% 5.52/5.86 ! [W: real] :
% 5.52/5.86 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.52/5.86 = ( minus_minus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( sin_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_double_sin
% 5.52/5.86 thf(fact_7715_cos__two__neq__zero,axiom,
% 5.52/5.86 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.52/5.86 != zero_zero_real ) ).
% 5.52/5.86
% 5.52/5.86 % cos_two_neq_zero
% 5.52/5.86 thf(fact_7716_cos__monotone__0__pi,axiom,
% 5.52/5.86 ! [Y2: real,X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.86 => ( ( ord_less_real @ Y2 @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.52/5.86 => ( ord_less_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_monotone_0_pi
% 5.52/5.86 thf(fact_7717_cos__mono__less__eq,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.52/5.86 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ Y2 @ pi )
% 5.52/5.86 => ( ( ord_less_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) )
% 5.52/5.86 = ( ord_less_real @ Y2 @ X2 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_mono_less_eq
% 5.52/5.86 thf(fact_7718_sin__eq__0__pi,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ X2 @ pi )
% 5.52/5.86 => ( ( ( sin_real @ X2 )
% 5.52/5.86 = zero_zero_real )
% 5.52/5.86 => ( X2 = zero_zero_real ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_eq_0_pi
% 5.52/5.86 thf(fact_7719_sin__zero__pi__iff,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ pi )
% 5.52/5.86 => ( ( ( sin_real @ X2 )
% 5.52/5.86 = zero_zero_real )
% 5.52/5.86 = ( X2 = zero_zero_real ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_zero_pi_iff
% 5.52/5.86 thf(fact_7720_choose__dvd,axiom,
% 5.52/5.86 ! [K: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.86 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % choose_dvd
% 5.52/5.86 thf(fact_7721_choose__dvd,axiom,
% 5.52/5.86 ! [K: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.86 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % choose_dvd
% 5.52/5.86 thf(fact_7722_choose__dvd,axiom,
% 5.52/5.86 ! [K: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.86 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % choose_dvd
% 5.52/5.86 thf(fact_7723_choose__dvd,axiom,
% 5.52/5.86 ! [K: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.86 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % choose_dvd
% 5.52/5.86 thf(fact_7724_choose__dvd,axiom,
% 5.52/5.86 ! [K: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.86 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % choose_dvd
% 5.52/5.86 thf(fact_7725_fact__numeral,axiom,
% 5.52/5.86 ! [K: num] :
% 5.52/5.86 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.52/5.86 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_numeral
% 5.52/5.86 thf(fact_7726_fact__numeral,axiom,
% 5.52/5.86 ! [K: num] :
% 5.52/5.86 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.52/5.86 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_numeral
% 5.52/5.86 thf(fact_7727_fact__numeral,axiom,
% 5.52/5.86 ! [K: num] :
% 5.52/5.86 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.52/5.86 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_numeral
% 5.52/5.86 thf(fact_7728_fact__numeral,axiom,
% 5.52/5.86 ! [K: num] :
% 5.52/5.86 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.52/5.86 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_numeral
% 5.52/5.86 thf(fact_7729_fact__numeral,axiom,
% 5.52/5.86 ! [K: num] :
% 5.52/5.86 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.52/5.86 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_numeral
% 5.52/5.86 thf(fact_7730_sincos__total__pi,axiom,
% 5.52/5.86 ! [Y2: real,X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.86 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = one_one_real )
% 5.52/5.86 => ? [T4: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.52/5.86 & ( ord_less_eq_real @ T4 @ pi )
% 5.52/5.86 & ( X2
% 5.52/5.86 = ( cos_real @ T4 ) )
% 5.52/5.86 & ( Y2
% 5.52/5.86 = ( sin_real @ T4 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sincos_total_pi
% 5.52/5.86 thf(fact_7731_sin__expansion__lemma,axiom,
% 5.52/5.86 ! [X2: real,M: nat] :
% 5.52/5.86 ( ( sin_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.52/5.86 = ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_expansion_lemma
% 5.52/5.86 thf(fact_7732_cos__expansion__lemma,axiom,
% 5.52/5.86 ! [X2: real,M: nat] :
% 5.52/5.86 ( ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.52/5.86 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_expansion_lemma
% 5.52/5.86 thf(fact_7733_sin__gt__zero__02,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.52/5.86 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_gt_zero_02
% 5.52/5.86 thf(fact_7734_cos__two__less__zero,axiom,
% 5.52/5.86 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.52/5.86
% 5.52/5.86 % cos_two_less_zero
% 5.52/5.86 thf(fact_7735_cos__is__zero,axiom,
% 5.52/5.86 ? [X4: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.52/5.86 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.52/5.86 & ( ( cos_real @ X4 )
% 5.52/5.86 = zero_zero_real )
% 5.52/5.86 & ! [Y4: real] :
% 5.52/5.86 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.52/5.86 & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.52/5.86 & ( ( cos_real @ Y4 )
% 5.52/5.86 = zero_zero_real ) )
% 5.52/5.86 => ( Y4 = X4 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_is_zero
% 5.52/5.86 thf(fact_7736_cos__two__le__zero,axiom,
% 5.52/5.86 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.52/5.86
% 5.52/5.86 % cos_two_le_zero
% 5.52/5.86 thf(fact_7737_cos__monotone__minus__pi__0,axiom,
% 5.52/5.86 ! [Y2: real,X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 5.52/5.86 => ( ( ord_less_real @ Y2 @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.52/5.86 => ( ord_less_real @ ( cos_real @ Y2 ) @ ( cos_real @ X2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_monotone_minus_pi_0
% 5.52/5.86 thf(fact_7738_sincos__total__pi__half,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.86 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = one_one_real )
% 5.52/5.86 => ? [T4: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.52/5.86 & ( ord_less_eq_real @ T4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 & ( X2
% 5.52/5.86 = ( cos_real @ T4 ) )
% 5.52/5.86 & ( Y2
% 5.52/5.86 = ( sin_real @ T4 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sincos_total_pi_half
% 5.52/5.86 thf(fact_7739_sincos__total__2pi__le,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = one_one_real )
% 5.52/5.86 => ? [T4: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.52/5.86 & ( ord_less_eq_real @ T4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.52/5.86 & ( X2
% 5.52/5.86 = ( cos_real @ T4 ) )
% 5.52/5.86 & ( Y2
% 5.52/5.86 = ( sin_real @ T4 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sincos_total_2pi_le
% 5.52/5.86 thf(fact_7740_square__fact__le__2__fact,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % square_fact_le_2_fact
% 5.52/5.86 thf(fact_7741_sincos__total__2pi,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.86 = one_one_real )
% 5.52/5.86 => ~ ! [T4: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.52/5.86 => ( ( ord_less_real @ T4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.52/5.86 => ( ( X2
% 5.52/5.86 = ( cos_real @ T4 ) )
% 5.52/5.86 => ( Y2
% 5.52/5.86 != ( sin_real @ T4 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sincos_total_2pi
% 5.52/5.86 thf(fact_7742_fact__num__eq__if,axiom,
% 5.52/5.86 ( semiri5044797733671781792omplex
% 5.52/5.86 = ( ^ [M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M3 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_num_eq_if
% 5.52/5.86 thf(fact_7743_fact__num__eq__if,axiom,
% 5.52/5.86 ( semiri1406184849735516958ct_int
% 5.52/5.86 = ( ^ [M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_num_eq_if
% 5.52/5.86 thf(fact_7744_fact__num__eq__if,axiom,
% 5.52/5.86 ( semiri773545260158071498ct_rat
% 5.52/5.86 = ( ^ [M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M3 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_num_eq_if
% 5.52/5.86 thf(fact_7745_fact__num__eq__if,axiom,
% 5.52/5.86 ( semiri4449623510593786356d_enat
% 5.52/5.86 = ( ^ [M3: nat] : ( if_Extended_enat @ ( M3 = zero_zero_nat ) @ one_on7984719198319812577d_enat @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ M3 ) @ ( semiri4449623510593786356d_enat @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_num_eq_if
% 5.52/5.86 thf(fact_7746_fact__num__eq__if,axiom,
% 5.52/5.86 ( semiri2265585572941072030t_real
% 5.52/5.86 = ( ^ [M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M3 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_num_eq_if
% 5.52/5.86 thf(fact_7747_fact__num__eq__if,axiom,
% 5.52/5.86 ( semiri1408675320244567234ct_nat
% 5.52/5.86 = ( ^ [M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M3 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_num_eq_if
% 5.52/5.86 thf(fact_7748_fact__reduce,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ( semiri1406184849735516958ct_int @ N )
% 5.52/5.86 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_reduce
% 5.52/5.86 thf(fact_7749_fact__reduce,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ( semiri773545260158071498ct_rat @ N )
% 5.52/5.86 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_reduce
% 5.52/5.86 thf(fact_7750_fact__reduce,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ( semiri4449623510593786356d_enat @ N )
% 5.52/5.86 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ ( semiri4449623510593786356d_enat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_reduce
% 5.52/5.86 thf(fact_7751_fact__reduce,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ( semiri2265585572941072030t_real @ N )
% 5.52/5.86 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_reduce
% 5.52/5.86 thf(fact_7752_fact__reduce,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ( semiri1408675320244567234ct_nat @ N )
% 5.52/5.86 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_reduce
% 5.52/5.86 thf(fact_7753_cos__times__cos,axiom,
% 5.52/5.86 ! [W: complex,Z: complex] :
% 5.52/5.86 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.52/5.86 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_times_cos
% 5.52/5.86 thf(fact_7754_cos__times__cos,axiom,
% 5.52/5.86 ! [W: real,Z: real] :
% 5.52/5.86 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.52/5.86 = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_times_cos
% 5.52/5.86 thf(fact_7755_cos__plus__cos,axiom,
% 5.52/5.86 ! [W: complex,Z: complex] :
% 5.52/5.86 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.52/5.86 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_plus_cos
% 5.52/5.86 thf(fact_7756_cos__plus__cos,axiom,
% 5.52/5.86 ! [W: real,Z: real] :
% 5.52/5.86 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.52/5.86 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_plus_cos
% 5.52/5.86 thf(fact_7757_sin__gt__zero2,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_gt_zero2
% 5.52/5.86 thf(fact_7758_sin__lt__zero,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ pi @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.52/5.86 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_lt_zero
% 5.52/5.86 thf(fact_7759_cos__double__less__one,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.52/5.86 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_double_less_one
% 5.52/5.86 thf(fact_7760_sin__30,axiom,
% 5.52/5.86 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.52/5.86 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_30
% 5.52/5.86 thf(fact_7761_cos__gt__zero,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_gt_zero
% 5.52/5.86 thf(fact_7762_sin__monotone__2pi__le,axiom,
% 5.52/5.86 ! [Y2: real,X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ Y2 @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ord_less_eq_real @ ( sin_real @ Y2 ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_monotone_2pi_le
% 5.52/5.86 thf(fact_7763_sin__mono__le__eq,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ( ord_less_eq_real @ ( sin_real @ X2 ) @ ( sin_real @ Y2 ) )
% 5.52/5.86 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_mono_le_eq
% 5.52/5.86 thf(fact_7764_sin__inj__pi,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ( ( sin_real @ X2 )
% 5.52/5.86 = ( sin_real @ Y2 ) )
% 5.52/5.86 => ( X2 = Y2 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_inj_pi
% 5.52/5.86 thf(fact_7765_cos__60,axiom,
% 5.52/5.86 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.52/5.86 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_60
% 5.52/5.86 thf(fact_7766_cos__one__2pi__int,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ( cos_real @ X2 )
% 5.52/5.86 = one_one_real )
% 5.52/5.86 = ( ? [X: int] :
% 5.52/5.86 ( X2
% 5.52/5.86 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_one_2pi_int
% 5.52/5.86 thf(fact_7767_cos__double__cos,axiom,
% 5.52/5.86 ! [W: complex] :
% 5.52/5.86 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.52/5.86 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_double_cos
% 5.52/5.86 thf(fact_7768_cos__double__cos,axiom,
% 5.52/5.86 ! [W: real] :
% 5.52/5.86 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.52/5.86 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_double_cos
% 5.52/5.86 thf(fact_7769_cos__treble__cos,axiom,
% 5.52/5.86 ! [X2: complex] :
% 5.52/5.86 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X2 ) )
% 5.52/5.86 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_treble_cos
% 5.52/5.86 thf(fact_7770_cos__treble__cos,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X2 ) )
% 5.52/5.86 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_treble_cos
% 5.52/5.86 thf(fact_7771_Maclaurin__cos__expansion,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ? [T4: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.52/5.86 & ( ( cos_real @ X2 )
% 5.52/5.86 = ( plus_plus_real
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_cos_expansion
% 5.52/5.86 thf(fact_7772_sin__le__zero,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ pi @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.52/5.86 => ( ord_less_eq_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_le_zero
% 5.52/5.86 thf(fact_7773_sin__less__zero,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.52/5.86 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_less_zero
% 5.52/5.86 thf(fact_7774_sin__monotone__2pi,axiom,
% 5.52/5.86 ! [Y2: real,X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.52/5.86 => ( ( ord_less_real @ Y2 @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ord_less_real @ ( sin_real @ Y2 ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_monotone_2pi
% 5.52/5.86 thf(fact_7775_sin__mono__less__eq,axiom,
% 5.52/5.86 ! [X2: real,Y2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ( ord_less_real @ ( sin_real @ X2 ) @ ( sin_real @ Y2 ) )
% 5.52/5.86 = ( ord_less_real @ X2 @ Y2 ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_mono_less_eq
% 5.52/5.86 thf(fact_7776_sin__total,axiom,
% 5.52/5.86 ! [Y2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.52/5.86 => ? [X4: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.52/5.86 & ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 & ( ( sin_real @ X4 )
% 5.52/5.86 = Y2 )
% 5.52/5.86 & ! [Y4: real] :
% 5.52/5.86 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.52/5.86 & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 & ( ( sin_real @ Y4 )
% 5.52/5.86 = Y2 ) )
% 5.52/5.86 => ( Y4 = X4 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_total
% 5.52/5.86 thf(fact_7777_cos__gt__zero__pi,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.86 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_gt_zero_pi
% 5.52/5.86 thf(fact_7778_cos__ge__zero,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.86 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.86 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_ge_zero
% 5.52/5.86 thf(fact_7779_cos__one__2pi,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ( cos_real @ X2 )
% 5.52/5.86 = one_one_real )
% 5.52/5.86 = ( ? [X: nat] :
% 5.52/5.86 ( X2
% 5.52/5.86 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.52/5.86 | ? [X: nat] :
% 5.52/5.86 ( X2
% 5.52/5.86 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_one_2pi
% 5.52/5.86 thf(fact_7780_and__int_Opinduct,axiom,
% 5.52/5.86 ! [A0: int,A1: int,P: int > int > $o] :
% 5.52/5.86 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.52/5.86 => ( ! [K3: int,L4: int] :
% 5.52/5.86 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L4 ) )
% 5.52/5.86 => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.52/5.86 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.52/5.86 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.52/5.86 => ( P @ K3 @ L4 ) ) )
% 5.52/5.86 => ( P @ A0 @ A1 ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % and_int.pinduct
% 5.52/5.86 thf(fact_7781_Maclaurin__zero,axiom,
% 5.52/5.86 ! [X2: real,N: nat,Diff: nat > literal > real] :
% 5.52/5.86 ( ( X2 = zero_zero_real )
% 5.52/5.86 => ( ( N != zero_zero_nat )
% 5.52/5.86 => ( ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_literal ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( Diff @ zero_zero_nat @ zero_zero_literal ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_zero
% 5.52/5.86 thf(fact_7782_Maclaurin__zero,axiom,
% 5.52/5.86 ! [X2: real,N: nat,Diff: nat > real > real] :
% 5.52/5.86 ( ( X2 = zero_zero_real )
% 5.52/5.86 => ( ( N != zero_zero_nat )
% 5.52/5.86 => ( ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_zero
% 5.52/5.86 thf(fact_7783_Maclaurin__zero,axiom,
% 5.52/5.86 ! [X2: real,N: nat,Diff: nat > rat > real] :
% 5.52/5.86 ( ( X2 = zero_zero_real )
% 5.52/5.86 => ( ( N != zero_zero_nat )
% 5.52/5.86 => ( ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_zero
% 5.52/5.86 thf(fact_7784_Maclaurin__zero,axiom,
% 5.52/5.86 ! [X2: real,N: nat,Diff: nat > nat > real] :
% 5.52/5.86 ( ( X2 = zero_zero_real )
% 5.52/5.86 => ( ( N != zero_zero_nat )
% 5.52/5.86 => ( ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_zero
% 5.52/5.86 thf(fact_7785_Maclaurin__zero,axiom,
% 5.52/5.86 ! [X2: real,N: nat,Diff: nat > int > real] :
% 5.52/5.86 ( ( X2 = zero_zero_real )
% 5.52/5.86 => ( ( N != zero_zero_nat )
% 5.52/5.86 => ( ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_zero
% 5.52/5.86 thf(fact_7786_Maclaurin__lemma,axiom,
% 5.52/5.86 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.52/5.86 => ? [B9: real] :
% 5.52/5.86 ( ( F @ H2 )
% 5.52/5.86 = ( plus_plus_real
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 @ ( times_times_real @ B9 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_lemma
% 5.52/5.86 thf(fact_7787_Maclaurin__minus__cos__expansion,axiom,
% 5.52/5.86 ! [N: nat,X2: real] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.52/5.86 => ? [T4: real] :
% 5.52/5.86 ( ( ord_less_real @ X2 @ T4 )
% 5.52/5.86 & ( ord_less_real @ T4 @ zero_zero_real )
% 5.52/5.86 & ( ( cos_real @ X2 )
% 5.52/5.86 = ( plus_plus_real
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_minus_cos_expansion
% 5.52/5.86 thf(fact_7788_Maclaurin__cos__expansion2,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ? [T4: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.52/5.86 & ( ord_less_real @ T4 @ X2 )
% 5.52/5.86 & ( ( cos_real @ X2 )
% 5.52/5.86 = ( plus_plus_real
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_cos_expansion2
% 5.52/5.86 thf(fact_7789_sin__pi__divide__n__gt__0,axiom,
% 5.52/5.86 ! [N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.86 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_pi_divide_n_gt_0
% 5.52/5.86 thf(fact_7790_Maclaurin__exp__le,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ? [T4: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.52/5.86 & ( ( exp_real @ X2 )
% 5.52/5.86 = ( plus_plus_real
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_exp_le
% 5.52/5.86 thf(fact_7791_sin__zero__iff__int,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ( sin_real @ X2 )
% 5.52/5.86 = zero_zero_real )
% 5.52/5.86 = ( ? [I4: int] :
% 5.52/5.86 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 5.52/5.86 & ( X2
% 5.52/5.86 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_zero_iff_int
% 5.52/5.86 thf(fact_7792_cos__zero__iff__int,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ( cos_real @ X2 )
% 5.52/5.86 = zero_zero_real )
% 5.52/5.86 = ( ? [I4: int] :
% 5.52/5.86 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 5.52/5.86 & ( X2
% 5.52/5.86 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_zero_iff_int
% 5.52/5.86 thf(fact_7793_sin__zero__lemma,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ( sin_real @ X2 )
% 5.52/5.86 = zero_zero_real )
% 5.52/5.86 => ? [N2: nat] :
% 5.52/5.86 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.52/5.86 & ( X2
% 5.52/5.86 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_zero_lemma
% 5.52/5.86 thf(fact_7794_sin__zero__iff,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ( sin_real @ X2 )
% 5.52/5.86 = zero_zero_real )
% 5.52/5.86 = ( ? [N3: nat] :
% 5.52/5.86 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.52/5.86 & ( X2
% 5.52/5.86 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.86 | ? [N3: nat] :
% 5.52/5.86 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.52/5.86 & ( X2
% 5.52/5.86 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_zero_iff
% 5.52/5.86 thf(fact_7795_cos__coeff__def,axiom,
% 5.52/5.86 ( cos_coeff
% 5.52/5.86 = ( ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N3 ) ) @ zero_zero_real ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_coeff_def
% 5.52/5.86 thf(fact_7796_cos__zero__lemma,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ( ( ( cos_real @ X2 )
% 5.52/5.86 = zero_zero_real )
% 5.52/5.86 => ? [N2: nat] :
% 5.52/5.86 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.52/5.86 & ( X2
% 5.52/5.86 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_zero_lemma
% 5.52/5.86 thf(fact_7797_cos__zero__iff,axiom,
% 5.52/5.86 ! [X2: real] :
% 5.52/5.86 ( ( ( cos_real @ X2 )
% 5.52/5.86 = zero_zero_real )
% 5.52/5.86 = ( ? [N3: nat] :
% 5.52/5.86 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.52/5.86 & ( X2
% 5.52/5.86 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.86 | ? [N3: nat] :
% 5.52/5.86 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.52/5.86 & ( X2
% 5.52/5.86 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % cos_zero_iff
% 5.52/5.86 thf(fact_7798_Maclaurin__sin__expansion3,axiom,
% 5.52/5.86 ! [N: nat,X2: real] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.86 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ? [T4: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.52/5.86 & ( ord_less_real @ T4 @ X2 )
% 5.52/5.86 & ( ( sin_real @ X2 )
% 5.52/5.86 = ( plus_plus_real
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_sin_expansion3
% 5.52/5.86 thf(fact_7799_Maclaurin__sin__expansion4,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.86 => ? [T4: real] :
% 5.52/5.86 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.52/5.86 & ( ord_less_eq_real @ T4 @ X2 )
% 5.52/5.86 & ( ( sin_real @ X2 )
% 5.52/5.86 = ( plus_plus_real
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_sin_expansion4
% 5.52/5.86 thf(fact_7800_Maclaurin__sin__expansion2,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ? [T4: real] :
% 5.52/5.86 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.52/5.86 & ( ( sin_real @ X2 )
% 5.52/5.86 = ( plus_plus_real
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_sin_expansion2
% 5.52/5.86 thf(fact_7801_Maclaurin__sin__expansion,axiom,
% 5.52/5.86 ! [X2: real,N: nat] :
% 5.52/5.86 ? [T4: real] :
% 5.52/5.86 ( ( sin_real @ X2 )
% 5.52/5.86 = ( plus_plus_real
% 5.52/5.86 @ ( groups6591440286371151544t_real
% 5.52/5.86 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.86 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.86 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % Maclaurin_sin_expansion
% 5.52/5.86 thf(fact_7802_sin__coeff__def,axiom,
% 5.52/5.86 ( sin_coeff
% 5.52/5.86 = ( ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N3 ) ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % sin_coeff_def
% 5.52/5.86 thf(fact_7803_fact__mono__nat,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.86 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_mono_nat
% 5.52/5.86 thf(fact_7804_fact__ge__self,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_ge_self
% 5.52/5.86 thf(fact_7805_fact__less__mono__nat,axiom,
% 5.52/5.86 ! [M: nat,N: nat] :
% 5.52/5.86 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.86 => ( ( ord_less_nat @ M @ N )
% 5.52/5.86 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.52/5.86
% 5.52/5.86 % fact_less_mono_nat
% 5.52/5.86 thf(fact_7806_fact__ge__Suc__0__nat,axiom,
% 5.52/5.86 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.52/5.87
% 5.52/5.87 % fact_ge_Suc_0_nat
% 5.52/5.87 thf(fact_7807_dvd__fact,axiom,
% 5.52/5.87 ! [M: nat,N: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.52/5.87 => ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.87 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % dvd_fact
% 5.52/5.87 thf(fact_7808_fact__diff__Suc,axiom,
% 5.52/5.87 ! [N: nat,M: nat] :
% 5.52/5.87 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.52/5.87 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 5.52/5.87 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % fact_diff_Suc
% 5.52/5.87 thf(fact_7809_fact__div__fact__le__pow,axiom,
% 5.52/5.87 ! [R: nat,N: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ R @ N )
% 5.52/5.87 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R ) ) ) @ ( power_power_nat @ N @ R ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % fact_div_fact_le_pow
% 5.52/5.87 thf(fact_7810_tan__double,axiom,
% 5.52/5.87 ! [X2: complex] :
% 5.52/5.87 ( ( ( cos_complex @ X2 )
% 5.52/5.87 != zero_zero_complex )
% 5.52/5.87 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.52/5.87 != zero_zero_complex )
% 5.52/5.87 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.52/5.87 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X2 ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_double
% 5.52/5.87 thf(fact_7811_tan__double,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ( cos_real @ X2 )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.52/5.87 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X2 ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_double
% 5.52/5.87 thf(fact_7812_sin__paired,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 5.52/5.87 @ ( sin_real @ X2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % sin_paired
% 5.52/5.87 thf(fact_7813_ceiling__log__eq__powr__iff,axiom,
% 5.52/5.87 ! [X2: real,B: real,K: nat] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.87 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X2 ) )
% 5.52/5.87 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.52/5.87 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X2 )
% 5.52/5.87 & ( ord_less_eq_real @ X2 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % ceiling_log_eq_powr_iff
% 5.52/5.87 thf(fact_7814_geometric__deriv__sums,axiom,
% 5.52/5.87 ! [Z: real] :
% 5.52/5.87 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.52/5.87 => ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) )
% 5.52/5.87 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % geometric_deriv_sums
% 5.52/5.87 thf(fact_7815_geometric__deriv__sums,axiom,
% 5.52/5.87 ! [Z: complex] :
% 5.52/5.87 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.52/5.87 => ( sums_complex
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) )
% 5.52/5.87 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % geometric_deriv_sums
% 5.52/5.87 thf(fact_7816_monoI1,axiom,
% 5.52/5.87 ! [X8: nat > real] :
% 5.52/5.87 ( ! [M4: nat,N2: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.87 => ( ord_less_eq_real @ ( X8 @ M4 ) @ ( X8 @ N2 ) ) )
% 5.52/5.87 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoI1
% 5.52/5.87 thf(fact_7817_monoI1,axiom,
% 5.52/5.87 ! [X8: nat > set_nat] :
% 5.52/5.87 ( ! [M4: nat,N2: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.87 => ( ord_less_eq_set_nat @ ( X8 @ M4 ) @ ( X8 @ N2 ) ) )
% 5.52/5.87 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoI1
% 5.52/5.87 thf(fact_7818_monoI1,axiom,
% 5.52/5.87 ! [X8: nat > rat] :
% 5.52/5.87 ( ! [M4: nat,N2: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.87 => ( ord_less_eq_rat @ ( X8 @ M4 ) @ ( X8 @ N2 ) ) )
% 5.52/5.87 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoI1
% 5.52/5.87 thf(fact_7819_monoI1,axiom,
% 5.52/5.87 ! [X8: nat > num] :
% 5.52/5.87 ( ! [M4: nat,N2: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.87 => ( ord_less_eq_num @ ( X8 @ M4 ) @ ( X8 @ N2 ) ) )
% 5.52/5.87 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoI1
% 5.52/5.87 thf(fact_7820_monoI1,axiom,
% 5.52/5.87 ! [X8: nat > nat] :
% 5.52/5.87 ( ! [M4: nat,N2: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.87 => ( ord_less_eq_nat @ ( X8 @ M4 ) @ ( X8 @ N2 ) ) )
% 5.52/5.87 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoI1
% 5.52/5.87 thf(fact_7821_monoI1,axiom,
% 5.52/5.87 ! [X8: nat > int] :
% 5.52/5.87 ( ! [M4: nat,N2: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.87 => ( ord_less_eq_int @ ( X8 @ M4 ) @ ( X8 @ N2 ) ) )
% 5.52/5.87 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoI1
% 5.52/5.87 thf(fact_7822_powr__one__eq__one,axiom,
% 5.52/5.87 ! [A: real] :
% 5.52/5.87 ( ( powr_real @ one_one_real @ A )
% 5.52/5.87 = one_one_real ) ).
% 5.52/5.87
% 5.52/5.87 % powr_one_eq_one
% 5.52/5.87 thf(fact_7823_powr__zero__eq__one,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ( X2 = zero_zero_real )
% 5.52/5.87 => ( ( powr_real @ X2 @ zero_zero_real )
% 5.52/5.87 = zero_zero_real ) )
% 5.52/5.87 & ( ( X2 != zero_zero_real )
% 5.52/5.87 => ( ( powr_real @ X2 @ zero_zero_real )
% 5.52/5.87 = one_one_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_zero_eq_one
% 5.52/5.87 thf(fact_7824_powr__gt__zero,axiom,
% 5.52/5.87 ! [X2: real,A: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X2 @ A ) )
% 5.52/5.87 = ( X2 != zero_zero_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_gt_zero
% 5.52/5.87 thf(fact_7825_powr__less__cancel__iff,axiom,
% 5.52/5.87 ! [X2: real,A: real,B: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.52/5.87 = ( ord_less_real @ A @ B ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_less_cancel_iff
% 5.52/5.87 thf(fact_7826_powr__eq__one__iff,axiom,
% 5.52/5.87 ! [A: real,X2: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ A )
% 5.52/5.87 => ( ( ( powr_real @ A @ X2 )
% 5.52/5.87 = one_one_real )
% 5.52/5.87 = ( X2 = zero_zero_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_eq_one_iff
% 5.52/5.87 thf(fact_7827_powr__le__cancel__iff,axiom,
% 5.52/5.87 ! [X2: real,A: real,B: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.52/5.87 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_le_cancel_iff
% 5.52/5.87 thf(fact_7828_numeral__powr__numeral__real,axiom,
% 5.52/5.87 ! [M: num,N: num] :
% 5.52/5.87 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.52/5.87 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % numeral_powr_numeral_real
% 5.52/5.87 thf(fact_7829_powr__log__cancel,axiom,
% 5.52/5.87 ! [A: real,X2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.87 => ( ( A != one_one_real )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( powr_real @ A @ ( log @ A @ X2 ) )
% 5.52/5.87 = X2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_log_cancel
% 5.52/5.87 thf(fact_7830_log__powr__cancel,axiom,
% 5.52/5.87 ! [A: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.87 => ( ( A != one_one_real )
% 5.52/5.87 => ( ( log @ A @ ( powr_real @ A @ Y2 ) )
% 5.52/5.87 = Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % log_powr_cancel
% 5.52/5.87 thf(fact_7831_powser__sums__zero__iff,axiom,
% 5.52/5.87 ! [A: nat > complex,X2: complex] :
% 5.52/5.87 ( ( sums_complex
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_complex @ ( A @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) )
% 5.52/5.87 @ X2 )
% 5.52/5.87 = ( ( A @ zero_zero_nat )
% 5.52/5.87 = X2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % powser_sums_zero_iff
% 5.52/5.87 thf(fact_7832_powser__sums__zero__iff,axiom,
% 5.52/5.87 ! [A: nat > real,X2: real] :
% 5.52/5.87 ( ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( A @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) )
% 5.52/5.87 @ X2 )
% 5.52/5.87 = ( ( A @ zero_zero_nat )
% 5.52/5.87 = X2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % powser_sums_zero_iff
% 5.52/5.87 thf(fact_7833_tan__periodic,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.52/5.87 = ( tan_real @ X2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_periodic
% 5.52/5.87 thf(fact_7834_powr__numeral,axiom,
% 5.52/5.87 ! [X2: real,N: num] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( powr_real @ X2 @ ( numeral_numeral_real @ N ) )
% 5.52/5.87 = ( power_power_real @ X2 @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_numeral
% 5.52/5.87 thf(fact_7835_square__powr__half,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( powr_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 = ( abs_abs_real @ X2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % square_powr_half
% 5.52/5.87 thf(fact_7836_sums__le,axiom,
% 5.52/5.87 ! [F: nat > real,G: nat > real,S: real,T: real] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.52/5.87 => ( ( sums_real @ F @ S )
% 5.52/5.87 => ( ( sums_real @ G @ T )
% 5.52/5.87 => ( ord_less_eq_real @ S @ T ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_le
% 5.52/5.87 thf(fact_7837_sums__le,axiom,
% 5.52/5.87 ! [F: nat > nat,G: nat > nat,S: nat,T: nat] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.52/5.87 => ( ( sums_nat @ F @ S )
% 5.52/5.87 => ( ( sums_nat @ G @ T )
% 5.52/5.87 => ( ord_less_eq_nat @ S @ T ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_le
% 5.52/5.87 thf(fact_7838_sums__le,axiom,
% 5.52/5.87 ! [F: nat > int,G: nat > int,S: int,T: int] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.52/5.87 => ( ( sums_int @ F @ S )
% 5.52/5.87 => ( ( sums_int @ G @ T )
% 5.52/5.87 => ( ord_less_eq_int @ S @ T ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_le
% 5.52/5.87 thf(fact_7839_sums__mult2,axiom,
% 5.52/5.87 ! [F: nat > real,A: real,C: real] :
% 5.52/5.87 ( ( sums_real @ F @ A )
% 5.52/5.87 => ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ C )
% 5.52/5.87 @ ( times_times_real @ A @ C ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_mult2
% 5.52/5.87 thf(fact_7840_sums__mult,axiom,
% 5.52/5.87 ! [F: nat > real,A: real,C: real] :
% 5.52/5.87 ( ( sums_real @ F @ A )
% 5.52/5.87 => ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) )
% 5.52/5.87 @ ( times_times_real @ C @ A ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_mult
% 5.52/5.87 thf(fact_7841_sums__add,axiom,
% 5.52/5.87 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.52/5.87 ( ( sums_real @ F @ A )
% 5.52/5.87 => ( ( sums_real @ G @ B )
% 5.52/5.87 => ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( plus_plus_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.52/5.87 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_add
% 5.52/5.87 thf(fact_7842_sums__add,axiom,
% 5.52/5.87 ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 5.52/5.87 ( ( sums_nat @ F @ A )
% 5.52/5.87 => ( ( sums_nat @ G @ B )
% 5.52/5.87 => ( sums_nat
% 5.52/5.87 @ ^ [N3: nat] : ( plus_plus_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.52/5.87 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_add
% 5.52/5.87 thf(fact_7843_sums__add,axiom,
% 5.52/5.87 ! [F: nat > int,A: int,G: nat > int,B: int] :
% 5.52/5.87 ( ( sums_int @ F @ A )
% 5.52/5.87 => ( ( sums_int @ G @ B )
% 5.52/5.87 => ( sums_int
% 5.52/5.87 @ ^ [N3: nat] : ( plus_plus_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.52/5.87 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_add
% 5.52/5.87 thf(fact_7844_sums__add,axiom,
% 5.52/5.87 ! [F: nat > complex,A: complex,G: nat > complex,B: complex] :
% 5.52/5.87 ( ( sums_complex @ F @ A )
% 5.52/5.87 => ( ( sums_complex @ G @ B )
% 5.52/5.87 => ( sums_complex
% 5.52/5.87 @ ^ [N3: nat] : ( plus_plus_complex @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.52/5.87 @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_add
% 5.52/5.87 thf(fact_7845_sums__divide,axiom,
% 5.52/5.87 ! [F: nat > complex,A: complex,C: complex] :
% 5.52/5.87 ( ( sums_complex @ F @ A )
% 5.52/5.87 => ( sums_complex
% 5.52/5.87 @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C )
% 5.52/5.87 @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_divide
% 5.52/5.87 thf(fact_7846_sums__divide,axiom,
% 5.52/5.87 ! [F: nat > real,A: real,C: real] :
% 5.52/5.87 ( ( sums_real @ F @ A )
% 5.52/5.87 => ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C )
% 5.52/5.87 @ ( divide_divide_real @ A @ C ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_divide
% 5.52/5.87 thf(fact_7847_powr__non__neg,axiom,
% 5.52/5.87 ! [A: real,X2: real] :
% 5.52/5.87 ~ ( ord_less_real @ ( powr_real @ A @ X2 ) @ zero_zero_real ) ).
% 5.52/5.87
% 5.52/5.87 % powr_non_neg
% 5.52/5.87 thf(fact_7848_powr__less__mono2__neg,axiom,
% 5.52/5.87 ! [A: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ A @ zero_zero_real )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ Y2 )
% 5.52/5.87 => ( ord_less_real @ ( powr_real @ Y2 @ A ) @ ( powr_real @ X2 @ A ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_less_mono2_neg
% 5.52/5.87 thf(fact_7849_powr__less__mono,axiom,
% 5.52/5.87 ! [A: real,B: real,X2: real] :
% 5.52/5.87 ( ( ord_less_real @ A @ B )
% 5.52/5.87 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.52/5.87 => ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_less_mono
% 5.52/5.87 thf(fact_7850_powr__less__cancel,axiom,
% 5.52/5.87 ! [X2: real,A: real,B: real] :
% 5.52/5.87 ( ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.52/5.87 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.52/5.87 => ( ord_less_real @ A @ B ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_less_cancel
% 5.52/5.87 thf(fact_7851_sums__mult2__iff,axiom,
% 5.52/5.87 ! [C: real,F: nat > real,D2: real] :
% 5.52/5.87 ( ( C != zero_zero_real )
% 5.52/5.87 => ( ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ C )
% 5.52/5.87 @ ( times_times_real @ D2 @ C ) )
% 5.52/5.87 = ( sums_real @ F @ D2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_mult2_iff
% 5.52/5.87 thf(fact_7852_sums__mult__iff,axiom,
% 5.52/5.87 ! [C: real,F: nat > real,D2: real] :
% 5.52/5.87 ( ( C != zero_zero_real )
% 5.52/5.87 => ( ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) )
% 5.52/5.87 @ ( times_times_real @ C @ D2 ) )
% 5.52/5.87 = ( sums_real @ F @ D2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_mult_iff
% 5.52/5.87 thf(fact_7853_powr__less__mono2,axiom,
% 5.52/5.87 ! [A: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ Y2 )
% 5.52/5.87 => ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_less_mono2
% 5.52/5.87 thf(fact_7854_powr__mono2_H,axiom,
% 5.52/5.87 ! [A: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.52/5.87 => ( ord_less_eq_real @ ( powr_real @ Y2 @ A ) @ ( powr_real @ X2 @ A ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_mono2'
% 5.52/5.87 thf(fact_7855_gr__one__powr,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( powr_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % gr_one_powr
% 5.52/5.87 thf(fact_7856_powr__inj,axiom,
% 5.52/5.87 ! [A: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.87 => ( ( A != one_one_real )
% 5.52/5.87 => ( ( ( powr_real @ A @ X2 )
% 5.52/5.87 = ( powr_real @ A @ Y2 ) )
% 5.52/5.87 = ( X2 = Y2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_inj
% 5.52/5.87 thf(fact_7857_sums__mult__D,axiom,
% 5.52/5.87 ! [C: complex,F: nat > complex,A: complex] :
% 5.52/5.87 ( ( sums_complex
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_complex @ C @ ( F @ N3 ) )
% 5.52/5.87 @ A )
% 5.52/5.87 => ( ( C != zero_zero_complex )
% 5.52/5.87 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_mult_D
% 5.52/5.87 thf(fact_7858_sums__mult__D,axiom,
% 5.52/5.87 ! [C: real,F: nat > real,A: real] :
% 5.52/5.87 ( ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) )
% 5.52/5.87 @ A )
% 5.52/5.87 => ( ( C != zero_zero_real )
% 5.52/5.87 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_mult_D
% 5.52/5.87 thf(fact_7859_sums__Suc__iff,axiom,
% 5.52/5.87 ! [F: nat > real,S: real] :
% 5.52/5.87 ( ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.52/5.87 @ S )
% 5.52/5.87 = ( sums_real @ F @ ( plus_plus_real @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_Suc_iff
% 5.52/5.87 thf(fact_7860_sums__Suc__iff,axiom,
% 5.52/5.87 ! [F: nat > complex,S: complex] :
% 5.52/5.87 ( ( sums_complex
% 5.52/5.87 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.52/5.87 @ S )
% 5.52/5.87 = ( sums_complex @ F @ ( plus_plus_complex @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_Suc_iff
% 5.52/5.87 thf(fact_7861_sums__Suc,axiom,
% 5.52/5.87 ! [F: nat > real,L: real] :
% 5.52/5.87 ( ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.52/5.87 @ L )
% 5.52/5.87 => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_Suc
% 5.52/5.87 thf(fact_7862_sums__Suc,axiom,
% 5.52/5.87 ! [F: nat > nat,L: nat] :
% 5.52/5.87 ( ( sums_nat
% 5.52/5.87 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.52/5.87 @ L )
% 5.52/5.87 => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_Suc
% 5.52/5.87 thf(fact_7863_sums__Suc,axiom,
% 5.52/5.87 ! [F: nat > int,L: int] :
% 5.52/5.87 ( ( sums_int
% 5.52/5.87 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.52/5.87 @ L )
% 5.52/5.87 => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_Suc
% 5.52/5.87 thf(fact_7864_sums__Suc,axiom,
% 5.52/5.87 ! [F: nat > complex,L: complex] :
% 5.52/5.87 ( ( sums_complex
% 5.52/5.87 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.52/5.87 @ L )
% 5.52/5.87 => ( sums_complex @ F @ ( plus_plus_complex @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_Suc
% 5.52/5.87 thf(fact_7865_sums__zero__iff__shift,axiom,
% 5.52/5.87 ! [N: nat,F: nat > real,S: real] :
% 5.52/5.87 ( ! [I2: nat] :
% 5.52/5.87 ( ( ord_less_nat @ I2 @ N )
% 5.52/5.87 => ( ( F @ I2 )
% 5.52/5.87 = zero_zero_real ) )
% 5.52/5.87 => ( ( sums_real
% 5.52/5.87 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.52/5.87 @ S )
% 5.52/5.87 = ( sums_real @ F @ S ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_zero_iff_shift
% 5.52/5.87 thf(fact_7866_powr__add,axiom,
% 5.52/5.87 ! [X2: real,A: real,B: real] :
% 5.52/5.87 ( ( powr_real @ X2 @ ( plus_plus_real @ A @ B ) )
% 5.52/5.87 = ( times_times_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_add
% 5.52/5.87 thf(fact_7867_powr__diff,axiom,
% 5.52/5.87 ! [W: real,Z1: real,Z22: real] :
% 5.52/5.87 ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 5.52/5.87 = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_diff
% 5.52/5.87 thf(fact_7868_powser__sums__if,axiom,
% 5.52/5.87 ! [M: nat,Z: complex] :
% 5.52/5.87 ( sums_complex
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_complex @ ( if_complex @ ( N3 = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N3 ) )
% 5.52/5.87 @ ( power_power_complex @ Z @ M ) ) ).
% 5.52/5.87
% 5.52/5.87 % powser_sums_if
% 5.52/5.87 thf(fact_7869_powser__sums__if,axiom,
% 5.52/5.87 ! [M: nat,Z: real] :
% 5.52/5.87 ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( if_real @ ( N3 = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N3 ) )
% 5.52/5.87 @ ( power_power_real @ Z @ M ) ) ).
% 5.52/5.87
% 5.52/5.87 % powser_sums_if
% 5.52/5.87 thf(fact_7870_powser__sums__if,axiom,
% 5.52/5.87 ! [M: nat,Z: int] :
% 5.52/5.87 ( sums_int
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_int @ ( if_int @ ( N3 = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N3 ) )
% 5.52/5.87 @ ( power_power_int @ Z @ M ) ) ).
% 5.52/5.87
% 5.52/5.87 % powser_sums_if
% 5.52/5.87 thf(fact_7871_powser__sums__zero,axiom,
% 5.52/5.87 ! [A: nat > complex] :
% 5.52/5.87 ( sums_complex
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_complex @ ( A @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) )
% 5.52/5.87 @ ( A @ zero_zero_nat ) ) ).
% 5.52/5.87
% 5.52/5.87 % powser_sums_zero
% 5.52/5.87 thf(fact_7872_powser__sums__zero,axiom,
% 5.52/5.87 ! [A: nat > real] :
% 5.52/5.87 ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( A @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) )
% 5.52/5.87 @ ( A @ zero_zero_nat ) ) ).
% 5.52/5.87
% 5.52/5.87 % powser_sums_zero
% 5.52/5.87 thf(fact_7873_tan__def,axiom,
% 5.52/5.87 ( tan_complex
% 5.52/5.87 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X ) @ ( cos_complex @ X ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_def
% 5.52/5.87 thf(fact_7874_tan__def,axiom,
% 5.52/5.87 ( tan_real
% 5.52/5.87 = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ X ) @ ( cos_real @ X ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_def
% 5.52/5.87 thf(fact_7875_powr__realpow,axiom,
% 5.52/5.87 ! [X2: real,N: nat] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( powr_real @ X2 @ ( semiri5074537144036343181t_real @ N ) )
% 5.52/5.87 = ( power_power_real @ X2 @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_realpow
% 5.52/5.87 thf(fact_7876_less__log__iff,axiom,
% 5.52/5.87 ! [B: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ Y2 @ ( log @ B @ X2 ) )
% 5.52/5.87 = ( ord_less_real @ ( powr_real @ B @ Y2 ) @ X2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_log_iff
% 5.52/5.87 thf(fact_7877_log__less__iff,axiom,
% 5.52/5.87 ! [B: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ ( log @ B @ X2 ) @ Y2 )
% 5.52/5.87 = ( ord_less_real @ X2 @ ( powr_real @ B @ Y2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % log_less_iff
% 5.52/5.87 thf(fact_7878_less__powr__iff,axiom,
% 5.52/5.87 ! [B: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ ( powr_real @ B @ Y2 ) )
% 5.52/5.87 = ( ord_less_real @ ( log @ B @ X2 ) @ Y2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_powr_iff
% 5.52/5.87 thf(fact_7879_powr__less__iff,axiom,
% 5.52/5.87 ! [B: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ ( powr_real @ B @ Y2 ) @ X2 )
% 5.52/5.87 = ( ord_less_real @ Y2 @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_less_iff
% 5.52/5.87 thf(fact_7880_sums__iff__shift,axiom,
% 5.52/5.87 ! [F: nat > complex,N: nat,S: complex] :
% 5.52/5.87 ( ( sums_complex
% 5.52/5.87 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.52/5.87 @ S )
% 5.52/5.87 = ( sums_complex @ F @ ( plus_plus_complex @ S @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_iff_shift
% 5.52/5.87 thf(fact_7881_sums__iff__shift,axiom,
% 5.52/5.87 ! [F: nat > real,N: nat,S: real] :
% 5.52/5.87 ( ( sums_real
% 5.52/5.87 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.52/5.87 @ S )
% 5.52/5.87 = ( sums_real @ F @ ( plus_plus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_iff_shift
% 5.52/5.87 thf(fact_7882_sums__iff__shift_H,axiom,
% 5.52/5.87 ! [F: nat > complex,N: nat,S: complex] :
% 5.52/5.87 ( ( sums_complex
% 5.52/5.87 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.52/5.87 @ ( minus_minus_complex @ S @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.52/5.87 = ( sums_complex @ F @ S ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_iff_shift'
% 5.52/5.87 thf(fact_7883_sums__iff__shift_H,axiom,
% 5.52/5.87 ! [F: nat > real,N: nat,S: real] :
% 5.52/5.87 ( ( sums_real
% 5.52/5.87 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.52/5.87 @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.52/5.87 = ( sums_real @ F @ S ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_iff_shift'
% 5.52/5.87 thf(fact_7884_sums__split__initial__segment,axiom,
% 5.52/5.87 ! [F: nat > complex,S: complex,N: nat] :
% 5.52/5.87 ( ( sums_complex @ F @ S )
% 5.52/5.87 => ( sums_complex
% 5.52/5.87 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.52/5.87 @ ( minus_minus_complex @ S @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_split_initial_segment
% 5.52/5.87 thf(fact_7885_sums__split__initial__segment,axiom,
% 5.52/5.87 ! [F: nat > real,S: real,N: nat] :
% 5.52/5.87 ( ( sums_real @ F @ S )
% 5.52/5.87 => ( sums_real
% 5.52/5.87 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.52/5.87 @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_split_initial_segment
% 5.52/5.87 thf(fact_7886_sums__If__finite__set_H,axiom,
% 5.52/5.87 ! [G: nat > complex,S3: complex,A2: set_nat,S5: complex,F: nat > complex] :
% 5.52/5.87 ( ( sums_complex @ G @ S3 )
% 5.52/5.87 => ( ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ( S5
% 5.52/5.87 = ( plus_plus_complex @ S3
% 5.52/5.87 @ ( groups2073611262835488442omplex
% 5.52/5.87 @ ^ [N3: nat] : ( minus_minus_complex @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.52/5.87 @ A2 ) ) )
% 5.52/5.87 => ( sums_complex
% 5.52/5.87 @ ^ [N3: nat] : ( if_complex @ ( member_nat @ N3 @ A2 ) @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.52/5.87 @ S5 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_If_finite_set'
% 5.52/5.87 thf(fact_7887_sums__If__finite__set_H,axiom,
% 5.52/5.87 ! [G: nat > real,S3: real,A2: set_nat,S5: real,F: nat > real] :
% 5.52/5.87 ( ( sums_real @ G @ S3 )
% 5.52/5.87 => ( ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ( S5
% 5.52/5.87 = ( plus_plus_real @ S3
% 5.52/5.87 @ ( groups6591440286371151544t_real
% 5.52/5.87 @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.52/5.87 @ A2 ) ) )
% 5.52/5.87 => ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( if_real @ ( member_nat @ N3 @ A2 ) @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.52/5.87 @ S5 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_If_finite_set'
% 5.52/5.87 thf(fact_7888_powr__minus__divide,axiom,
% 5.52/5.87 ! [X2: real,A: real] :
% 5.52/5.87 ( ( powr_real @ X2 @ ( uminus_uminus_real @ A ) )
% 5.52/5.87 = ( divide_divide_real @ one_one_real @ ( powr_real @ X2 @ A ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_minus_divide
% 5.52/5.87 thf(fact_7889_powr__neg__one,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.87 = ( divide_divide_real @ one_one_real @ X2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_neg_one
% 5.52/5.87 thf(fact_7890_powr__le__iff,axiom,
% 5.52/5.87 ! [B: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y2 ) @ X2 )
% 5.52/5.87 = ( ord_less_eq_real @ Y2 @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_le_iff
% 5.52/5.87 thf(fact_7891_le__powr__iff,axiom,
% 5.52/5.87 ! [B: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ X2 @ ( powr_real @ B @ Y2 ) )
% 5.52/5.87 = ( ord_less_eq_real @ ( log @ B @ X2 ) @ Y2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % le_powr_iff
% 5.52/5.87 thf(fact_7892_log__le__iff,axiom,
% 5.52/5.87 ! [B: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ ( log @ B @ X2 ) @ Y2 )
% 5.52/5.87 = ( ord_less_eq_real @ X2 @ ( powr_real @ B @ Y2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % log_le_iff
% 5.52/5.87 thf(fact_7893_le__log__iff,axiom,
% 5.52/5.87 ! [B: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ Y2 @ ( log @ B @ X2 ) )
% 5.52/5.87 = ( ord_less_eq_real @ ( powr_real @ B @ Y2 ) @ X2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % le_log_iff
% 5.52/5.87 thf(fact_7894_ln__powr__bound,axiom,
% 5.52/5.87 ! [X2: real,A: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.87 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( divide_divide_real @ ( powr_real @ X2 @ A ) @ A ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % ln_powr_bound
% 5.52/5.87 thf(fact_7895_ln__powr__bound2,axiom,
% 5.52/5.87 ! [X2: real,A: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.87 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X2 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % ln_powr_bound2
% 5.52/5.87 thf(fact_7896_tan__45,axiom,
% 5.52/5.87 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.52/5.87 = one_one_real ) ).
% 5.52/5.87
% 5.52/5.87 % tan_45
% 5.52/5.87 thf(fact_7897_log__add__eq__powr,axiom,
% 5.52/5.87 ! [B: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.87 => ( ( B != one_one_real )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( plus_plus_real @ ( log @ B @ X2 ) @ Y2 )
% 5.52/5.87 = ( log @ B @ ( times_times_real @ X2 @ ( powr_real @ B @ Y2 ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % log_add_eq_powr
% 5.52/5.87 thf(fact_7898_add__log__eq__powr,axiom,
% 5.52/5.87 ! [B: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.87 => ( ( B != one_one_real )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( plus_plus_real @ Y2 @ ( log @ B @ X2 ) )
% 5.52/5.87 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y2 ) @ X2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % add_log_eq_powr
% 5.52/5.87 thf(fact_7899_minus__log__eq__powr,axiom,
% 5.52/5.87 ! [B: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.87 => ( ( B != one_one_real )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( minus_minus_real @ Y2 @ ( log @ B @ X2 ) )
% 5.52/5.87 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y2 ) @ X2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % minus_log_eq_powr
% 5.52/5.87 thf(fact_7900_powr__def,axiom,
% 5.52/5.87 ( powr_real
% 5.52/5.87 = ( ^ [X: real,A4: real] : ( if_real @ ( X = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A4 @ ( ln_ln_real @ X ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_def
% 5.52/5.87 thf(fact_7901_geometric__sums,axiom,
% 5.52/5.87 ! [C: real] :
% 5.52/5.87 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.52/5.87 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % geometric_sums
% 5.52/5.87 thf(fact_7902_geometric__sums,axiom,
% 5.52/5.87 ! [C: complex] :
% 5.52/5.87 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.52/5.87 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % geometric_sums
% 5.52/5.87 thf(fact_7903_power__half__series,axiom,
% 5.52/5.87 ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N3 ) )
% 5.52/5.87 @ one_one_real ) ).
% 5.52/5.87
% 5.52/5.87 % power_half_series
% 5.52/5.87 thf(fact_7904_lemma__tan__total,axiom,
% 5.52/5.87 ! [Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.52/5.87 => ? [X4: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.52/5.87 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 & ( ord_less_real @ Y2 @ ( tan_real @ X4 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % lemma_tan_total
% 5.52/5.87 thf(fact_7905_tan__gt__zero,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_gt_zero
% 5.52/5.87 thf(fact_7906_lemma__tan__total1,axiom,
% 5.52/5.87 ! [Y2: real] :
% 5.52/5.87 ? [X4: real] :
% 5.52/5.87 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.52/5.87 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 & ( ( tan_real @ X4 )
% 5.52/5.87 = Y2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % lemma_tan_total1
% 5.52/5.87 thf(fact_7907_tan__mono__lt__eq,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.52/5.87 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ( ord_less_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) )
% 5.52/5.87 = ( ord_less_real @ X2 @ Y2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_mono_lt_eq
% 5.52/5.87 thf(fact_7908_tan__monotone_H,axiom,
% 5.52/5.87 ! [Y2: real,X2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.52/5.87 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ( ord_less_real @ Y2 @ X2 )
% 5.52/5.87 = ( ord_less_real @ ( tan_real @ Y2 ) @ ( tan_real @ X2 ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_monotone'
% 5.52/5.87 thf(fact_7909_tan__monotone,axiom,
% 5.52/5.87 ! [Y2: real,X2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.52/5.87 => ( ( ord_less_real @ Y2 @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ord_less_real @ ( tan_real @ Y2 ) @ ( tan_real @ X2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_monotone
% 5.52/5.87 thf(fact_7910_tan__total,axiom,
% 5.52/5.87 ! [Y2: real] :
% 5.52/5.87 ? [X4: real] :
% 5.52/5.87 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.52/5.87 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 & ( ( tan_real @ X4 )
% 5.52/5.87 = Y2 )
% 5.52/5.87 & ! [Y4: real] :
% 5.52/5.87 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.52/5.87 & ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 & ( ( tan_real @ Y4 )
% 5.52/5.87 = Y2 ) )
% 5.52/5.87 => ( Y4 = X4 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_total
% 5.52/5.87 thf(fact_7911_tan__minus__45,axiom,
% 5.52/5.87 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.87 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_minus_45
% 5.52/5.87 thf(fact_7912_tan__inverse,axiom,
% 5.52/5.87 ! [Y2: real] :
% 5.52/5.87 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y2 ) )
% 5.52/5.87 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_inverse
% 5.52/5.87 thf(fact_7913_log__minus__eq__powr,axiom,
% 5.52/5.87 ! [B: real,X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.87 => ( ( B != one_one_real )
% 5.52/5.87 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( minus_minus_real @ ( log @ B @ X2 ) @ Y2 )
% 5.52/5.87 = ( log @ B @ ( times_times_real @ X2 @ ( powr_real @ B @ ( uminus_uminus_real @ Y2 ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % log_minus_eq_powr
% 5.52/5.87 thf(fact_7914_add__tan__eq,axiom,
% 5.52/5.87 ! [X2: complex,Y2: complex] :
% 5.52/5.87 ( ( ( cos_complex @ X2 )
% 5.52/5.87 != zero_zero_complex )
% 5.52/5.87 => ( ( ( cos_complex @ Y2 )
% 5.52/5.87 != zero_zero_complex )
% 5.52/5.87 => ( ( plus_plus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y2 ) )
% 5.52/5.87 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X2 @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % add_tan_eq
% 5.52/5.87 thf(fact_7915_add__tan__eq,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ( cos_real @ X2 )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( ( cos_real @ Y2 )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( plus_plus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) )
% 5.52/5.87 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % add_tan_eq
% 5.52/5.87 thf(fact_7916_sums__if_H,axiom,
% 5.52/5.87 ! [G: nat > real,X2: real] :
% 5.52/5.87 ( ( sums_real @ G @ X2 )
% 5.52/5.87 => ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.87 @ X2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_if'
% 5.52/5.87 thf(fact_7917_sums__if,axiom,
% 5.52/5.87 ! [G: nat > real,X2: real,F: nat > real,Y2: real] :
% 5.52/5.87 ( ( sums_real @ G @ X2 )
% 5.52/5.87 => ( ( sums_real @ F @ Y2 )
% 5.52/5.87 => ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ ( F @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.87 @ ( plus_plus_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sums_if
% 5.52/5.87 thf(fact_7918_powr__neg__numeral,axiom,
% 5.52/5.87 ! [X2: real,N: num] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.52/5.87 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_neg_numeral
% 5.52/5.87 thf(fact_7919_tan__pos__pi2__le,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_pos_pi2_le
% 5.52/5.87 thf(fact_7920_tan__total__pos,axiom,
% 5.52/5.87 ! [Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.87 => ? [X4: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.52/5.87 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 & ( ( tan_real @ X4 )
% 5.52/5.87 = Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_total_pos
% 5.52/5.87 thf(fact_7921_tan__less__zero,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.52/5.87 => ( ord_less_real @ ( tan_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_less_zero
% 5.52/5.87 thf(fact_7922_tan__mono__le__eq,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.52/5.87 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) )
% 5.52/5.87 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_mono_le_eq
% 5.52/5.87 thf(fact_7923_tan__mono__le,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.52/5.87 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_mono_le
% 5.52/5.87 thf(fact_7924_tan__bound__pi2,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.52/5.87 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X2 ) ) @ one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_bound_pi2
% 5.52/5.87 thf(fact_7925_arctan__unique,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ( ( tan_real @ X2 )
% 5.52/5.87 = Y2 )
% 5.52/5.87 => ( ( arctan @ Y2 )
% 5.52/5.87 = X2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % arctan_unique
% 5.52/5.87 thf(fact_7926_arctan__tan,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ( arctan @ ( tan_real @ X2 ) )
% 5.52/5.87 = X2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % arctan_tan
% 5.52/5.87 thf(fact_7927_arctan,axiom,
% 5.52/5.87 ! [Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) )
% 5.52/5.87 & ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 & ( ( tan_real @ ( arctan @ Y2 ) )
% 5.52/5.87 = Y2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % arctan
% 5.52/5.87 thf(fact_7928_lemma__tan__add1,axiom,
% 5.52/5.87 ! [X2: complex,Y2: complex] :
% 5.52/5.87 ( ( ( cos_complex @ X2 )
% 5.52/5.87 != zero_zero_complex )
% 5.52/5.87 => ( ( ( cos_complex @ Y2 )
% 5.52/5.87 != zero_zero_complex )
% 5.52/5.87 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y2 ) ) )
% 5.52/5.87 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X2 @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % lemma_tan_add1
% 5.52/5.87 thf(fact_7929_lemma__tan__add1,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ( cos_real @ X2 )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( ( cos_real @ Y2 )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) ) )
% 5.52/5.87 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % lemma_tan_add1
% 5.52/5.87 thf(fact_7930_tan__diff,axiom,
% 5.52/5.87 ! [X2: complex,Y2: complex] :
% 5.52/5.87 ( ( ( cos_complex @ X2 )
% 5.52/5.87 != zero_zero_complex )
% 5.52/5.87 => ( ( ( cos_complex @ Y2 )
% 5.52/5.87 != zero_zero_complex )
% 5.52/5.87 => ( ( ( cos_complex @ ( minus_minus_complex @ X2 @ Y2 ) )
% 5.52/5.87 != zero_zero_complex )
% 5.52/5.87 => ( ( tan_complex @ ( minus_minus_complex @ X2 @ Y2 ) )
% 5.52/5.87 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y2 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y2 ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_diff
% 5.52/5.87 thf(fact_7931_tan__diff,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ( cos_real @ X2 )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( ( cos_real @ Y2 )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( ( cos_real @ ( minus_minus_real @ X2 @ Y2 ) )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( tan_real @ ( minus_minus_real @ X2 @ Y2 ) )
% 5.52/5.87 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_diff
% 5.52/5.87 thf(fact_7932_tan__add,axiom,
% 5.52/5.87 ! [X2: complex,Y2: complex] :
% 5.52/5.87 ( ( ( cos_complex @ X2 )
% 5.52/5.87 != zero_zero_complex )
% 5.52/5.87 => ( ( ( cos_complex @ Y2 )
% 5.52/5.87 != zero_zero_complex )
% 5.52/5.87 => ( ( ( cos_complex @ ( plus_plus_complex @ X2 @ Y2 ) )
% 5.52/5.87 != zero_zero_complex )
% 5.52/5.87 => ( ( tan_complex @ ( plus_plus_complex @ X2 @ Y2 ) )
% 5.52/5.87 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y2 ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y2 ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_add
% 5.52/5.87 thf(fact_7933_tan__add,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ( cos_real @ X2 )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( ( cos_real @ Y2 )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( ( cos_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( tan_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.52/5.87 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_add
% 5.52/5.87 thf(fact_7934_tan__total__pi4,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.52/5.87 => ? [Z3: real] :
% 5.52/5.87 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 5.52/5.87 & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.52/5.87 & ( ( tan_real @ Z3 )
% 5.52/5.87 = X2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_total_pi4
% 5.52/5.87 thf(fact_7935_cos__paired,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) @ ( power_power_real @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.52/5.87 @ ( cos_real @ X2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % cos_paired
% 5.52/5.87 thf(fact_7936_tan__half,axiom,
% 5.52/5.87 ( tan_complex
% 5.52/5.87 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ one_one_complex ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_half
% 5.52/5.87 thf(fact_7937_tan__half,axiom,
% 5.52/5.87 ( tan_real
% 5.52/5.87 = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_half
% 5.52/5.87 thf(fact_7938_monoseq__Suc,axiom,
% 5.52/5.87 ( topolo6980174941875973593q_real
% 5.52/5.87 = ( ^ [X7: nat > real] :
% 5.52/5.87 ( ! [N3: nat] : ( ord_less_eq_real @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.52/5.87 | ! [N3: nat] : ( ord_less_eq_real @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoseq_Suc
% 5.52/5.87 thf(fact_7939_monoseq__Suc,axiom,
% 5.52/5.87 ( topolo7278393974255667507et_nat
% 5.52/5.87 = ( ^ [X7: nat > set_nat] :
% 5.52/5.87 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.52/5.87 | ! [N3: nat] : ( ord_less_eq_set_nat @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoseq_Suc
% 5.52/5.87 thf(fact_7940_monoseq__Suc,axiom,
% 5.52/5.87 ( topolo4267028734544971653eq_rat
% 5.52/5.87 = ( ^ [X7: nat > rat] :
% 5.52/5.87 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.52/5.87 | ! [N3: nat] : ( ord_less_eq_rat @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoseq_Suc
% 5.52/5.87 thf(fact_7941_monoseq__Suc,axiom,
% 5.52/5.87 ( topolo1459490580787246023eq_num
% 5.52/5.87 = ( ^ [X7: nat > num] :
% 5.52/5.87 ( ! [N3: nat] : ( ord_less_eq_num @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.52/5.87 | ! [N3: nat] : ( ord_less_eq_num @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoseq_Suc
% 5.52/5.87 thf(fact_7942_monoseq__Suc,axiom,
% 5.52/5.87 ( topolo4902158794631467389eq_nat
% 5.52/5.87 = ( ^ [X7: nat > nat] :
% 5.52/5.87 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.52/5.87 | ! [N3: nat] : ( ord_less_eq_nat @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoseq_Suc
% 5.52/5.87 thf(fact_7943_monoseq__Suc,axiom,
% 5.52/5.87 ( topolo4899668324122417113eq_int
% 5.52/5.87 = ( ^ [X7: nat > int] :
% 5.52/5.87 ( ! [N3: nat] : ( ord_less_eq_int @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.52/5.87 | ! [N3: nat] : ( ord_less_eq_int @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoseq_Suc
% 5.52/5.87 thf(fact_7944_mono__SucI2,axiom,
% 5.52/5.87 ! [X8: nat > real] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N2 ) ) @ ( X8 @ N2 ) )
% 5.52/5.87 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % mono_SucI2
% 5.52/5.87 thf(fact_7945_mono__SucI2,axiom,
% 5.52/5.87 ! [X8: nat > set_nat] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( X8 @ ( suc @ N2 ) ) @ ( X8 @ N2 ) )
% 5.52/5.87 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % mono_SucI2
% 5.52/5.87 thf(fact_7946_mono__SucI2,axiom,
% 5.52/5.87 ! [X8: nat > rat] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N2 ) ) @ ( X8 @ N2 ) )
% 5.52/5.87 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % mono_SucI2
% 5.52/5.87 thf(fact_7947_mono__SucI2,axiom,
% 5.52/5.87 ! [X8: nat > num] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N2 ) ) @ ( X8 @ N2 ) )
% 5.52/5.87 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % mono_SucI2
% 5.52/5.87 thf(fact_7948_mono__SucI2,axiom,
% 5.52/5.87 ! [X8: nat > nat] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N2 ) ) @ ( X8 @ N2 ) )
% 5.52/5.87 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % mono_SucI2
% 5.52/5.87 thf(fact_7949_mono__SucI2,axiom,
% 5.52/5.87 ! [X8: nat > int] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N2 ) ) @ ( X8 @ N2 ) )
% 5.52/5.87 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % mono_SucI2
% 5.52/5.87 thf(fact_7950_mono__SucI1,axiom,
% 5.52/5.87 ! [X8: nat > real] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_real @ ( X8 @ N2 ) @ ( X8 @ ( suc @ N2 ) ) )
% 5.52/5.87 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % mono_SucI1
% 5.52/5.87 thf(fact_7951_mono__SucI1,axiom,
% 5.52/5.87 ! [X8: nat > set_nat] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( X8 @ N2 ) @ ( X8 @ ( suc @ N2 ) ) )
% 5.52/5.87 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % mono_SucI1
% 5.52/5.87 thf(fact_7952_mono__SucI1,axiom,
% 5.52/5.87 ! [X8: nat > rat] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_rat @ ( X8 @ N2 ) @ ( X8 @ ( suc @ N2 ) ) )
% 5.52/5.87 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % mono_SucI1
% 5.52/5.87 thf(fact_7953_mono__SucI1,axiom,
% 5.52/5.87 ! [X8: nat > num] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_num @ ( X8 @ N2 ) @ ( X8 @ ( suc @ N2 ) ) )
% 5.52/5.87 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % mono_SucI1
% 5.52/5.87 thf(fact_7954_mono__SucI1,axiom,
% 5.52/5.87 ! [X8: nat > nat] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_nat @ ( X8 @ N2 ) @ ( X8 @ ( suc @ N2 ) ) )
% 5.52/5.87 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % mono_SucI1
% 5.52/5.87 thf(fact_7955_mono__SucI1,axiom,
% 5.52/5.87 ! [X8: nat > int] :
% 5.52/5.87 ( ! [N2: nat] : ( ord_less_eq_int @ ( X8 @ N2 ) @ ( X8 @ ( suc @ N2 ) ) )
% 5.52/5.87 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % mono_SucI1
% 5.52/5.87 thf(fact_7956_monoseq__def,axiom,
% 5.52/5.87 ( topolo6980174941875973593q_real
% 5.52/5.87 = ( ^ [X7: nat > real] :
% 5.52/5.87 ( ! [M3: nat,N3: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.87 => ( ord_less_eq_real @ ( X7 @ M3 ) @ ( X7 @ N3 ) ) )
% 5.52/5.87 | ! [M3: nat,N3: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.87 => ( ord_less_eq_real @ ( X7 @ N3 ) @ ( X7 @ M3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoseq_def
% 5.52/5.87 thf(fact_7957_monoseq__def,axiom,
% 5.52/5.87 ( topolo7278393974255667507et_nat
% 5.52/5.87 = ( ^ [X7: nat > set_nat] :
% 5.52/5.87 ( ! [M3: nat,N3: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.87 => ( ord_less_eq_set_nat @ ( X7 @ M3 ) @ ( X7 @ N3 ) ) )
% 5.52/5.87 | ! [M3: nat,N3: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.87 => ( ord_less_eq_set_nat @ ( X7 @ N3 ) @ ( X7 @ M3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoseq_def
% 5.52/5.87 thf(fact_7958_monoseq__def,axiom,
% 5.52/5.87 ( topolo4267028734544971653eq_rat
% 5.52/5.87 = ( ^ [X7: nat > rat] :
% 5.52/5.87 ( ! [M3: nat,N3: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.87 => ( ord_less_eq_rat @ ( X7 @ M3 ) @ ( X7 @ N3 ) ) )
% 5.52/5.87 | ! [M3: nat,N3: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.87 => ( ord_less_eq_rat @ ( X7 @ N3 ) @ ( X7 @ M3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoseq_def
% 5.52/5.87 thf(fact_7959_monoseq__def,axiom,
% 5.52/5.87 ( topolo1459490580787246023eq_num
% 5.52/5.87 = ( ^ [X7: nat > num] :
% 5.52/5.87 ( ! [M3: nat,N3: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.87 => ( ord_less_eq_num @ ( X7 @ M3 ) @ ( X7 @ N3 ) ) )
% 5.52/5.87 | ! [M3: nat,N3: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.87 => ( ord_less_eq_num @ ( X7 @ N3 ) @ ( X7 @ M3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoseq_def
% 5.52/5.87 thf(fact_7960_monoseq__def,axiom,
% 5.52/5.87 ( topolo4902158794631467389eq_nat
% 5.52/5.87 = ( ^ [X7: nat > nat] :
% 5.52/5.87 ( ! [M3: nat,N3: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.87 => ( ord_less_eq_nat @ ( X7 @ M3 ) @ ( X7 @ N3 ) ) )
% 5.52/5.87 | ! [M3: nat,N3: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.87 => ( ord_less_eq_nat @ ( X7 @ N3 ) @ ( X7 @ M3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoseq_def
% 5.52/5.87 thf(fact_7961_monoseq__def,axiom,
% 5.52/5.87 ( topolo4899668324122417113eq_int
% 5.52/5.87 = ( ^ [X7: nat > int] :
% 5.52/5.87 ( ! [M3: nat,N3: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.87 => ( ord_less_eq_int @ ( X7 @ M3 ) @ ( X7 @ N3 ) ) )
% 5.52/5.87 | ! [M3: nat,N3: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M3 @ N3 )
% 5.52/5.87 => ( ord_less_eq_int @ ( X7 @ N3 ) @ ( X7 @ M3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoseq_def
% 5.52/5.87 thf(fact_7962_monoI2,axiom,
% 5.52/5.87 ! [X8: nat > real] :
% 5.52/5.87 ( ! [M4: nat,N2: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.87 => ( ord_less_eq_real @ ( X8 @ N2 ) @ ( X8 @ M4 ) ) )
% 5.52/5.87 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoI2
% 5.52/5.87 thf(fact_7963_monoI2,axiom,
% 5.52/5.87 ! [X8: nat > set_nat] :
% 5.52/5.87 ( ! [M4: nat,N2: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.87 => ( ord_less_eq_set_nat @ ( X8 @ N2 ) @ ( X8 @ M4 ) ) )
% 5.52/5.87 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoI2
% 5.52/5.87 thf(fact_7964_monoI2,axiom,
% 5.52/5.87 ! [X8: nat > rat] :
% 5.52/5.87 ( ! [M4: nat,N2: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.87 => ( ord_less_eq_rat @ ( X8 @ N2 ) @ ( X8 @ M4 ) ) )
% 5.52/5.87 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoI2
% 5.52/5.87 thf(fact_7965_monoI2,axiom,
% 5.52/5.87 ! [X8: nat > num] :
% 5.52/5.87 ( ! [M4: nat,N2: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.87 => ( ord_less_eq_num @ ( X8 @ N2 ) @ ( X8 @ M4 ) ) )
% 5.52/5.87 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoI2
% 5.52/5.87 thf(fact_7966_monoI2,axiom,
% 5.52/5.87 ! [X8: nat > nat] :
% 5.52/5.87 ( ! [M4: nat,N2: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.87 => ( ord_less_eq_nat @ ( X8 @ N2 ) @ ( X8 @ M4 ) ) )
% 5.52/5.87 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoI2
% 5.52/5.87 thf(fact_7967_monoI2,axiom,
% 5.52/5.87 ! [X8: nat > int] :
% 5.52/5.87 ( ! [M4: nat,N2: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.87 => ( ord_less_eq_int @ ( X8 @ N2 ) @ ( X8 @ M4 ) ) )
% 5.52/5.87 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.52/5.87
% 5.52/5.87 % monoI2
% 5.52/5.87 thf(fact_7968_diffs__equiv,axiom,
% 5.52/5.87 ! [C: nat > complex,X2: complex] :
% 5.52/5.87 ( ( summable_complex
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_complex @ ( diffs_complex @ C @ N3 ) @ ( power_power_complex @ X2 @ N3 ) ) )
% 5.52/5.87 => ( sums_complex
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N3 ) @ ( C @ N3 ) ) @ ( power_power_complex @ X2 @ ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) ) ) )
% 5.52/5.87 @ ( suminf_complex
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_complex @ ( diffs_complex @ C @ N3 ) @ ( power_power_complex @ X2 @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % diffs_equiv
% 5.52/5.87 thf(fact_7969_diffs__equiv,axiom,
% 5.52/5.87 ! [C: nat > real,X2: real] :
% 5.52/5.87 ( ( summable_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( diffs_real @ C @ N3 ) @ ( power_power_real @ X2 @ N3 ) ) )
% 5.52/5.87 => ( sums_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( C @ N3 ) ) @ ( power_power_real @ X2 @ ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) ) ) )
% 5.52/5.87 @ ( suminf_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( diffs_real @ C @ N3 ) @ ( power_power_real @ X2 @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % diffs_equiv
% 5.52/5.87 thf(fact_7970_arcosh__def,axiom,
% 5.52/5.87 ( arcosh_real
% 5.52/5.87 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % arcosh_def
% 5.52/5.87 thf(fact_7971_sin__tan,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ( sin_real @ X2 )
% 5.52/5.87 = ( divide_divide_real @ ( tan_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sin_tan
% 5.52/5.87 thf(fact_7972_cos__tan,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ( cos_real @ X2 )
% 5.52/5.87 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % cos_tan
% 5.52/5.87 thf(fact_7973_pochhammer__double,axiom,
% 5.52/5.87 ! [Z: complex,N: nat] :
% 5.52/5.87 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.87 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_double
% 5.52/5.87 thf(fact_7974_pochhammer__double,axiom,
% 5.52/5.87 ! [Z: real,N: nat] :
% 5.52/5.87 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.87 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_double
% 5.52/5.87 thf(fact_7975_pochhammer__double,axiom,
% 5.52/5.87 ! [Z: rat,N: nat] :
% 5.52/5.87 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.87 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_double
% 5.52/5.87 thf(fact_7976_real__sqrt__eq__iff,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ( sqrt @ X2 )
% 5.52/5.87 = ( sqrt @ Y2 ) )
% 5.52/5.87 = ( X2 = Y2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_eq_iff
% 5.52/5.87 thf(fact_7977_real__sqrt__zero,axiom,
% 5.52/5.87 ( ( sqrt @ zero_zero_real )
% 5.52/5.87 = zero_zero_real ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_zero
% 5.52/5.87 thf(fact_7978_real__sqrt__eq__zero__cancel__iff,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ( sqrt @ X2 )
% 5.52/5.87 = zero_zero_real )
% 5.52/5.87 = ( X2 = zero_zero_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_eq_zero_cancel_iff
% 5.52/5.87 thf(fact_7979_real__sqrt__less__iff,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) )
% 5.52/5.87 = ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_less_iff
% 5.52/5.87 thf(fact_7980_real__sqrt__le__iff,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) )
% 5.52/5.87 = ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_le_iff
% 5.52/5.87 thf(fact_7981_real__sqrt__eq__1__iff,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ( sqrt @ X2 )
% 5.52/5.87 = one_one_real )
% 5.52/5.87 = ( X2 = one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_eq_1_iff
% 5.52/5.87 thf(fact_7982_real__sqrt__one,axiom,
% 5.52/5.87 ( ( sqrt @ one_one_real )
% 5.52/5.87 = one_one_real ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_one
% 5.52/5.87 thf(fact_7983_of__real__1,axiom,
% 5.52/5.87 ( ( real_V1803761363581548252l_real @ one_one_real )
% 5.52/5.87 = one_one_real ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_1
% 5.52/5.87 thf(fact_7984_of__real__1,axiom,
% 5.52/5.87 ( ( real_V4546457046886955230omplex @ one_one_real )
% 5.52/5.87 = one_one_complex ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_1
% 5.52/5.87 thf(fact_7985_of__real__eq__1__iff,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ( real_V1803761363581548252l_real @ X2 )
% 5.52/5.87 = one_one_real )
% 5.52/5.87 = ( X2 = one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_eq_1_iff
% 5.52/5.87 thf(fact_7986_of__real__eq__1__iff,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ( real_V4546457046886955230omplex @ X2 )
% 5.52/5.87 = one_one_complex )
% 5.52/5.87 = ( X2 = one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_eq_1_iff
% 5.52/5.87 thf(fact_7987_of__real__numeral,axiom,
% 5.52/5.87 ! [W: num] :
% 5.52/5.87 ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 5.52/5.87 = ( numeral_numeral_real @ W ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_numeral
% 5.52/5.87 thf(fact_7988_of__real__numeral,axiom,
% 5.52/5.87 ! [W: num] :
% 5.52/5.87 ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 5.52/5.87 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_numeral
% 5.52/5.87 thf(fact_7989_of__real__mult,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( real_V1803761363581548252l_real @ ( times_times_real @ X2 @ Y2 ) )
% 5.52/5.87 = ( times_times_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_mult
% 5.52/5.87 thf(fact_7990_of__real__mult,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( real_V4546457046886955230omplex @ ( times_times_real @ X2 @ Y2 ) )
% 5.52/5.87 = ( times_times_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_mult
% 5.52/5.87 thf(fact_7991_real__sqrt__gt__0__iff,axiom,
% 5.52/5.87 ! [Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y2 ) )
% 5.52/5.87 = ( ord_less_real @ zero_zero_real @ Y2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_gt_0_iff
% 5.52/5.87 thf(fact_7992_real__sqrt__lt__0__iff,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( sqrt @ X2 ) @ zero_zero_real )
% 5.52/5.87 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_lt_0_iff
% 5.52/5.87 thf(fact_7993_of__real__divide,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.52/5.87 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_divide
% 5.52/5.87 thf(fact_7994_of__real__divide,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.52/5.87 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_divide
% 5.52/5.87 thf(fact_7995_real__sqrt__ge__0__iff,axiom,
% 5.52/5.87 ! [Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y2 ) )
% 5.52/5.87 = ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_ge_0_iff
% 5.52/5.87 thf(fact_7996_real__sqrt__le__0__iff,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ zero_zero_real )
% 5.52/5.87 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_le_0_iff
% 5.52/5.87 thf(fact_7997_of__real__add,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.52/5.87 = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_add
% 5.52/5.87 thf(fact_7998_of__real__add,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.52/5.87 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_add
% 5.52/5.87 thf(fact_7999_of__real__power,axiom,
% 5.52/5.87 ! [X2: real,N: nat] :
% 5.52/5.87 ( ( real_V1803761363581548252l_real @ ( power_power_real @ X2 @ N ) )
% 5.52/5.87 = ( power_power_real @ ( real_V1803761363581548252l_real @ X2 ) @ N ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_power
% 5.52/5.87 thf(fact_8000_of__real__power,axiom,
% 5.52/5.87 ! [X2: real,N: nat] :
% 5.52/5.87 ( ( real_V4546457046886955230omplex @ ( power_power_real @ X2 @ N ) )
% 5.52/5.87 = ( power_power_complex @ ( real_V4546457046886955230omplex @ X2 ) @ N ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_power
% 5.52/5.87 thf(fact_8001_real__sqrt__lt__1__iff,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.52/5.87 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_lt_1_iff
% 5.52/5.87 thf(fact_8002_real__sqrt__gt__1__iff,axiom,
% 5.52/5.87 ! [Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y2 ) )
% 5.52/5.87 = ( ord_less_real @ one_one_real @ Y2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_gt_1_iff
% 5.52/5.87 thf(fact_8003_pochhammer__0,axiom,
% 5.52/5.87 ! [A: complex] :
% 5.52/5.87 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.52/5.87 = one_one_complex ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_0
% 5.52/5.87 thf(fact_8004_pochhammer__0,axiom,
% 5.52/5.87 ! [A: real] :
% 5.52/5.87 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.52/5.87 = one_one_real ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_0
% 5.52/5.87 thf(fact_8005_pochhammer__0,axiom,
% 5.52/5.87 ! [A: rat] :
% 5.52/5.87 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.52/5.87 = one_one_rat ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_0
% 5.52/5.87 thf(fact_8006_pochhammer__0,axiom,
% 5.52/5.87 ! [A: nat] :
% 5.52/5.87 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.52/5.87 = one_one_nat ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_0
% 5.52/5.87 thf(fact_8007_pochhammer__0,axiom,
% 5.52/5.87 ! [A: int] :
% 5.52/5.87 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.52/5.87 = one_one_int ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_0
% 5.52/5.87 thf(fact_8008_real__sqrt__ge__1__iff,axiom,
% 5.52/5.87 ! [Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y2 ) )
% 5.52/5.87 = ( ord_less_eq_real @ one_one_real @ Y2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_ge_1_iff
% 5.52/5.87 thf(fact_8009_real__sqrt__le__1__iff,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.52/5.87 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_le_1_iff
% 5.52/5.87 thf(fact_8010_real__sqrt__mult__self,axiom,
% 5.52/5.87 ! [A: real] :
% 5.52/5.87 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.52/5.87 = ( abs_abs_real @ A ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_mult_self
% 5.52/5.87 thf(fact_8011_real__sqrt__abs2,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( sqrt @ ( times_times_real @ X2 @ X2 ) )
% 5.52/5.87 = ( abs_abs_real @ X2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_abs2
% 5.52/5.87 thf(fact_8012_real__sqrt__four,axiom,
% 5.52/5.87 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.52/5.87 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_four
% 5.52/5.87 thf(fact_8013_of__real__neg__numeral,axiom,
% 5.52/5.87 ! [W: num] :
% 5.52/5.87 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.52/5.87 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_neg_numeral
% 5.52/5.87 thf(fact_8014_of__real__neg__numeral,axiom,
% 5.52/5.87 ! [W: num] :
% 5.52/5.87 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.52/5.87 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % of_real_neg_numeral
% 5.52/5.87 thf(fact_8015_cos__of__real__pi,axiom,
% 5.52/5.87 ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 5.52/5.87 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % cos_of_real_pi
% 5.52/5.87 thf(fact_8016_cos__of__real__pi,axiom,
% 5.52/5.87 ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 5.52/5.87 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.52/5.87
% 5.52/5.87 % cos_of_real_pi
% 5.52/5.87 thf(fact_8017_real__sqrt__abs,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( sqrt @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.87 = ( abs_abs_real @ X2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_abs
% 5.52/5.87 thf(fact_8018_real__sqrt__pow2,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.87 = X2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_pow2
% 5.52/5.87 thf(fact_8019_real__sqrt__pow2__iff,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.87 = X2 )
% 5.52/5.87 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_pow2_iff
% 5.52/5.87 thf(fact_8020_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.52/5.87 ! [X2: real,Y2: real,Xa2: real,Ya: real] :
% 5.52/5.87 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.87 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_sum_squares_mult_squared_eq
% 5.52/5.87 thf(fact_8021_norm__of__real__add1,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X2 ) @ one_one_real ) )
% 5.52/5.87 = ( abs_abs_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % norm_of_real_add1
% 5.52/5.87 thf(fact_8022_norm__of__real__add1,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ one_one_complex ) )
% 5.52/5.87 = ( abs_abs_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % norm_of_real_add1
% 5.52/5.87 thf(fact_8023_norm__of__real__addn,axiom,
% 5.52/5.87 ! [X2: real,B: num] :
% 5.52/5.87 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( numeral_numeral_real @ B ) ) )
% 5.52/5.87 = ( abs_abs_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % norm_of_real_addn
% 5.52/5.87 thf(fact_8024_norm__of__real__addn,axiom,
% 5.52/5.87 ! [X2: real,B: num] :
% 5.52/5.87 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( numera6690914467698888265omplex @ B ) ) )
% 5.52/5.87 = ( abs_abs_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % norm_of_real_addn
% 5.52/5.87 thf(fact_8025_cos__of__real__pi__half,axiom,
% 5.52/5.87 ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 = zero_zero_real ) ).
% 5.52/5.87
% 5.52/5.87 % cos_of_real_pi_half
% 5.52/5.87 thf(fact_8026_cos__of__real__pi__half,axiom,
% 5.52/5.87 ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.52/5.87 = zero_zero_complex ) ).
% 5.52/5.87
% 5.52/5.87 % cos_of_real_pi_half
% 5.52/5.87 thf(fact_8027_sin__of__real__pi__half,axiom,
% 5.52/5.87 ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 = one_one_real ) ).
% 5.52/5.87
% 5.52/5.87 % sin_of_real_pi_half
% 5.52/5.87 thf(fact_8028_sin__of__real__pi__half,axiom,
% 5.52/5.87 ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.52/5.87 = one_one_complex ) ).
% 5.52/5.87
% 5.52/5.87 % sin_of_real_pi_half
% 5.52/5.87 thf(fact_8029_real__sqrt__minus,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( sqrt @ ( uminus_uminus_real @ X2 ) )
% 5.52/5.87 = ( uminus_uminus_real @ ( sqrt @ X2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_minus
% 5.52/5.87 thf(fact_8030_real__sqrt__power,axiom,
% 5.52/5.87 ! [X2: real,K: nat] :
% 5.52/5.87 ( ( sqrt @ ( power_power_real @ X2 @ K ) )
% 5.52/5.87 = ( power_power_real @ ( sqrt @ X2 ) @ K ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_power
% 5.52/5.87 thf(fact_8031_real__sqrt__mult,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( sqrt @ ( times_times_real @ X2 @ Y2 ) )
% 5.52/5.87 = ( times_times_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_mult
% 5.52/5.87 thf(fact_8032_real__sqrt__divide,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( sqrt @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.52/5.87 = ( divide_divide_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_divide
% 5.52/5.87 thf(fact_8033_real__sqrt__le__mono,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.52/5.87 => ( ord_less_eq_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_le_mono
% 5.52/5.87 thf(fact_8034_real__sqrt__less__mono,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ X2 @ Y2 )
% 5.52/5.87 => ( ord_less_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_less_mono
% 5.52/5.87 thf(fact_8035_real__sqrt__gt__zero,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_gt_zero
% 5.52/5.87 thf(fact_8036_real__sqrt__ge__zero,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_ge_zero
% 5.52/5.87 thf(fact_8037_real__sqrt__eq__zero__cancel,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ( sqrt @ X2 )
% 5.52/5.87 = zero_zero_real )
% 5.52/5.87 => ( X2 = zero_zero_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_eq_zero_cancel
% 5.52/5.87 thf(fact_8038_real__sqrt__ge__one,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.52/5.87 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_ge_one
% 5.52/5.87 thf(fact_8039_pochhammer__pos,axiom,
% 5.52/5.87 ! [X2: real,N: nat] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X2 @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_pos
% 5.52/5.87 thf(fact_8040_pochhammer__pos,axiom,
% 5.52/5.87 ! [X2: rat,N: nat] :
% 5.52/5.87 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.52/5.87 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_pos
% 5.52/5.87 thf(fact_8041_pochhammer__pos,axiom,
% 5.52/5.87 ! [X2: nat,N: nat] :
% 5.52/5.87 ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.52/5.87 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_pos
% 5.52/5.87 thf(fact_8042_pochhammer__pos,axiom,
% 5.52/5.87 ! [X2: int,N: nat] :
% 5.52/5.87 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.52/5.87 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_pos
% 5.52/5.87 thf(fact_8043_pochhammer__eq__0__mono,axiom,
% 5.52/5.87 ! [A: real,N: nat,M: nat] :
% 5.52/5.87 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.52/5.87 = zero_zero_real )
% 5.52/5.87 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.87 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.52/5.87 = zero_zero_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_eq_0_mono
% 5.52/5.87 thf(fact_8044_pochhammer__eq__0__mono,axiom,
% 5.52/5.87 ! [A: rat,N: nat,M: nat] :
% 5.52/5.87 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.52/5.87 = zero_zero_rat )
% 5.52/5.87 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.87 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.52/5.87 = zero_zero_rat ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_eq_0_mono
% 5.52/5.87 thf(fact_8045_pochhammer__neq__0__mono,axiom,
% 5.52/5.87 ! [A: real,M: nat,N: nat] :
% 5.52/5.87 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.52/5.87 != zero_zero_real )
% 5.52/5.87 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.87 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.52/5.87 != zero_zero_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_neq_0_mono
% 5.52/5.87 thf(fact_8046_pochhammer__neq__0__mono,axiom,
% 5.52/5.87 ! [A: rat,M: nat,N: nat] :
% 5.52/5.87 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.52/5.87 != zero_zero_rat )
% 5.52/5.87 => ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.87 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.52/5.87 != zero_zero_rat ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_neq_0_mono
% 5.52/5.87 thf(fact_8047_pochhammer__fact,axiom,
% 5.52/5.87 ( semiri5044797733671781792omplex
% 5.52/5.87 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_fact
% 5.52/5.87 thf(fact_8048_pochhammer__fact,axiom,
% 5.52/5.87 ( semiri773545260158071498ct_rat
% 5.52/5.87 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_fact
% 5.52/5.87 thf(fact_8049_pochhammer__fact,axiom,
% 5.52/5.87 ( semiri1406184849735516958ct_int
% 5.52/5.87 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_fact
% 5.52/5.87 thf(fact_8050_pochhammer__fact,axiom,
% 5.52/5.87 ( semiri2265585572941072030t_real
% 5.52/5.87 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_fact
% 5.52/5.87 thf(fact_8051_pochhammer__fact,axiom,
% 5.52/5.87 ( semiri1408675320244567234ct_nat
% 5.52/5.87 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_fact
% 5.52/5.87 thf(fact_8052_nonzero__of__real__divide,axiom,
% 5.52/5.87 ! [Y2: real,X2: real] :
% 5.52/5.87 ( ( Y2 != zero_zero_real )
% 5.52/5.87 => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.52/5.87 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % nonzero_of_real_divide
% 5.52/5.87 thf(fact_8053_nonzero__of__real__divide,axiom,
% 5.52/5.87 ! [Y2: real,X2: real] :
% 5.52/5.87 ( ( Y2 != zero_zero_real )
% 5.52/5.87 => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.52/5.87 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % nonzero_of_real_divide
% 5.52/5.87 thf(fact_8054_real__div__sqrt,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( divide_divide_real @ X2 @ ( sqrt @ X2 ) )
% 5.52/5.87 = ( sqrt @ X2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_div_sqrt
% 5.52/5.87 thf(fact_8055_sqrt__add__le__add__sqrt,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.87 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X2 @ Y2 ) ) @ ( plus_plus_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sqrt_add_le_add_sqrt
% 5.52/5.87 thf(fact_8056_le__real__sqrt__sumsq,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % le_real_sqrt_sumsq
% 5.52/5.87 thf(fact_8057_pochhammer__nonneg,axiom,
% 5.52/5.87 ! [X2: real,N: nat] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X2 @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_nonneg
% 5.52/5.87 thf(fact_8058_pochhammer__nonneg,axiom,
% 5.52/5.87 ! [X2: rat,N: nat] :
% 5.52/5.87 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.52/5.87 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_nonneg
% 5.52/5.87 thf(fact_8059_pochhammer__nonneg,axiom,
% 5.52/5.87 ! [X2: nat,N: nat] :
% 5.52/5.87 ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.52/5.87 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_nonneg
% 5.52/5.87 thf(fact_8060_pochhammer__nonneg,axiom,
% 5.52/5.87 ! [X2: int,N: nat] :
% 5.52/5.87 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.52/5.87 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_nonneg
% 5.52/5.87 thf(fact_8061_pochhammer__0__left,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( ( N = zero_zero_nat )
% 5.52/5.87 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 & ( ( N != zero_zero_nat )
% 5.52/5.87 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.52/5.87 = zero_zero_complex ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_0_left
% 5.52/5.87 thf(fact_8062_pochhammer__0__left,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( ( N = zero_zero_nat )
% 5.52/5.87 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.52/5.87 = one_one_real ) )
% 5.52/5.87 & ( ( N != zero_zero_nat )
% 5.52/5.87 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.52/5.87 = zero_zero_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_0_left
% 5.52/5.87 thf(fact_8063_pochhammer__0__left,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( ( N = zero_zero_nat )
% 5.52/5.87 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.52/5.87 = one_one_rat ) )
% 5.52/5.87 & ( ( N != zero_zero_nat )
% 5.52/5.87 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.52/5.87 = zero_zero_rat ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_0_left
% 5.52/5.87 thf(fact_8064_pochhammer__0__left,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( ( N = zero_zero_nat )
% 5.52/5.87 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.52/5.87 = one_one_nat ) )
% 5.52/5.87 & ( ( N != zero_zero_nat )
% 5.52/5.87 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.52/5.87 = zero_zero_nat ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_0_left
% 5.52/5.87 thf(fact_8065_pochhammer__0__left,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( ( N = zero_zero_nat )
% 5.52/5.87 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.52/5.87 = one_one_int ) )
% 5.52/5.87 & ( ( N != zero_zero_nat )
% 5.52/5.87 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.52/5.87 = zero_zero_int ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_0_left
% 5.52/5.87 thf(fact_8066_norm__less__p1,axiom,
% 5.52/5.87 ! [X2: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X2 ) ) @ one_one_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % norm_less_p1
% 5.52/5.87 thf(fact_8067_norm__less__p1,axiom,
% 5.52/5.87 ! [X2: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X2 ) ) @ one_one_complex ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % norm_less_p1
% 5.52/5.87 thf(fact_8068_sqrt2__less__2,axiom,
% 5.52/5.87 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.52/5.87
% 5.52/5.87 % sqrt2_less_2
% 5.52/5.87 thf(fact_8069_pochhammer__rec,axiom,
% 5.52/5.87 ! [A: complex,N: nat] :
% 5.52/5.87 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_rec
% 5.52/5.87 thf(fact_8070_pochhammer__rec,axiom,
% 5.52/5.87 ! [A: real,N: nat] :
% 5.52/5.87 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_rec
% 5.52/5.87 thf(fact_8071_pochhammer__rec,axiom,
% 5.52/5.87 ! [A: rat,N: nat] :
% 5.52/5.87 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_rec
% 5.52/5.87 thf(fact_8072_pochhammer__rec,axiom,
% 5.52/5.87 ! [A: nat,N: nat] :
% 5.52/5.87 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_rec
% 5.52/5.87 thf(fact_8073_pochhammer__rec,axiom,
% 5.52/5.87 ! [A: int,N: nat] :
% 5.52/5.87 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_rec
% 5.52/5.87 thf(fact_8074_diffs__def,axiom,
% 5.52/5.87 ( diffs_int
% 5.52/5.87 = ( ^ [C3: nat > int,N3: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) @ ( C3 @ ( suc @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % diffs_def
% 5.52/5.87 thf(fact_8075_diffs__def,axiom,
% 5.52/5.87 ( diffs_real
% 5.52/5.87 = ( ^ [C3: nat > real,N3: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) @ ( C3 @ ( suc @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % diffs_def
% 5.52/5.87 thf(fact_8076_diffs__def,axiom,
% 5.52/5.87 ( diffs_rat
% 5.52/5.87 = ( ^ [C3: nat > rat,N3: nat] : ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) @ ( C3 @ ( suc @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % diffs_def
% 5.52/5.87 thf(fact_8077_pochhammer__Suc,axiom,
% 5.52/5.87 ! [A: complex,N: nat] :
% 5.52/5.87 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_Suc
% 5.52/5.87 thf(fact_8078_pochhammer__Suc,axiom,
% 5.52/5.87 ! [A: int,N: nat] :
% 5.52/5.87 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_Suc
% 5.52/5.87 thf(fact_8079_pochhammer__Suc,axiom,
% 5.52/5.87 ! [A: real,N: nat] :
% 5.52/5.87 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_Suc
% 5.52/5.87 thf(fact_8080_pochhammer__Suc,axiom,
% 5.52/5.87 ! [A: nat,N: nat] :
% 5.52/5.87 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_Suc
% 5.52/5.87 thf(fact_8081_pochhammer__Suc,axiom,
% 5.52/5.87 ! [A: rat,N: nat] :
% 5.52/5.87 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_Suc
% 5.52/5.87 thf(fact_8082_pochhammer__Suc,axiom,
% 5.52/5.87 ! [A: extended_enat,N: nat] :
% 5.52/5.87 ( ( comm_s3181272606743183617d_enat @ A @ ( suc @ N ) )
% 5.52/5.87 = ( times_7803423173614009249d_enat @ ( comm_s3181272606743183617d_enat @ A @ N ) @ ( plus_p3455044024723400733d_enat @ A @ ( semiri4216267220026989637d_enat @ N ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_Suc
% 5.52/5.87 thf(fact_8083_pochhammer__rec_H,axiom,
% 5.52/5.87 ! [Z: complex,N: nat] :
% 5.52/5.87 ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_rec'
% 5.52/5.87 thf(fact_8084_pochhammer__rec_H,axiom,
% 5.52/5.87 ! [Z: int,N: nat] :
% 5.52/5.87 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_rec'
% 5.52/5.87 thf(fact_8085_pochhammer__rec_H,axiom,
% 5.52/5.87 ! [Z: real,N: nat] :
% 5.52/5.87 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_rec'
% 5.52/5.87 thf(fact_8086_pochhammer__rec_H,axiom,
% 5.52/5.87 ! [Z: nat,N: nat] :
% 5.52/5.87 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_rec'
% 5.52/5.87 thf(fact_8087_pochhammer__rec_H,axiom,
% 5.52/5.87 ! [Z: rat,N: nat] :
% 5.52/5.87 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 5.52/5.87 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_rec'
% 5.52/5.87 thf(fact_8088_pochhammer__rec_H,axiom,
% 5.52/5.87 ! [Z: extended_enat,N: nat] :
% 5.52/5.87 ( ( comm_s3181272606743183617d_enat @ Z @ ( suc @ N ) )
% 5.52/5.87 = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ Z @ ( semiri4216267220026989637d_enat @ N ) ) @ ( comm_s3181272606743183617d_enat @ Z @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_rec'
% 5.52/5.87 thf(fact_8089_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.52/5.87 ! [N: nat,K: nat] :
% 5.52/5.87 ( ( ord_less_nat @ N @ K )
% 5.52/5.87 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.52/5.87 = zero_zero_complex ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_lemma
% 5.52/5.87 thf(fact_8090_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.52/5.87 ! [N: nat,K: nat] :
% 5.52/5.87 ( ( ord_less_nat @ N @ K )
% 5.52/5.87 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.52/5.87 = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_lemma
% 5.52/5.87 thf(fact_8091_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.52/5.87 ! [N: nat,K: nat] :
% 5.52/5.87 ( ( ord_less_nat @ N @ K )
% 5.52/5.87 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.52/5.87 = zero_zero_int ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_lemma
% 5.52/5.87 thf(fact_8092_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.52/5.87 ! [N: nat,K: nat] :
% 5.52/5.87 ( ( ord_less_nat @ N @ K )
% 5.52/5.87 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.52/5.87 = zero_zero_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_lemma
% 5.52/5.87 thf(fact_8093_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.52/5.87 ! [N: nat,K: nat] :
% 5.52/5.87 ( ( ord_less_nat @ N @ K )
% 5.52/5.87 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.52/5.87 = zero_zero_rat ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_lemma
% 5.52/5.87 thf(fact_8094_pochhammer__of__nat__eq__0__iff,axiom,
% 5.52/5.87 ! [N: nat,K: nat] :
% 5.52/5.87 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.52/5.87 = zero_zero_complex )
% 5.52/5.87 = ( ord_less_nat @ N @ K ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_iff
% 5.52/5.87 thf(fact_8095_pochhammer__of__nat__eq__0__iff,axiom,
% 5.52/5.87 ! [N: nat,K: nat] :
% 5.52/5.87 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.52/5.87 = zero_z3403309356797280102nteger )
% 5.52/5.87 = ( ord_less_nat @ N @ K ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_iff
% 5.52/5.87 thf(fact_8096_pochhammer__of__nat__eq__0__iff,axiom,
% 5.52/5.87 ! [N: nat,K: nat] :
% 5.52/5.87 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.52/5.87 = zero_zero_int )
% 5.52/5.87 = ( ord_less_nat @ N @ K ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_iff
% 5.52/5.87 thf(fact_8097_pochhammer__of__nat__eq__0__iff,axiom,
% 5.52/5.87 ! [N: nat,K: nat] :
% 5.52/5.87 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.52/5.87 = zero_zero_real )
% 5.52/5.87 = ( ord_less_nat @ N @ K ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_iff
% 5.52/5.87 thf(fact_8098_pochhammer__of__nat__eq__0__iff,axiom,
% 5.52/5.87 ! [N: nat,K: nat] :
% 5.52/5.87 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.52/5.87 = zero_zero_rat )
% 5.52/5.87 = ( ord_less_nat @ N @ K ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_iff
% 5.52/5.87 thf(fact_8099_pochhammer__eq__0__iff,axiom,
% 5.52/5.87 ! [A: complex,N: nat] :
% 5.52/5.87 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.52/5.87 = zero_zero_complex )
% 5.52/5.87 = ( ? [K2: nat] :
% 5.52/5.87 ( ( ord_less_nat @ K2 @ N )
% 5.52/5.87 & ( A
% 5.52/5.87 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_eq_0_iff
% 5.52/5.87 thf(fact_8100_pochhammer__eq__0__iff,axiom,
% 5.52/5.87 ! [A: real,N: nat] :
% 5.52/5.87 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.52/5.87 = zero_zero_real )
% 5.52/5.87 = ( ? [K2: nat] :
% 5.52/5.87 ( ( ord_less_nat @ K2 @ N )
% 5.52/5.87 & ( A
% 5.52/5.87 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_eq_0_iff
% 5.52/5.87 thf(fact_8101_pochhammer__eq__0__iff,axiom,
% 5.52/5.87 ! [A: rat,N: nat] :
% 5.52/5.87 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.52/5.87 = zero_zero_rat )
% 5.52/5.87 = ( ? [K2: nat] :
% 5.52/5.87 ( ( ord_less_nat @ K2 @ N )
% 5.52/5.87 & ( A
% 5.52/5.87 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_eq_0_iff
% 5.52/5.87 thf(fact_8102_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.52/5.87 ! [K: nat,N: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.87 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.52/5.87 != zero_zero_complex ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_lemma'
% 5.52/5.87 thf(fact_8103_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.52/5.87 ! [K: nat,N: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.87 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.52/5.87 != zero_z3403309356797280102nteger ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_lemma'
% 5.52/5.87 thf(fact_8104_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.52/5.87 ! [K: nat,N: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.87 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.52/5.87 != zero_zero_int ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_lemma'
% 5.52/5.87 thf(fact_8105_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.52/5.87 ! [K: nat,N: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.87 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.52/5.87 != zero_zero_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_lemma'
% 5.52/5.87 thf(fact_8106_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.52/5.87 ! [K: nat,N: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.87 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.52/5.87 != zero_zero_rat ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_of_nat_eq_0_lemma'
% 5.52/5.87 thf(fact_8107_pochhammer__product_H,axiom,
% 5.52/5.87 ! [Z: complex,N: nat,M: nat] :
% 5.52/5.87 ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.52/5.87 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ M ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_product'
% 5.52/5.87 thf(fact_8108_pochhammer__product_H,axiom,
% 5.52/5.87 ! [Z: int,N: nat,M: nat] :
% 5.52/5.87 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.52/5.87 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_product'
% 5.52/5.87 thf(fact_8109_pochhammer__product_H,axiom,
% 5.52/5.87 ! [Z: real,N: nat,M: nat] :
% 5.52/5.87 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.52/5.87 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_product'
% 5.52/5.87 thf(fact_8110_pochhammer__product_H,axiom,
% 5.52/5.87 ! [Z: nat,N: nat,M: nat] :
% 5.52/5.87 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.52/5.87 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_product'
% 5.52/5.87 thf(fact_8111_pochhammer__product_H,axiom,
% 5.52/5.87 ! [Z: rat,N: nat,M: nat] :
% 5.52/5.87 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.52/5.87 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_product'
% 5.52/5.87 thf(fact_8112_pochhammer__product_H,axiom,
% 5.52/5.87 ! [Z: extended_enat,N: nat,M: nat] :
% 5.52/5.87 ( ( comm_s3181272606743183617d_enat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.52/5.87 = ( times_7803423173614009249d_enat @ ( comm_s3181272606743183617d_enat @ Z @ N ) @ ( comm_s3181272606743183617d_enat @ ( plus_p3455044024723400733d_enat @ Z @ ( semiri4216267220026989637d_enat @ N ) ) @ M ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_product'
% 5.52/5.87 thf(fact_8113_real__less__rsqrt,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 )
% 5.52/5.87 => ( ord_less_real @ X2 @ ( sqrt @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_less_rsqrt
% 5.52/5.87 thf(fact_8114_sqrt__le__D,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y2 )
% 5.52/5.87 => ( ord_less_eq_real @ X2 @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sqrt_le_D
% 5.52/5.87 thf(fact_8115_real__le__rsqrt,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 )
% 5.52/5.87 => ( ord_less_eq_real @ X2 @ ( sqrt @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_le_rsqrt
% 5.52/5.87 thf(fact_8116_termdiff__converges__all,axiom,
% 5.52/5.87 ! [C: nat > complex,X2: complex] :
% 5.52/5.87 ( ! [X4: complex] :
% 5.52/5.87 ( summable_complex
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_complex @ ( C @ N3 ) @ ( power_power_complex @ X4 @ N3 ) ) )
% 5.52/5.87 => ( summable_complex
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_complex @ ( diffs_complex @ C @ N3 ) @ ( power_power_complex @ X2 @ N3 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % termdiff_converges_all
% 5.52/5.87 thf(fact_8117_termdiff__converges__all,axiom,
% 5.52/5.87 ! [C: nat > real,X2: real] :
% 5.52/5.87 ( ! [X4: real] :
% 5.52/5.87 ( summable_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( C @ N3 ) @ ( power_power_real @ X4 @ N3 ) ) )
% 5.52/5.87 => ( summable_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( diffs_real @ C @ N3 ) @ ( power_power_real @ X2 @ N3 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % termdiff_converges_all
% 5.52/5.87 thf(fact_8118_tan__60,axiom,
% 5.52/5.87 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.52/5.87 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_60
% 5.52/5.87 thf(fact_8119_pochhammer__product,axiom,
% 5.52/5.87 ! [M: nat,N: nat,Z: complex] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.87 => ( ( comm_s2602460028002588243omplex @ Z @ N )
% 5.52/5.87 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_product
% 5.52/5.87 thf(fact_8120_pochhammer__product,axiom,
% 5.52/5.87 ! [M: nat,N: nat,Z: int] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.87 => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 5.52/5.87 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_product
% 5.52/5.87 thf(fact_8121_pochhammer__product,axiom,
% 5.52/5.87 ! [M: nat,N: nat,Z: real] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.87 => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 5.52/5.87 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_product
% 5.52/5.87 thf(fact_8122_pochhammer__product,axiom,
% 5.52/5.87 ! [M: nat,N: nat,Z: nat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.87 => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 5.52/5.87 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_product
% 5.52/5.87 thf(fact_8123_pochhammer__product,axiom,
% 5.52/5.87 ! [M: nat,N: nat,Z: rat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.87 => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 5.52/5.87 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_product
% 5.52/5.87 thf(fact_8124_pochhammer__product,axiom,
% 5.52/5.87 ! [M: nat,N: nat,Z: extended_enat] :
% 5.52/5.87 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.87 => ( ( comm_s3181272606743183617d_enat @ Z @ N )
% 5.52/5.87 = ( times_7803423173614009249d_enat @ ( comm_s3181272606743183617d_enat @ Z @ M ) @ ( comm_s3181272606743183617d_enat @ ( plus_p3455044024723400733d_enat @ Z @ ( semiri4216267220026989637d_enat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_product
% 5.52/5.87 thf(fact_8125_real__le__lsqrt,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ X2 @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_le_lsqrt
% 5.52/5.87 thf(fact_8126_real__sqrt__unique,axiom,
% 5.52/5.87 ! [Y2: real,X2: real] :
% 5.52/5.87 ( ( ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.87 = X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.87 => ( ( sqrt @ X2 )
% 5.52/5.87 = Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_unique
% 5.52/5.87 thf(fact_8127_lemma__real__divide__sqrt__less,axiom,
% 5.52/5.87 ! [U: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ U )
% 5.52/5.87 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.52/5.87
% 5.52/5.87 % lemma_real_divide_sqrt_less
% 5.52/5.87 thf(fact_8128_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.87 = X2 )
% 5.52/5.87 => ( Y2 = zero_zero_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_sum_squares_eq_cancel
% 5.52/5.87 thf(fact_8129_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.87 = Y2 )
% 5.52/5.87 => ( X2 = zero_zero_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_sum_squares_eq_cancel2
% 5.52/5.87 thf(fact_8130_real__sqrt__sum__squares__ge1,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_sum_squares_ge1
% 5.52/5.87 thf(fact_8131_real__sqrt__sum__squares__ge2,axiom,
% 5.52/5.87 ! [Y2: real,X2: real] : ( ord_less_eq_real @ Y2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_sum_squares_ge2
% 5.52/5.87 thf(fact_8132_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.52/5.87 ! [A: real,C: real,B: real,D2: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A @ C ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B @ D2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_sum_squares_triangle_ineq
% 5.52/5.87 thf(fact_8133_sqrt__ge__absD,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ Y2 ) )
% 5.52/5.87 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % sqrt_ge_absD
% 5.52/5.87 thf(fact_8134_cos__45,axiom,
% 5.52/5.87 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.52/5.87 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % cos_45
% 5.52/5.87 thf(fact_8135_sin__45,axiom,
% 5.52/5.87 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.52/5.87 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sin_45
% 5.52/5.87 thf(fact_8136_cos__int__times__real,axiom,
% 5.52/5.87 ! [M: int,X2: real] :
% 5.52/5.87 ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X2 ) ) )
% 5.52/5.87 = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % cos_int_times_real
% 5.52/5.87 thf(fact_8137_cos__int__times__real,axiom,
% 5.52/5.87 ! [M: int,X2: real] :
% 5.52/5.87 ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X2 ) ) )
% 5.52/5.87 = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % cos_int_times_real
% 5.52/5.87 thf(fact_8138_sin__int__times__real,axiom,
% 5.52/5.87 ! [M: int,X2: real] :
% 5.52/5.87 ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X2 ) ) )
% 5.52/5.87 = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sin_int_times_real
% 5.52/5.87 thf(fact_8139_sin__int__times__real,axiom,
% 5.52/5.87 ! [M: int,X2: real] :
% 5.52/5.87 ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X2 ) ) )
% 5.52/5.87 = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sin_int_times_real
% 5.52/5.87 thf(fact_8140_pochhammer__absorb__comp,axiom,
% 5.52/5.87 ! [R: complex,K: nat] :
% 5.52/5.87 ( ( times_times_complex @ ( minus_minus_complex @ R @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R ) @ K ) )
% 5.52/5.87 = ( times_times_complex @ R @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R ) @ one_one_complex ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_absorb_comp
% 5.52/5.87 thf(fact_8141_pochhammer__absorb__comp,axiom,
% 5.52/5.87 ! [R: code_integer,K: nat] :
% 5.52/5.87 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R ) @ K ) )
% 5.52/5.87 = ( times_3573771949741848930nteger @ R @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_absorb_comp
% 5.52/5.87 thf(fact_8142_pochhammer__absorb__comp,axiom,
% 5.52/5.87 ! [R: int,K: nat] :
% 5.52/5.87 ( ( times_times_int @ ( minus_minus_int @ R @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R ) @ K ) )
% 5.52/5.87 = ( times_times_int @ R @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R ) @ one_one_int ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_absorb_comp
% 5.52/5.87 thf(fact_8143_pochhammer__absorb__comp,axiom,
% 5.52/5.87 ! [R: real,K: nat] :
% 5.52/5.87 ( ( times_times_real @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R ) @ K ) )
% 5.52/5.87 = ( times_times_real @ R @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R ) @ one_one_real ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_absorb_comp
% 5.52/5.87 thf(fact_8144_pochhammer__absorb__comp,axiom,
% 5.52/5.87 ! [R: rat,K: nat] :
% 5.52/5.87 ( ( times_times_rat @ ( minus_minus_rat @ R @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R ) @ K ) )
% 5.52/5.87 = ( times_times_rat @ R @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R ) @ one_one_rat ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_absorb_comp
% 5.52/5.87 thf(fact_8145_pochhammer__same,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 5.52/5.87 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_same
% 5.52/5.87 thf(fact_8146_pochhammer__same,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 5.52/5.87 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_same
% 5.52/5.87 thf(fact_8147_pochhammer__same,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 5.52/5.87 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_same
% 5.52/5.87 thf(fact_8148_pochhammer__same,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 5.52/5.87 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_same
% 5.52/5.87 thf(fact_8149_pochhammer__same,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 5.52/5.87 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_same
% 5.52/5.87 thf(fact_8150_real__less__lsqrt,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.87 => ( ( ord_less_real @ X2 @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ord_less_real @ ( sqrt @ X2 ) @ Y2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_less_lsqrt
% 5.52/5.87 thf(fact_8151_sqrt__sum__squares__le__sum,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.87 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sqrt_sum_squares_le_sum
% 5.52/5.87 thf(fact_8152_tan__30,axiom,
% 5.52/5.87 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.52/5.87 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % tan_30
% 5.52/5.87 thf(fact_8153_sqrt__even__pow2,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.87 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.87 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sqrt_even_pow2
% 5.52/5.87 thf(fact_8154_sqrt__sum__squares__le__sum__abs,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ Y2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sqrt_sum_squares_le_sum_abs
% 5.52/5.87 thf(fact_8155_real__sqrt__ge__abs2,axiom,
% 5.52/5.87 ! [Y2: real,X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_ge_abs2
% 5.52/5.87 thf(fact_8156_real__sqrt__ge__abs1,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_ge_abs1
% 5.52/5.87 thf(fact_8157_ln__sqrt,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ln_ln_real @ ( sqrt @ X2 ) )
% 5.52/5.87 = ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % ln_sqrt
% 5.52/5.87 thf(fact_8158_cos__30,axiom,
% 5.52/5.87 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.52/5.87 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % cos_30
% 5.52/5.87 thf(fact_8159_sin__60,axiom,
% 5.52/5.87 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.52/5.87 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sin_60
% 5.52/5.87 thf(fact_8160_pochhammer__minus_H,axiom,
% 5.52/5.87 ! [B: complex,K: nat] :
% 5.52/5.87 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.52/5.87 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_minus'
% 5.52/5.87 thf(fact_8161_pochhammer__minus_H,axiom,
% 5.52/5.87 ! [B: code_integer,K: nat] :
% 5.52/5.87 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.52/5.87 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_minus'
% 5.52/5.87 thf(fact_8162_pochhammer__minus_H,axiom,
% 5.52/5.87 ! [B: int,K: nat] :
% 5.52/5.87 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.52/5.87 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_minus'
% 5.52/5.87 thf(fact_8163_pochhammer__minus_H,axiom,
% 5.52/5.87 ! [B: real,K: nat] :
% 5.52/5.87 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.52/5.87 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_minus'
% 5.52/5.87 thf(fact_8164_pochhammer__minus_H,axiom,
% 5.52/5.87 ! [B: rat,K: nat] :
% 5.52/5.87 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.52/5.87 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_minus'
% 5.52/5.87 thf(fact_8165_pochhammer__minus,axiom,
% 5.52/5.87 ! [B: complex,K: nat] :
% 5.52/5.87 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.52/5.87 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_minus
% 5.52/5.87 thf(fact_8166_pochhammer__minus,axiom,
% 5.52/5.87 ! [B: code_integer,K: nat] :
% 5.52/5.87 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.52/5.87 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_minus
% 5.52/5.87 thf(fact_8167_pochhammer__minus,axiom,
% 5.52/5.87 ! [B: int,K: nat] :
% 5.52/5.87 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.52/5.87 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_minus
% 5.52/5.87 thf(fact_8168_pochhammer__minus,axiom,
% 5.52/5.87 ! [B: real,K: nat] :
% 5.52/5.87 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.52/5.87 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_minus
% 5.52/5.87 thf(fact_8169_pochhammer__minus,axiom,
% 5.52/5.87 ! [B: rat,K: nat] :
% 5.52/5.87 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.52/5.87 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_minus
% 5.52/5.87 thf(fact_8170_cos__sin__eq,axiom,
% 5.52/5.87 ( cos_real
% 5.52/5.87 = ( ^ [X: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % cos_sin_eq
% 5.52/5.87 thf(fact_8171_cos__sin__eq,axiom,
% 5.52/5.87 ( cos_complex
% 5.52/5.87 = ( ^ [X: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % cos_sin_eq
% 5.52/5.87 thf(fact_8172_sin__cos__eq,axiom,
% 5.52/5.87 ( sin_real
% 5.52/5.87 = ( ^ [X: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sin_cos_eq
% 5.52/5.87 thf(fact_8173_sin__cos__eq,axiom,
% 5.52/5.87 ( sin_complex
% 5.52/5.87 = ( ^ [X: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sin_cos_eq
% 5.52/5.87 thf(fact_8174_termdiff__converges,axiom,
% 5.52/5.87 ! [X2: real,K5: real,C: nat > real] :
% 5.52/5.87 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ K5 )
% 5.52/5.87 => ( ! [X4: real] :
% 5.52/5.87 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ K5 )
% 5.52/5.87 => ( summable_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( C @ N3 ) @ ( power_power_real @ X4 @ N3 ) ) ) )
% 5.52/5.87 => ( summable_real
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_real @ ( diffs_real @ C @ N3 ) @ ( power_power_real @ X2 @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % termdiff_converges
% 5.52/5.87 thf(fact_8175_termdiff__converges,axiom,
% 5.52/5.87 ! [X2: complex,K5: real,C: nat > complex] :
% 5.52/5.87 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ K5 )
% 5.52/5.87 => ( ! [X4: complex] :
% 5.52/5.87 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ K5 )
% 5.52/5.87 => ( summable_complex
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_complex @ ( C @ N3 ) @ ( power_power_complex @ X4 @ N3 ) ) ) )
% 5.52/5.87 => ( summable_complex
% 5.52/5.87 @ ^ [N3: nat] : ( times_times_complex @ ( diffs_complex @ C @ N3 ) @ ( power_power_complex @ X2 @ N3 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % termdiff_converges
% 5.52/5.87 thf(fact_8176_arsinh__real__aux,axiom,
% 5.52/5.87 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % arsinh_real_aux
% 5.52/5.87 thf(fact_8177_real__sqrt__power__even,axiom,
% 5.52/5.87 ! [N: nat,X2: real] :
% 5.52/5.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( power_power_real @ ( sqrt @ X2 ) @ N )
% 5.52/5.87 = ( power_power_real @ X2 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_power_even
% 5.52/5.87 thf(fact_8178_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.52/5.87 ! [X2: real,Y2: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_sum_squares_mult_ge_zero
% 5.52/5.87 thf(fact_8179_arith__geo__mean__sqrt,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.87 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X2 @ Y2 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % arith_geo_mean_sqrt
% 5.52/5.87 thf(fact_8180_powr__half__sqrt,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 = ( sqrt @ X2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % powr_half_sqrt
% 5.52/5.87 thf(fact_8181_minus__sin__cos__eq,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( uminus_uminus_real @ ( sin_real @ X2 ) )
% 5.52/5.87 = ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % minus_sin_cos_eq
% 5.52/5.87 thf(fact_8182_minus__sin__cos__eq,axiom,
% 5.52/5.87 ! [X2: complex] :
% 5.52/5.87 ( ( uminus1482373934393186551omplex @ ( sin_complex @ X2 ) )
% 5.52/5.87 = ( cos_complex @ ( plus_plus_complex @ X2 @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % minus_sin_cos_eq
% 5.52/5.87 thf(fact_8183_cos__x__y__le__one,axiom,
% 5.52/5.87 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.52/5.87
% 5.52/5.87 % cos_x_y_le_one
% 5.52/5.87 thf(fact_8184_real__sqrt__sum__squares__less,axiom,
% 5.52/5.87 ! [X2: real,U: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.52/5.87 => ( ( ord_less_real @ ( abs_abs_real @ Y2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.52/5.87 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % real_sqrt_sum_squares_less
% 5.52/5.87 thf(fact_8185_arcosh__real__def,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.52/5.87 => ( ( arcosh_real @ X2 )
% 5.52/5.87 = ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % arcosh_real_def
% 5.52/5.87 thf(fact_8186_cos__arctan,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( cos_real @ ( arctan @ X2 ) )
% 5.52/5.87 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % cos_arctan
% 5.52/5.87 thf(fact_8187_sin__arctan,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( sin_real @ ( arctan @ X2 ) )
% 5.52/5.87 = ( divide_divide_real @ X2 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sin_arctan
% 5.52/5.87 thf(fact_8188_sqrt__sum__squares__half__less,axiom,
% 5.52/5.87 ! [X2: real,U: real,Y2: real] :
% 5.52/5.87 ( ( ord_less_real @ X2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.87 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sqrt_sum_squares_half_less
% 5.52/5.87 thf(fact_8189_sin__cos__sqrt,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X2 ) )
% 5.52/5.87 => ( ( sin_real @ X2 )
% 5.52/5.87 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % sin_cos_sqrt
% 5.52/5.87 thf(fact_8190_arctan__half,axiom,
% 5.52/5.87 ( arctan
% 5.52/5.87 = ( ^ [X: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % arctan_half
% 5.52/5.87 thf(fact_8191_fact__double,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.87 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % fact_double
% 5.52/5.87 thf(fact_8192_fact__double,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.87 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % fact_double
% 5.52/5.87 thf(fact_8193_fact__double,axiom,
% 5.52/5.87 ! [N: nat] :
% 5.52/5.87 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.87 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % fact_double
% 5.52/5.87 thf(fact_8194_arsinh__def,axiom,
% 5.52/5.87 ( arsinh_real
% 5.52/5.87 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % arsinh_def
% 5.52/5.87 thf(fact_8195_pochhammer__times__pochhammer__half,axiom,
% 5.52/5.87 ! [Z: complex,N: nat] :
% 5.52/5.87 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.52/5.87 = ( groups6464643781859351333omplex
% 5.52/5.87 @ ^ [K2: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.52/5.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_times_pochhammer_half
% 5.52/5.87 thf(fact_8196_pochhammer__times__pochhammer__half,axiom,
% 5.52/5.87 ! [Z: real,N: nat] :
% 5.52/5.87 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.52/5.87 = ( groups129246275422532515t_real
% 5.52/5.87 @ ^ [K2: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_times_pochhammer_half
% 5.52/5.87 thf(fact_8197_pochhammer__times__pochhammer__half,axiom,
% 5.52/5.87 ! [Z: rat,N: nat] :
% 5.52/5.87 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.52/5.87 = ( groups73079841787564623at_rat
% 5.52/5.87 @ ^ [K2: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.52/5.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_times_pochhammer_half
% 5.52/5.87 thf(fact_8198_pochhammer__code,axiom,
% 5.52/5.87 ( comm_s2602460028002588243omplex
% 5.52/5.87 = ( ^ [A4: complex,N3: nat] :
% 5.52/5.87 ( if_complex @ ( N3 = zero_zero_nat ) @ one_one_complex
% 5.52/5.87 @ ( set_fo1517530859248394432omplex
% 5.52/5.87 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.52/5.87 @ zero_zero_nat
% 5.52/5.87 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.52/5.87 @ one_one_complex ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_code
% 5.52/5.87 thf(fact_8199_pochhammer__code,axiom,
% 5.52/5.87 ( comm_s4660882817536571857er_int
% 5.52/5.87 = ( ^ [A4: int,N3: nat] :
% 5.52/5.87 ( if_int @ ( N3 = zero_zero_nat ) @ one_one_int
% 5.52/5.87 @ ( set_fo2581907887559384638at_int
% 5.52/5.87 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.52/5.87 @ zero_zero_nat
% 5.52/5.87 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.52/5.87 @ one_one_int ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_code
% 5.52/5.87 thf(fact_8200_pochhammer__code,axiom,
% 5.52/5.87 ( comm_s7457072308508201937r_real
% 5.52/5.87 = ( ^ [A4: real,N3: nat] :
% 5.52/5.87 ( if_real @ ( N3 = zero_zero_nat ) @ one_one_real
% 5.52/5.87 @ ( set_fo3111899725591712190t_real
% 5.52/5.87 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.52/5.87 @ zero_zero_nat
% 5.52/5.87 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.52/5.87 @ one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_code
% 5.52/5.87 thf(fact_8201_pochhammer__code,axiom,
% 5.52/5.87 ( comm_s4028243227959126397er_rat
% 5.52/5.87 = ( ^ [A4: rat,N3: nat] :
% 5.52/5.87 ( if_rat @ ( N3 = zero_zero_nat ) @ one_one_rat
% 5.52/5.87 @ ( set_fo1949268297981939178at_rat
% 5.52/5.87 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.52/5.87 @ zero_zero_nat
% 5.52/5.87 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.52/5.87 @ one_one_rat ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_code
% 5.52/5.87 thf(fact_8202_pochhammer__code,axiom,
% 5.52/5.87 ( comm_s3181272606743183617d_enat
% 5.52/5.87 = ( ^ [A4: extended_enat,N3: nat] :
% 5.52/5.87 ( if_Extended_enat @ ( N3 = zero_zero_nat ) @ one_on7984719198319812577d_enat
% 5.52/5.87 @ ( set_fo2538466533108834004d_enat
% 5.52/5.87 @ ^ [O: nat] : ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A4 @ ( semiri4216267220026989637d_enat @ O ) ) )
% 5.52/5.87 @ zero_zero_nat
% 5.52/5.87 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.52/5.87 @ one_on7984719198319812577d_enat ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_code
% 5.52/5.87 thf(fact_8203_pochhammer__code,axiom,
% 5.52/5.87 ( comm_s4663373288045622133er_nat
% 5.52/5.87 = ( ^ [A4: nat,N3: nat] :
% 5.52/5.87 ( if_nat @ ( N3 = zero_zero_nat ) @ one_one_nat
% 5.52/5.87 @ ( set_fo2584398358068434914at_nat
% 5.52/5.87 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.52/5.87 @ zero_zero_nat
% 5.52/5.87 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.52/5.87 @ one_one_nat ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % pochhammer_code
% 5.52/5.87 thf(fact_8204_arsinh__real__def,axiom,
% 5.52/5.87 ( arsinh_real
% 5.52/5.87 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % arsinh_real_def
% 5.52/5.87 thf(fact_8205_cos__arcsin,axiom,
% 5.52/5.87 ! [X2: real] :
% 5.52/5.87 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.52/5.87 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.52/5.87 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % cos_arcsin
% 5.52/5.87 thf(fact_8206_prod_Oneutral__const,axiom,
% 5.52/5.87 ! [A2: set_nat] :
% 5.52/5.87 ( ( groups708209901874060359at_nat
% 5.52/5.87 @ ^ [Uu3: nat] : one_one_nat
% 5.52/5.87 @ A2 )
% 5.52/5.87 = one_one_nat ) ).
% 5.52/5.87
% 5.52/5.87 % prod.neutral_const
% 5.52/5.87 thf(fact_8207_prod_Oneutral__const,axiom,
% 5.52/5.87 ! [A2: set_nat] :
% 5.52/5.87 ( ( groups705719431365010083at_int
% 5.52/5.87 @ ^ [Uu3: nat] : one_one_int
% 5.52/5.87 @ A2 )
% 5.52/5.87 = one_one_int ) ).
% 5.52/5.87
% 5.52/5.87 % prod.neutral_const
% 5.52/5.87 thf(fact_8208_prod_Oneutral__const,axiom,
% 5.52/5.87 ! [A2: set_int] :
% 5.52/5.87 ( ( groups1705073143266064639nt_int
% 5.52/5.87 @ ^ [Uu3: int] : one_one_int
% 5.52/5.87 @ A2 )
% 5.52/5.87 = one_one_int ) ).
% 5.52/5.87
% 5.52/5.87 % prod.neutral_const
% 5.52/5.87 thf(fact_8209_prod_Oempty,axiom,
% 5.52/5.87 ! [G: nat > complex] :
% 5.52/5.87 ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 5.52/5.87 = one_one_complex ) ).
% 5.52/5.87
% 5.52/5.87 % prod.empty
% 5.52/5.87 thf(fact_8210_prod_Oempty,axiom,
% 5.52/5.87 ! [G: nat > real] :
% 5.52/5.87 ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 5.52/5.87 = one_one_real ) ).
% 5.52/5.87
% 5.52/5.87 % prod.empty
% 5.52/5.87 thf(fact_8211_prod_Oempty,axiom,
% 5.52/5.87 ! [G: nat > rat] :
% 5.52/5.87 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 5.52/5.87 = one_one_rat ) ).
% 5.52/5.87
% 5.52/5.87 % prod.empty
% 5.52/5.87 thf(fact_8212_prod_Oempty,axiom,
% 5.52/5.87 ! [G: int > complex] :
% 5.52/5.87 ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 5.52/5.87 = one_one_complex ) ).
% 5.52/5.87
% 5.52/5.87 % prod.empty
% 5.52/5.87 thf(fact_8213_prod_Oempty,axiom,
% 5.52/5.87 ! [G: int > real] :
% 5.52/5.87 ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 5.52/5.87 = one_one_real ) ).
% 5.52/5.87
% 5.52/5.87 % prod.empty
% 5.52/5.87 thf(fact_8214_prod_Oempty,axiom,
% 5.52/5.87 ! [G: int > rat] :
% 5.52/5.87 ( ( groups1072433553688619179nt_rat @ G @ bot_bot_set_int )
% 5.52/5.87 = one_one_rat ) ).
% 5.52/5.87
% 5.52/5.87 % prod.empty
% 5.52/5.87 thf(fact_8215_prod_Oempty,axiom,
% 5.52/5.87 ! [G: int > nat] :
% 5.52/5.87 ( ( groups1707563613775114915nt_nat @ G @ bot_bot_set_int )
% 5.52/5.87 = one_one_nat ) ).
% 5.52/5.87
% 5.52/5.87 % prod.empty
% 5.52/5.87 thf(fact_8216_prod_Oempty,axiom,
% 5.52/5.87 ! [G: extended_enat > complex] :
% 5.52/5.87 ( ( groups4622424608036095791omplex @ G @ bot_bo7653980558646680370d_enat )
% 5.52/5.87 = one_one_complex ) ).
% 5.52/5.87
% 5.52/5.87 % prod.empty
% 5.52/5.87 thf(fact_8217_prod_Oempty,axiom,
% 5.52/5.87 ! [G: extended_enat > real] :
% 5.52/5.87 ( ( groups97031904164794029t_real @ G @ bot_bo7653980558646680370d_enat )
% 5.52/5.87 = one_one_real ) ).
% 5.52/5.87
% 5.52/5.87 % prod.empty
% 5.52/5.87 thf(fact_8218_prod_Oempty,axiom,
% 5.52/5.87 ! [G: extended_enat > rat] :
% 5.52/5.87 ( ( groups2245840878043517529at_rat @ G @ bot_bo7653980558646680370d_enat )
% 5.52/5.87 = one_one_rat ) ).
% 5.52/5.87
% 5.52/5.87 % prod.empty
% 5.52/5.87 thf(fact_8219_prod_Oinfinite,axiom,
% 5.52/5.87 ! [A2: set_nat,G: nat > complex] :
% 5.52/5.87 ( ~ ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.52/5.87 = one_one_complex ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.infinite
% 5.52/5.87 thf(fact_8220_prod_Oinfinite,axiom,
% 5.52/5.87 ! [A2: set_int,G: int > complex] :
% 5.52/5.87 ( ~ ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.52/5.87 = one_one_complex ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.infinite
% 5.52/5.87 thf(fact_8221_prod_Oinfinite,axiom,
% 5.52/5.87 ! [A2: set_complex,G: complex > complex] :
% 5.52/5.87 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.52/5.87 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.52/5.87 = one_one_complex ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.infinite
% 5.52/5.87 thf(fact_8222_prod_Oinfinite,axiom,
% 5.52/5.87 ! [A2: set_Extended_enat,G: extended_enat > complex] :
% 5.52/5.87 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.87 => ( ( groups4622424608036095791omplex @ G @ A2 )
% 5.52/5.87 = one_one_complex ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.infinite
% 5.52/5.87 thf(fact_8223_prod_Oinfinite,axiom,
% 5.52/5.87 ! [A2: set_nat,G: nat > real] :
% 5.52/5.87 ( ~ ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ( groups129246275422532515t_real @ G @ A2 )
% 5.52/5.87 = one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.infinite
% 5.52/5.87 thf(fact_8224_prod_Oinfinite,axiom,
% 5.52/5.87 ! [A2: set_int,G: int > real] :
% 5.52/5.87 ( ~ ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.52/5.87 = one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.infinite
% 5.52/5.87 thf(fact_8225_prod_Oinfinite,axiom,
% 5.52/5.87 ! [A2: set_complex,G: complex > real] :
% 5.52/5.87 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.52/5.87 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.52/5.87 = one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.infinite
% 5.52/5.87 thf(fact_8226_prod_Oinfinite,axiom,
% 5.52/5.87 ! [A2: set_Extended_enat,G: extended_enat > real] :
% 5.52/5.87 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.87 => ( ( groups97031904164794029t_real @ G @ A2 )
% 5.52/5.87 = one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.infinite
% 5.52/5.87 thf(fact_8227_prod_Oinfinite,axiom,
% 5.52/5.87 ! [A2: set_nat,G: nat > rat] :
% 5.52/5.87 ( ~ ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ( groups73079841787564623at_rat @ G @ A2 )
% 5.52/5.87 = one_one_rat ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.infinite
% 5.52/5.87 thf(fact_8228_prod_Oinfinite,axiom,
% 5.52/5.87 ! [A2: set_int,G: int > rat] :
% 5.52/5.87 ( ~ ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 5.52/5.87 = one_one_rat ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.infinite
% 5.52/5.87 thf(fact_8229_prod_Odelta_H,axiom,
% 5.52/5.87 ! [S3: set_real,A: real,B: real > complex] :
% 5.52/5.87 ( ( finite_finite_real @ S3 )
% 5.52/5.87 => ( ( ( member_real @ A @ S3 )
% 5.52/5.87 => ( ( groups713298508707869441omplex
% 5.52/5.87 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_real @ A @ S3 )
% 5.52/5.87 => ( ( groups713298508707869441omplex
% 5.52/5.87 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_complex ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta'
% 5.52/5.87 thf(fact_8230_prod_Odelta_H,axiom,
% 5.52/5.87 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.52/5.87 ( ( finite_finite_nat @ S3 )
% 5.52/5.87 => ( ( ( member_nat @ A @ S3 )
% 5.52/5.87 => ( ( groups6464643781859351333omplex
% 5.52/5.87 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_nat @ A @ S3 )
% 5.52/5.87 => ( ( groups6464643781859351333omplex
% 5.52/5.87 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_complex ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta'
% 5.52/5.87 thf(fact_8231_prod_Odelta_H,axiom,
% 5.52/5.87 ! [S3: set_int,A: int,B: int > complex] :
% 5.52/5.87 ( ( finite_finite_int @ S3 )
% 5.52/5.87 => ( ( ( member_int @ A @ S3 )
% 5.52/5.87 => ( ( groups7440179247065528705omplex
% 5.52/5.87 @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_int @ A @ S3 )
% 5.52/5.87 => ( ( groups7440179247065528705omplex
% 5.52/5.87 @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_complex ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta'
% 5.52/5.87 thf(fact_8232_prod_Odelta_H,axiom,
% 5.52/5.87 ! [S3: set_complex,A: complex,B: complex > complex] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.87 => ( ( ( member_complex @ A @ S3 )
% 5.52/5.87 => ( ( groups3708469109370488835omplex
% 5.52/5.87 @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_complex @ A @ S3 )
% 5.52/5.87 => ( ( groups3708469109370488835omplex
% 5.52/5.87 @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_complex ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta'
% 5.52/5.87 thf(fact_8233_prod_Odelta_H,axiom,
% 5.52/5.87 ! [S3: set_Extended_enat,A: extended_enat,B: extended_enat > complex] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.87 => ( ( ( member_Extended_enat @ A @ S3 )
% 5.52/5.87 => ( ( groups4622424608036095791omplex
% 5.52/5.87 @ ^ [K2: extended_enat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_Extended_enat @ A @ S3 )
% 5.52/5.87 => ( ( groups4622424608036095791omplex
% 5.52/5.87 @ ^ [K2: extended_enat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_complex ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta'
% 5.52/5.87 thf(fact_8234_prod_Odelta_H,axiom,
% 5.52/5.87 ! [S3: set_real,A: real,B: real > real] :
% 5.52/5.87 ( ( finite_finite_real @ S3 )
% 5.52/5.87 => ( ( ( member_real @ A @ S3 )
% 5.52/5.87 => ( ( groups1681761925125756287l_real
% 5.52/5.87 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_real @ A @ S3 )
% 5.52/5.87 => ( ( groups1681761925125756287l_real
% 5.52/5.87 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta'
% 5.52/5.87 thf(fact_8235_prod_Odelta_H,axiom,
% 5.52/5.87 ! [S3: set_nat,A: nat,B: nat > real] :
% 5.52/5.87 ( ( finite_finite_nat @ S3 )
% 5.52/5.87 => ( ( ( member_nat @ A @ S3 )
% 5.52/5.87 => ( ( groups129246275422532515t_real
% 5.52/5.87 @ ^ [K2: nat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_nat @ A @ S3 )
% 5.52/5.87 => ( ( groups129246275422532515t_real
% 5.52/5.87 @ ^ [K2: nat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta'
% 5.52/5.87 thf(fact_8236_prod_Odelta_H,axiom,
% 5.52/5.87 ! [S3: set_int,A: int,B: int > real] :
% 5.52/5.87 ( ( finite_finite_int @ S3 )
% 5.52/5.87 => ( ( ( member_int @ A @ S3 )
% 5.52/5.87 => ( ( groups2316167850115554303t_real
% 5.52/5.87 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_int @ A @ S3 )
% 5.52/5.87 => ( ( groups2316167850115554303t_real
% 5.52/5.87 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta'
% 5.52/5.87 thf(fact_8237_prod_Odelta_H,axiom,
% 5.52/5.87 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.87 => ( ( ( member_complex @ A @ S3 )
% 5.52/5.87 => ( ( groups766887009212190081x_real
% 5.52/5.87 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_complex @ A @ S3 )
% 5.52/5.87 => ( ( groups766887009212190081x_real
% 5.52/5.87 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta'
% 5.52/5.87 thf(fact_8238_prod_Odelta_H,axiom,
% 5.52/5.87 ! [S3: set_Extended_enat,A: extended_enat,B: extended_enat > real] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.87 => ( ( ( member_Extended_enat @ A @ S3 )
% 5.52/5.87 => ( ( groups97031904164794029t_real
% 5.52/5.87 @ ^ [K2: extended_enat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_Extended_enat @ A @ S3 )
% 5.52/5.87 => ( ( groups97031904164794029t_real
% 5.52/5.87 @ ^ [K2: extended_enat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta'
% 5.52/5.87 thf(fact_8239_prod_Odelta,axiom,
% 5.52/5.87 ! [S3: set_real,A: real,B: real > complex] :
% 5.52/5.87 ( ( finite_finite_real @ S3 )
% 5.52/5.87 => ( ( ( member_real @ A @ S3 )
% 5.52/5.87 => ( ( groups713298508707869441omplex
% 5.52/5.87 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_real @ A @ S3 )
% 5.52/5.87 => ( ( groups713298508707869441omplex
% 5.52/5.87 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_complex ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta
% 5.52/5.87 thf(fact_8240_prod_Odelta,axiom,
% 5.52/5.87 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.52/5.87 ( ( finite_finite_nat @ S3 )
% 5.52/5.87 => ( ( ( member_nat @ A @ S3 )
% 5.52/5.87 => ( ( groups6464643781859351333omplex
% 5.52/5.87 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_nat @ A @ S3 )
% 5.52/5.87 => ( ( groups6464643781859351333omplex
% 5.52/5.87 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_complex ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta
% 5.52/5.87 thf(fact_8241_prod_Odelta,axiom,
% 5.52/5.87 ! [S3: set_int,A: int,B: int > complex] :
% 5.52/5.87 ( ( finite_finite_int @ S3 )
% 5.52/5.87 => ( ( ( member_int @ A @ S3 )
% 5.52/5.87 => ( ( groups7440179247065528705omplex
% 5.52/5.87 @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_int @ A @ S3 )
% 5.52/5.87 => ( ( groups7440179247065528705omplex
% 5.52/5.87 @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_complex ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta
% 5.52/5.87 thf(fact_8242_prod_Odelta,axiom,
% 5.52/5.87 ! [S3: set_complex,A: complex,B: complex > complex] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.87 => ( ( ( member_complex @ A @ S3 )
% 5.52/5.87 => ( ( groups3708469109370488835omplex
% 5.52/5.87 @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_complex @ A @ S3 )
% 5.52/5.87 => ( ( groups3708469109370488835omplex
% 5.52/5.87 @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_complex ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta
% 5.52/5.87 thf(fact_8243_prod_Odelta,axiom,
% 5.52/5.87 ! [S3: set_Extended_enat,A: extended_enat,B: extended_enat > complex] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.87 => ( ( ( member_Extended_enat @ A @ S3 )
% 5.52/5.87 => ( ( groups4622424608036095791omplex
% 5.52/5.87 @ ^ [K2: extended_enat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_Extended_enat @ A @ S3 )
% 5.52/5.87 => ( ( groups4622424608036095791omplex
% 5.52/5.87 @ ^ [K2: extended_enat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_complex ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta
% 5.52/5.87 thf(fact_8244_prod_Odelta,axiom,
% 5.52/5.87 ! [S3: set_real,A: real,B: real > real] :
% 5.52/5.87 ( ( finite_finite_real @ S3 )
% 5.52/5.87 => ( ( ( member_real @ A @ S3 )
% 5.52/5.87 => ( ( groups1681761925125756287l_real
% 5.52/5.87 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_real @ A @ S3 )
% 5.52/5.87 => ( ( groups1681761925125756287l_real
% 5.52/5.87 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta
% 5.52/5.87 thf(fact_8245_prod_Odelta,axiom,
% 5.52/5.87 ! [S3: set_nat,A: nat,B: nat > real] :
% 5.52/5.87 ( ( finite_finite_nat @ S3 )
% 5.52/5.87 => ( ( ( member_nat @ A @ S3 )
% 5.52/5.87 => ( ( groups129246275422532515t_real
% 5.52/5.87 @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_nat @ A @ S3 )
% 5.52/5.87 => ( ( groups129246275422532515t_real
% 5.52/5.87 @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta
% 5.52/5.87 thf(fact_8246_prod_Odelta,axiom,
% 5.52/5.87 ! [S3: set_int,A: int,B: int > real] :
% 5.52/5.87 ( ( finite_finite_int @ S3 )
% 5.52/5.87 => ( ( ( member_int @ A @ S3 )
% 5.52/5.87 => ( ( groups2316167850115554303t_real
% 5.52/5.87 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_int @ A @ S3 )
% 5.52/5.87 => ( ( groups2316167850115554303t_real
% 5.52/5.87 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta
% 5.52/5.87 thf(fact_8247_prod_Odelta,axiom,
% 5.52/5.87 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.87 => ( ( ( member_complex @ A @ S3 )
% 5.52/5.87 => ( ( groups766887009212190081x_real
% 5.52/5.87 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_complex @ A @ S3 )
% 5.52/5.87 => ( ( groups766887009212190081x_real
% 5.52/5.87 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta
% 5.52/5.87 thf(fact_8248_prod_Odelta,axiom,
% 5.52/5.87 ! [S3: set_Extended_enat,A: extended_enat,B: extended_enat > real] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.87 => ( ( ( member_Extended_enat @ A @ S3 )
% 5.52/5.87 => ( ( groups97031904164794029t_real
% 5.52/5.87 @ ^ [K2: extended_enat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = ( B @ A ) ) )
% 5.52/5.87 & ( ~ ( member_Extended_enat @ A @ S3 )
% 5.52/5.87 => ( ( groups97031904164794029t_real
% 5.52/5.87 @ ^ [K2: extended_enat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.52/5.87 @ S3 )
% 5.52/5.87 = one_one_real ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.delta
% 5.52/5.87 thf(fact_8249_prod_Oinsert,axiom,
% 5.52/5.87 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.52/5.87 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.87 => ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.87 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_real @ ( G @ X2 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert
% 5.52/5.87 thf(fact_8250_prod_Oinsert,axiom,
% 5.52/5.87 ! [A2: set_real,X2: real,G: real > real] :
% 5.52/5.87 ( ( finite_finite_real @ A2 )
% 5.52/5.87 => ( ~ ( member_real @ X2 @ A2 )
% 5.52/5.87 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_real @ ( G @ X2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert
% 5.52/5.87 thf(fact_8251_prod_Oinsert,axiom,
% 5.52/5.87 ! [A2: set_nat,X2: nat,G: nat > real] :
% 5.52/5.87 ( ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ~ ( member_nat @ X2 @ A2 )
% 5.52/5.87 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_real @ ( G @ X2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert
% 5.52/5.87 thf(fact_8252_prod_Oinsert,axiom,
% 5.52/5.87 ! [A2: set_int,X2: int,G: int > real] :
% 5.52/5.87 ( ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ~ ( member_int @ X2 @ A2 )
% 5.52/5.87 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_real @ ( G @ X2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert
% 5.52/5.87 thf(fact_8253_prod_Oinsert,axiom,
% 5.52/5.87 ! [A2: set_complex,X2: complex,G: complex > real] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.87 => ( ~ ( member_complex @ X2 @ A2 )
% 5.52/5.87 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_real @ ( G @ X2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert
% 5.52/5.87 thf(fact_8254_prod_Oinsert,axiom,
% 5.52/5.87 ! [A2: set_Extended_enat,X2: extended_enat,G: extended_enat > real] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.87 => ( ~ ( member_Extended_enat @ X2 @ A2 )
% 5.52/5.87 => ( ( groups97031904164794029t_real @ G @ ( insert_Extended_enat @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_real @ ( G @ X2 ) @ ( groups97031904164794029t_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert
% 5.52/5.87 thf(fact_8255_prod_Oinsert,axiom,
% 5.52/5.87 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.52/5.87 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.87 => ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.87 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_rat @ ( G @ X2 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert
% 5.52/5.87 thf(fact_8256_prod_Oinsert,axiom,
% 5.52/5.87 ! [A2: set_real,X2: real,G: real > rat] :
% 5.52/5.87 ( ( finite_finite_real @ A2 )
% 5.52/5.87 => ( ~ ( member_real @ X2 @ A2 )
% 5.52/5.87 => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_rat @ ( G @ X2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert
% 5.52/5.87 thf(fact_8257_prod_Oinsert,axiom,
% 5.52/5.87 ! [A2: set_nat,X2: nat,G: nat > rat] :
% 5.52/5.87 ( ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ~ ( member_nat @ X2 @ A2 )
% 5.52/5.87 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_rat @ ( G @ X2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert
% 5.52/5.87 thf(fact_8258_prod_Oinsert,axiom,
% 5.52/5.87 ! [A2: set_int,X2: int,G: int > rat] :
% 5.52/5.87 ( ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ~ ( member_int @ X2 @ A2 )
% 5.52/5.87 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_rat @ ( G @ X2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert
% 5.52/5.87 thf(fact_8259_prod_OlessThan__Suc,axiom,
% 5.52/5.87 ! [G: nat > real,N: nat] :
% 5.52/5.87 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.87 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.lessThan_Suc
% 5.52/5.87 thf(fact_8260_prod_OlessThan__Suc,axiom,
% 5.52/5.87 ! [G: nat > rat,N: nat] :
% 5.52/5.87 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.87 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.lessThan_Suc
% 5.52/5.87 thf(fact_8261_prod_OlessThan__Suc,axiom,
% 5.52/5.87 ! [G: nat > nat,N: nat] :
% 5.52/5.87 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.87 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.lessThan_Suc
% 5.52/5.87 thf(fact_8262_prod_OlessThan__Suc,axiom,
% 5.52/5.87 ! [G: nat > int,N: nat] :
% 5.52/5.87 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.87 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.lessThan_Suc
% 5.52/5.87 thf(fact_8263_prod_Ocl__ivl__Suc,axiom,
% 5.52/5.87 ! [N: nat,M: nat,G: nat > complex] :
% 5.52/5.87 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.87 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.87 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.87 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.cl_ivl_Suc
% 5.52/5.87 thf(fact_8264_prod_Ocl__ivl__Suc,axiom,
% 5.52/5.87 ! [N: nat,M: nat,G: nat > real] :
% 5.52/5.87 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.87 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.87 = one_one_real ) )
% 5.52/5.87 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.87 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.87 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.cl_ivl_Suc
% 5.52/5.87 thf(fact_8265_prod_Ocl__ivl__Suc,axiom,
% 5.52/5.87 ! [N: nat,M: nat,G: nat > rat] :
% 5.52/5.87 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.87 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.87 = one_one_rat ) )
% 5.52/5.87 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.87 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.87 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.cl_ivl_Suc
% 5.52/5.87 thf(fact_8266_prod_Ocl__ivl__Suc,axiom,
% 5.52/5.87 ! [N: nat,M: nat,G: nat > nat] :
% 5.52/5.87 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.87 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.87 = one_one_nat ) )
% 5.52/5.87 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.87 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.87 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.cl_ivl_Suc
% 5.52/5.87 thf(fact_8267_prod_Ocl__ivl__Suc,axiom,
% 5.52/5.87 ! [N: nat,M: nat,G: nat > int] :
% 5.52/5.87 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.87 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.87 = one_one_int ) )
% 5.52/5.87 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.52/5.87 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.87 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.cl_ivl_Suc
% 5.52/5.87 thf(fact_8268_arcsin__1,axiom,
% 5.52/5.87 ( ( arcsin @ one_one_real )
% 5.52/5.87 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % arcsin_1
% 5.52/5.87 thf(fact_8269_arcsin__minus__1,axiom,
% 5.52/5.87 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.52/5.87 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % arcsin_minus_1
% 5.52/5.87 thf(fact_8270_prod_Oneutral,axiom,
% 5.52/5.87 ! [A2: set_nat,G: nat > nat] :
% 5.52/5.87 ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ A2 )
% 5.52/5.87 => ( ( G @ X4 )
% 5.52/5.87 = one_one_nat ) )
% 5.52/5.87 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 5.52/5.87 = one_one_nat ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.neutral
% 5.52/5.87 thf(fact_8271_prod_Oneutral,axiom,
% 5.52/5.87 ! [A2: set_nat,G: nat > int] :
% 5.52/5.87 ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ A2 )
% 5.52/5.87 => ( ( G @ X4 )
% 5.52/5.87 = one_one_int ) )
% 5.52/5.87 => ( ( groups705719431365010083at_int @ G @ A2 )
% 5.52/5.87 = one_one_int ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.neutral
% 5.52/5.87 thf(fact_8272_prod_Oneutral,axiom,
% 5.52/5.87 ! [A2: set_int,G: int > int] :
% 5.52/5.87 ( ! [X4: int] :
% 5.52/5.87 ( ( member_int @ X4 @ A2 )
% 5.52/5.87 => ( ( G @ X4 )
% 5.52/5.87 = one_one_int ) )
% 5.52/5.87 => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 5.52/5.87 = one_one_int ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.neutral
% 5.52/5.87 thf(fact_8273_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.52/5.87 ! [G: real > complex,A2: set_real] :
% 5.52/5.87 ( ( ( groups713298508707869441omplex @ G @ A2 )
% 5.52/5.87 != one_one_complex )
% 5.52/5.87 => ~ ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ A2 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.not_neutral_contains_not_neutral
% 5.52/5.87 thf(fact_8274_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.52/5.87 ! [G: nat > complex,A2: set_nat] :
% 5.52/5.87 ( ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.52/5.87 != one_one_complex )
% 5.52/5.87 => ~ ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ A2 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.not_neutral_contains_not_neutral
% 5.52/5.87 thf(fact_8275_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.52/5.87 ! [G: int > complex,A2: set_int] :
% 5.52/5.87 ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.52/5.87 != one_one_complex )
% 5.52/5.87 => ~ ! [A3: int] :
% 5.52/5.87 ( ( member_int @ A3 @ A2 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.not_neutral_contains_not_neutral
% 5.52/5.87 thf(fact_8276_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.52/5.87 ! [G: real > real,A2: set_real] :
% 5.52/5.87 ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.52/5.87 != one_one_real )
% 5.52/5.87 => ~ ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ A2 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.not_neutral_contains_not_neutral
% 5.52/5.87 thf(fact_8277_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.52/5.87 ! [G: nat > real,A2: set_nat] :
% 5.52/5.87 ( ( ( groups129246275422532515t_real @ G @ A2 )
% 5.52/5.87 != one_one_real )
% 5.52/5.87 => ~ ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ A2 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.not_neutral_contains_not_neutral
% 5.52/5.87 thf(fact_8278_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.52/5.87 ! [G: int > real,A2: set_int] :
% 5.52/5.87 ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.52/5.87 != one_one_real )
% 5.52/5.87 => ~ ! [A3: int] :
% 5.52/5.87 ( ( member_int @ A3 @ A2 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_real ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.not_neutral_contains_not_neutral
% 5.52/5.87 thf(fact_8279_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.52/5.87 ! [G: real > rat,A2: set_real] :
% 5.52/5.87 ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.52/5.87 != one_one_rat )
% 5.52/5.87 => ~ ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ A2 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_rat ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.not_neutral_contains_not_neutral
% 5.52/5.87 thf(fact_8280_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.52/5.87 ! [G: nat > rat,A2: set_nat] :
% 5.52/5.87 ( ( ( groups73079841787564623at_rat @ G @ A2 )
% 5.52/5.87 != one_one_rat )
% 5.52/5.87 => ~ ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ A2 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_rat ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.not_neutral_contains_not_neutral
% 5.52/5.87 thf(fact_8281_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.52/5.87 ! [G: int > rat,A2: set_int] :
% 5.52/5.87 ( ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 5.52/5.87 != one_one_rat )
% 5.52/5.87 => ~ ! [A3: int] :
% 5.52/5.87 ( ( member_int @ A3 @ A2 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_rat ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.not_neutral_contains_not_neutral
% 5.52/5.87 thf(fact_8282_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.52/5.87 ! [G: real > nat,A2: set_real] :
% 5.52/5.87 ( ( ( groups4696554848551431203al_nat @ G @ A2 )
% 5.52/5.87 != one_one_nat )
% 5.52/5.87 => ~ ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ A2 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_nat ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.not_neutral_contains_not_neutral
% 5.52/5.87 thf(fact_8283_prod_Odistrib,axiom,
% 5.52/5.87 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.52/5.87 ( ( groups708209901874060359at_nat
% 5.52/5.87 @ ^ [X: nat] : ( times_times_nat @ ( G @ X ) @ ( H2 @ X ) )
% 5.52/5.87 @ A2 )
% 5.52/5.87 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.distrib
% 5.52/5.87 thf(fact_8284_prod_Odistrib,axiom,
% 5.52/5.87 ! [G: nat > int,H2: nat > int,A2: set_nat] :
% 5.52/5.87 ( ( groups705719431365010083at_int
% 5.52/5.87 @ ^ [X: nat] : ( times_times_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.52/5.87 @ A2 )
% 5.52/5.87 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A2 ) @ ( groups705719431365010083at_int @ H2 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.distrib
% 5.52/5.87 thf(fact_8285_prod_Odistrib,axiom,
% 5.52/5.87 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.52/5.87 ( ( groups1705073143266064639nt_int
% 5.52/5.87 @ ^ [X: int] : ( times_times_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.52/5.87 @ A2 )
% 5.52/5.87 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A2 ) @ ( groups1705073143266064639nt_int @ H2 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.distrib
% 5.52/5.87 thf(fact_8286_prod__power__distrib,axiom,
% 5.52/5.87 ! [F: nat > nat,A2: set_nat,N: nat] :
% 5.52/5.87 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N )
% 5.52/5.87 = ( groups708209901874060359at_nat
% 5.52/5.87 @ ^ [X: nat] : ( power_power_nat @ ( F @ X ) @ N )
% 5.52/5.87 @ A2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_power_distrib
% 5.52/5.87 thf(fact_8287_prod__power__distrib,axiom,
% 5.52/5.87 ! [F: nat > int,A2: set_nat,N: nat] :
% 5.52/5.87 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N )
% 5.52/5.87 = ( groups705719431365010083at_int
% 5.52/5.87 @ ^ [X: nat] : ( power_power_int @ ( F @ X ) @ N )
% 5.52/5.87 @ A2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_power_distrib
% 5.52/5.87 thf(fact_8288_prod__power__distrib,axiom,
% 5.52/5.87 ! [F: int > int,A2: set_int,N: nat] :
% 5.52/5.87 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N )
% 5.52/5.87 = ( groups1705073143266064639nt_int
% 5.52/5.87 @ ^ [X: int] : ( power_power_int @ ( F @ X ) @ N )
% 5.52/5.87 @ A2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_power_distrib
% 5.52/5.87 thf(fact_8289_mod__prod__eq,axiom,
% 5.52/5.87 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.52/5.87 ( ( modulo_modulo_nat
% 5.52/5.87 @ ( groups708209901874060359at_nat
% 5.52/5.87 @ ^ [I4: nat] : ( modulo_modulo_nat @ ( F @ I4 ) @ A )
% 5.52/5.87 @ A2 )
% 5.52/5.87 @ A )
% 5.52/5.87 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 5.52/5.87
% 5.52/5.87 % mod_prod_eq
% 5.52/5.87 thf(fact_8290_mod__prod__eq,axiom,
% 5.52/5.87 ! [F: nat > int,A: int,A2: set_nat] :
% 5.52/5.87 ( ( modulo_modulo_int
% 5.52/5.87 @ ( groups705719431365010083at_int
% 5.52/5.87 @ ^ [I4: nat] : ( modulo_modulo_int @ ( F @ I4 ) @ A )
% 5.52/5.87 @ A2 )
% 5.52/5.87 @ A )
% 5.52/5.87 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 5.52/5.87
% 5.52/5.87 % mod_prod_eq
% 5.52/5.87 thf(fact_8291_mod__prod__eq,axiom,
% 5.52/5.87 ! [F: int > int,A: int,A2: set_int] :
% 5.52/5.87 ( ( modulo_modulo_int
% 5.52/5.87 @ ( groups1705073143266064639nt_int
% 5.52/5.87 @ ^ [I4: int] : ( modulo_modulo_int @ ( F @ I4 ) @ A )
% 5.52/5.87 @ A2 )
% 5.52/5.87 @ A )
% 5.52/5.87 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 5.52/5.87
% 5.52/5.87 % mod_prod_eq
% 5.52/5.87 thf(fact_8292_prod__nonneg,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > nat] :
% 5.52/5.87 ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_nonneg
% 5.52/5.87 thf(fact_8293_prod__nonneg,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > int] :
% 5.52/5.87 ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_nonneg
% 5.52/5.87 thf(fact_8294_prod__nonneg,axiom,
% 5.52/5.87 ! [A2: set_int,F: int > int] :
% 5.52/5.87 ( ! [X4: int] :
% 5.52/5.87 ( ( member_int @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_nonneg
% 5.52/5.87 thf(fact_8295_prod__mono,axiom,
% 5.52/5.87 ! [A2: set_real,F: real > real,G: real > real] :
% 5.52/5.87 ( ! [I2: real] :
% 5.52/5.87 ( ( member_real @ I2 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.52/5.87 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.87 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_mono
% 5.52/5.87 thf(fact_8296_prod__mono,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.52/5.87 ( ! [I2: nat] :
% 5.52/5.87 ( ( member_nat @ I2 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.52/5.87 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.87 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_mono
% 5.52/5.87 thf(fact_8297_prod__mono,axiom,
% 5.52/5.87 ! [A2: set_int,F: int > real,G: int > real] :
% 5.52/5.87 ( ! [I2: int] :
% 5.52/5.87 ( ( member_int @ I2 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.52/5.87 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.87 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_mono
% 5.52/5.87 thf(fact_8298_prod__mono,axiom,
% 5.52/5.87 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.52/5.87 ( ! [I2: real] :
% 5.52/5.87 ( ( member_real @ I2 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.52/5.87 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.87 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_mono
% 5.52/5.87 thf(fact_8299_prod__mono,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.52/5.87 ( ! [I2: nat] :
% 5.52/5.87 ( ( member_nat @ I2 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.52/5.87 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.87 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_mono
% 5.52/5.87 thf(fact_8300_prod__mono,axiom,
% 5.52/5.87 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.52/5.87 ( ! [I2: int] :
% 5.52/5.87 ( ( member_int @ I2 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.52/5.87 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.87 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_mono
% 5.52/5.87 thf(fact_8301_prod__mono,axiom,
% 5.52/5.87 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.52/5.87 ( ! [I2: real] :
% 5.52/5.87 ( ( member_real @ I2 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.52/5.87 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.87 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_mono
% 5.52/5.87 thf(fact_8302_prod__mono,axiom,
% 5.52/5.87 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.52/5.87 ( ! [I2: int] :
% 5.52/5.87 ( ( member_int @ I2 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.52/5.87 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.87 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_mono
% 5.52/5.87 thf(fact_8303_prod__mono,axiom,
% 5.52/5.87 ! [A2: set_real,F: real > int,G: real > int] :
% 5.52/5.87 ( ! [I2: real] :
% 5.52/5.87 ( ( member_real @ I2 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I2 ) )
% 5.52/5.87 & ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.87 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_mono
% 5.52/5.87 thf(fact_8304_prod__mono,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.52/5.87 ( ! [I2: nat] :
% 5.52/5.87 ( ( member_nat @ I2 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.52/5.87 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.87 => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_mono
% 5.52/5.87 thf(fact_8305_prod__pos,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > nat] :
% 5.52/5.87 ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_pos
% 5.52/5.87 thf(fact_8306_prod__pos,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > int] :
% 5.52/5.87 ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_pos
% 5.52/5.87 thf(fact_8307_prod__pos,axiom,
% 5.52/5.87 ! [A2: set_int,F: int > int] :
% 5.52/5.87 ( ! [X4: int] :
% 5.52/5.87 ( ( member_int @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_pos
% 5.52/5.87 thf(fact_8308_prod__ge__1,axiom,
% 5.52/5.87 ! [A2: set_real,F: real > real] :
% 5.52/5.87 ( ! [X4: real] :
% 5.52/5.87 ( ( member_real @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_ge_1
% 5.52/5.87 thf(fact_8309_prod__ge__1,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > real] :
% 5.52/5.87 ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_ge_1
% 5.52/5.87 thf(fact_8310_prod__ge__1,axiom,
% 5.52/5.87 ! [A2: set_int,F: int > real] :
% 5.52/5.87 ( ! [X4: int] :
% 5.52/5.87 ( ( member_int @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_ge_1
% 5.52/5.87 thf(fact_8311_prod__ge__1,axiom,
% 5.52/5.87 ! [A2: set_real,F: real > rat] :
% 5.52/5.87 ( ! [X4: real] :
% 5.52/5.87 ( ( member_real @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_ge_1
% 5.52/5.87 thf(fact_8312_prod__ge__1,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > rat] :
% 5.52/5.87 ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_ge_1
% 5.52/5.87 thf(fact_8313_prod__ge__1,axiom,
% 5.52/5.87 ! [A2: set_int,F: int > rat] :
% 5.52/5.87 ( ! [X4: int] :
% 5.52/5.87 ( ( member_int @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_ge_1
% 5.52/5.87 thf(fact_8314_prod__ge__1,axiom,
% 5.52/5.87 ! [A2: set_real,F: real > nat] :
% 5.52/5.87 ( ! [X4: real] :
% 5.52/5.87 ( ( member_real @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_ge_1
% 5.52/5.87 thf(fact_8315_prod__ge__1,axiom,
% 5.52/5.87 ! [A2: set_int,F: int > nat] :
% 5.52/5.87 ( ! [X4: int] :
% 5.52/5.87 ( ( member_int @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_ge_1
% 5.52/5.87 thf(fact_8316_prod__ge__1,axiom,
% 5.52/5.87 ! [A2: set_real,F: real > int] :
% 5.52/5.87 ( ! [X4: real] :
% 5.52/5.87 ( ( member_real @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_int @ one_one_int @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_ge_1
% 5.52/5.87 thf(fact_8317_prod__ge__1,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > nat] :
% 5.52/5.87 ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ A2 )
% 5.52/5.87 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 5.52/5.87 => ( ord_less_eq_nat @ one_one_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_ge_1
% 5.52/5.87 thf(fact_8318_prod__atLeastAtMost__code,axiom,
% 5.52/5.87 ! [F: nat > complex,A: nat,B: nat] :
% 5.52/5.87 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.52/5.87 = ( set_fo1517530859248394432omplex
% 5.52/5.87 @ ^ [A4: nat] : ( times_times_complex @ ( F @ A4 ) )
% 5.52/5.87 @ A
% 5.52/5.87 @ B
% 5.52/5.87 @ one_one_complex ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_atLeastAtMost_code
% 5.52/5.87 thf(fact_8319_prod__atLeastAtMost__code,axiom,
% 5.52/5.87 ! [F: nat > real,A: nat,B: nat] :
% 5.52/5.87 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.52/5.87 = ( set_fo3111899725591712190t_real
% 5.52/5.87 @ ^ [A4: nat] : ( times_times_real @ ( F @ A4 ) )
% 5.52/5.87 @ A
% 5.52/5.87 @ B
% 5.52/5.87 @ one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_atLeastAtMost_code
% 5.52/5.87 thf(fact_8320_prod__atLeastAtMost__code,axiom,
% 5.52/5.87 ! [F: nat > rat,A: nat,B: nat] :
% 5.52/5.87 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.52/5.87 = ( set_fo1949268297981939178at_rat
% 5.52/5.87 @ ^ [A4: nat] : ( times_times_rat @ ( F @ A4 ) )
% 5.52/5.87 @ A
% 5.52/5.87 @ B
% 5.52/5.87 @ one_one_rat ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_atLeastAtMost_code
% 5.52/5.87 thf(fact_8321_prod__atLeastAtMost__code,axiom,
% 5.52/5.87 ! [F: nat > nat,A: nat,B: nat] :
% 5.52/5.87 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.52/5.87 = ( set_fo2584398358068434914at_nat
% 5.52/5.87 @ ^ [A4: nat] : ( times_times_nat @ ( F @ A4 ) )
% 5.52/5.87 @ A
% 5.52/5.87 @ B
% 5.52/5.87 @ one_one_nat ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_atLeastAtMost_code
% 5.52/5.87 thf(fact_8322_prod__atLeastAtMost__code,axiom,
% 5.52/5.87 ! [F: nat > int,A: nat,B: nat] :
% 5.52/5.87 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.52/5.87 = ( set_fo2581907887559384638at_int
% 5.52/5.87 @ ^ [A4: nat] : ( times_times_int @ ( F @ A4 ) )
% 5.52/5.87 @ A
% 5.52/5.87 @ B
% 5.52/5.87 @ one_one_int ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_atLeastAtMost_code
% 5.52/5.87 thf(fact_8323_prod_Ointer__filter,axiom,
% 5.52/5.87 ! [A2: set_real,G: real > complex,P: real > $o] :
% 5.52/5.87 ( ( finite_finite_real @ A2 )
% 5.52/5.87 => ( ( groups713298508707869441omplex @ G
% 5.52/5.87 @ ( collect_real
% 5.52/5.87 @ ^ [X: real] :
% 5.52/5.87 ( ( member_real @ X @ A2 )
% 5.52/5.87 & ( P @ X ) ) ) )
% 5.52/5.87 = ( groups713298508707869441omplex
% 5.52/5.87 @ ^ [X: real] : ( if_complex @ ( P @ X ) @ ( G @ X ) @ one_one_complex )
% 5.52/5.87 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.inter_filter
% 5.52/5.87 thf(fact_8324_prod_Ointer__filter,axiom,
% 5.52/5.87 ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 5.52/5.87 ( ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ( groups6464643781859351333omplex @ G
% 5.52/5.87 @ ( collect_nat
% 5.52/5.87 @ ^ [X: nat] :
% 5.52/5.87 ( ( member_nat @ X @ A2 )
% 5.52/5.87 & ( P @ X ) ) ) )
% 5.52/5.87 = ( groups6464643781859351333omplex
% 5.52/5.87 @ ^ [X: nat] : ( if_complex @ ( P @ X ) @ ( G @ X ) @ one_one_complex )
% 5.52/5.87 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.inter_filter
% 5.52/5.87 thf(fact_8325_prod_Ointer__filter,axiom,
% 5.52/5.87 ! [A2: set_int,G: int > complex,P: int > $o] :
% 5.52/5.87 ( ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( groups7440179247065528705omplex @ G
% 5.52/5.87 @ ( collect_int
% 5.52/5.87 @ ^ [X: int] :
% 5.52/5.87 ( ( member_int @ X @ A2 )
% 5.52/5.87 & ( P @ X ) ) ) )
% 5.52/5.87 = ( groups7440179247065528705omplex
% 5.52/5.87 @ ^ [X: int] : ( if_complex @ ( P @ X ) @ ( G @ X ) @ one_one_complex )
% 5.52/5.87 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.inter_filter
% 5.52/5.87 thf(fact_8326_prod_Ointer__filter,axiom,
% 5.52/5.87 ! [A2: set_complex,G: complex > complex,P: complex > $o] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.87 => ( ( groups3708469109370488835omplex @ G
% 5.52/5.87 @ ( collect_complex
% 5.52/5.87 @ ^ [X: complex] :
% 5.52/5.87 ( ( member_complex @ X @ A2 )
% 5.52/5.87 & ( P @ X ) ) ) )
% 5.52/5.87 = ( groups3708469109370488835omplex
% 5.52/5.87 @ ^ [X: complex] : ( if_complex @ ( P @ X ) @ ( G @ X ) @ one_one_complex )
% 5.52/5.87 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.inter_filter
% 5.52/5.87 thf(fact_8327_prod_Ointer__filter,axiom,
% 5.52/5.87 ! [A2: set_Extended_enat,G: extended_enat > complex,P: extended_enat > $o] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.87 => ( ( groups4622424608036095791omplex @ G
% 5.52/5.87 @ ( collec4429806609662206161d_enat
% 5.52/5.87 @ ^ [X: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ X @ A2 )
% 5.52/5.87 & ( P @ X ) ) ) )
% 5.52/5.87 = ( groups4622424608036095791omplex
% 5.52/5.87 @ ^ [X: extended_enat] : ( if_complex @ ( P @ X ) @ ( G @ X ) @ one_one_complex )
% 5.52/5.87 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.inter_filter
% 5.52/5.87 thf(fact_8328_prod_Ointer__filter,axiom,
% 5.52/5.87 ! [A2: set_real,G: real > real,P: real > $o] :
% 5.52/5.87 ( ( finite_finite_real @ A2 )
% 5.52/5.87 => ( ( groups1681761925125756287l_real @ G
% 5.52/5.87 @ ( collect_real
% 5.52/5.87 @ ^ [X: real] :
% 5.52/5.87 ( ( member_real @ X @ A2 )
% 5.52/5.87 & ( P @ X ) ) ) )
% 5.52/5.87 = ( groups1681761925125756287l_real
% 5.52/5.87 @ ^ [X: real] : ( if_real @ ( P @ X ) @ ( G @ X ) @ one_one_real )
% 5.52/5.87 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.inter_filter
% 5.52/5.87 thf(fact_8329_prod_Ointer__filter,axiom,
% 5.52/5.87 ! [A2: set_nat,G: nat > real,P: nat > $o] :
% 5.52/5.87 ( ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ( groups129246275422532515t_real @ G
% 5.52/5.87 @ ( collect_nat
% 5.52/5.87 @ ^ [X: nat] :
% 5.52/5.87 ( ( member_nat @ X @ A2 )
% 5.52/5.87 & ( P @ X ) ) ) )
% 5.52/5.87 = ( groups129246275422532515t_real
% 5.52/5.87 @ ^ [X: nat] : ( if_real @ ( P @ X ) @ ( G @ X ) @ one_one_real )
% 5.52/5.87 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.inter_filter
% 5.52/5.87 thf(fact_8330_prod_Ointer__filter,axiom,
% 5.52/5.87 ! [A2: set_int,G: int > real,P: int > $o] :
% 5.52/5.87 ( ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( groups2316167850115554303t_real @ G
% 5.52/5.87 @ ( collect_int
% 5.52/5.87 @ ^ [X: int] :
% 5.52/5.87 ( ( member_int @ X @ A2 )
% 5.52/5.87 & ( P @ X ) ) ) )
% 5.52/5.87 = ( groups2316167850115554303t_real
% 5.52/5.87 @ ^ [X: int] : ( if_real @ ( P @ X ) @ ( G @ X ) @ one_one_real )
% 5.52/5.87 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.inter_filter
% 5.52/5.87 thf(fact_8331_prod_Ointer__filter,axiom,
% 5.52/5.87 ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.87 => ( ( groups766887009212190081x_real @ G
% 5.52/5.87 @ ( collect_complex
% 5.52/5.87 @ ^ [X: complex] :
% 5.52/5.87 ( ( member_complex @ X @ A2 )
% 5.52/5.87 & ( P @ X ) ) ) )
% 5.52/5.87 = ( groups766887009212190081x_real
% 5.52/5.87 @ ^ [X: complex] : ( if_real @ ( P @ X ) @ ( G @ X ) @ one_one_real )
% 5.52/5.87 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.inter_filter
% 5.52/5.87 thf(fact_8332_prod_Ointer__filter,axiom,
% 5.52/5.87 ! [A2: set_Extended_enat,G: extended_enat > real,P: extended_enat > $o] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.87 => ( ( groups97031904164794029t_real @ G
% 5.52/5.87 @ ( collec4429806609662206161d_enat
% 5.52/5.87 @ ^ [X: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ X @ A2 )
% 5.52/5.87 & ( P @ X ) ) ) )
% 5.52/5.87 = ( groups97031904164794029t_real
% 5.52/5.87 @ ^ [X: extended_enat] : ( if_real @ ( P @ X ) @ ( G @ X ) @ one_one_real )
% 5.52/5.87 @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.inter_filter
% 5.52/5.87 thf(fact_8333_power__sum,axiom,
% 5.52/5.87 ! [C: real,F: nat > nat,A2: set_nat] :
% 5.52/5.87 ( ( power_power_real @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.52/5.87 = ( groups129246275422532515t_real
% 5.52/5.87 @ ^ [A4: nat] : ( power_power_real @ C @ ( F @ A4 ) )
% 5.52/5.87 @ A2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % power_sum
% 5.52/5.87 thf(fact_8334_power__sum,axiom,
% 5.52/5.87 ! [C: complex,F: nat > nat,A2: set_nat] :
% 5.52/5.87 ( ( power_power_complex @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.52/5.87 = ( groups6464643781859351333omplex
% 5.52/5.87 @ ^ [A4: nat] : ( power_power_complex @ C @ ( F @ A4 ) )
% 5.52/5.87 @ A2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % power_sum
% 5.52/5.87 thf(fact_8335_power__sum,axiom,
% 5.52/5.87 ! [C: nat,F: nat > nat,A2: set_nat] :
% 5.52/5.87 ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.52/5.87 = ( groups708209901874060359at_nat
% 5.52/5.87 @ ^ [A4: nat] : ( power_power_nat @ C @ ( F @ A4 ) )
% 5.52/5.87 @ A2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % power_sum
% 5.52/5.87 thf(fact_8336_power__sum,axiom,
% 5.52/5.87 ! [C: int,F: nat > nat,A2: set_nat] :
% 5.52/5.87 ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.52/5.87 = ( groups705719431365010083at_int
% 5.52/5.87 @ ^ [A4: nat] : ( power_power_int @ C @ ( F @ A4 ) )
% 5.52/5.87 @ A2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % power_sum
% 5.52/5.87 thf(fact_8337_power__sum,axiom,
% 5.52/5.87 ! [C: int,F: int > nat,A2: set_int] :
% 5.52/5.87 ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 5.52/5.87 = ( groups1705073143266064639nt_int
% 5.52/5.87 @ ^ [A4: int] : ( power_power_int @ C @ ( F @ A4 ) )
% 5.52/5.87 @ A2 ) ) ).
% 5.52/5.87
% 5.52/5.87 % power_sum
% 5.52/5.87 thf(fact_8338_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.52/5.87 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.52/5.87 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.52/5.87 = ( groups708209901874060359at_nat
% 5.52/5.87 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.52/5.87 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.shift_bounds_cl_nat_ivl
% 5.52/5.87 thf(fact_8339_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.52/5.87 ! [G: nat > int,M: nat,K: nat,N: nat] :
% 5.52/5.87 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.52/5.87 = ( groups705719431365010083at_int
% 5.52/5.87 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.52/5.87 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.shift_bounds_cl_nat_ivl
% 5.52/5.87 thf(fact_8340_prod__le__1,axiom,
% 5.52/5.87 ! [A2: set_real,F: real > real] :
% 5.52/5.87 ( ! [X4: real] :
% 5.52/5.87 ( ( member_real @ X4 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 5.52/5.87 & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 5.52/5.87 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_le_1
% 5.52/5.87 thf(fact_8341_prod__le__1,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > real] :
% 5.52/5.87 ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 5.52/5.87 & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 5.52/5.87 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_le_1
% 5.52/5.87 thf(fact_8342_prod__le__1,axiom,
% 5.52/5.87 ! [A2: set_int,F: int > real] :
% 5.52/5.87 ( ! [X4: int] :
% 5.52/5.87 ( ( member_int @ X4 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 5.52/5.87 & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 5.52/5.87 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_le_1
% 5.52/5.87 thf(fact_8343_prod__le__1,axiom,
% 5.52/5.87 ! [A2: set_real,F: real > rat] :
% 5.52/5.87 ( ! [X4: real] :
% 5.52/5.87 ( ( member_real @ X4 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 5.52/5.87 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 5.52/5.87 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_le_1
% 5.52/5.87 thf(fact_8344_prod__le__1,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > rat] :
% 5.52/5.87 ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 5.52/5.87 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 5.52/5.87 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_le_1
% 5.52/5.87 thf(fact_8345_prod__le__1,axiom,
% 5.52/5.87 ! [A2: set_int,F: int > rat] :
% 5.52/5.87 ( ! [X4: int] :
% 5.52/5.87 ( ( member_int @ X4 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 5.52/5.87 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 5.52/5.87 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_le_1
% 5.52/5.87 thf(fact_8346_prod__le__1,axiom,
% 5.52/5.87 ! [A2: set_real,F: real > nat] :
% 5.52/5.87 ( ! [X4: real] :
% 5.52/5.87 ( ( member_real @ X4 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 5.52/5.87 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 5.52/5.87 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_le_1
% 5.52/5.87 thf(fact_8347_prod__le__1,axiom,
% 5.52/5.87 ! [A2: set_int,F: int > nat] :
% 5.52/5.87 ( ! [X4: int] :
% 5.52/5.87 ( ( member_int @ X4 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 5.52/5.87 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 5.52/5.87 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_le_1
% 5.52/5.87 thf(fact_8348_prod__le__1,axiom,
% 5.52/5.87 ! [A2: set_real,F: real > int] :
% 5.52/5.87 ( ! [X4: real] :
% 5.52/5.87 ( ( member_real @ X4 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) )
% 5.52/5.87 & ( ord_less_eq_int @ ( F @ X4 ) @ one_one_int ) ) )
% 5.52/5.87 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ one_one_int ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_le_1
% 5.52/5.87 thf(fact_8349_prod__le__1,axiom,
% 5.52/5.87 ! [A2: set_nat,F: nat > nat] :
% 5.52/5.87 ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ A2 )
% 5.52/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 5.52/5.87 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 5.52/5.87 => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod_le_1
% 5.52/5.87 thf(fact_8350_prod_Orelated,axiom,
% 5.52/5.87 ! [R2: complex > complex > $o,S3: set_nat,H2: nat > complex,G: nat > complex] :
% 5.52/5.87 ( ( R2 @ one_one_complex @ one_one_complex )
% 5.52/5.87 => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 5.52/5.87 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.87 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.87 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X22 @ Y23 ) ) )
% 5.52/5.87 => ( ( finite_finite_nat @ S3 )
% 5.52/5.87 => ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ S3 )
% 5.52/5.87 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.87 => ( R2 @ ( groups6464643781859351333omplex @ H2 @ S3 ) @ ( groups6464643781859351333omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.related
% 5.52/5.87 thf(fact_8351_prod_Orelated,axiom,
% 5.52/5.87 ! [R2: complex > complex > $o,S3: set_int,H2: int > complex,G: int > complex] :
% 5.52/5.87 ( ( R2 @ one_one_complex @ one_one_complex )
% 5.52/5.87 => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 5.52/5.87 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.87 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.87 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X22 @ Y23 ) ) )
% 5.52/5.87 => ( ( finite_finite_int @ S3 )
% 5.52/5.87 => ( ! [X4: int] :
% 5.52/5.87 ( ( member_int @ X4 @ S3 )
% 5.52/5.87 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.87 => ( R2 @ ( groups7440179247065528705omplex @ H2 @ S3 ) @ ( groups7440179247065528705omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.related
% 5.52/5.87 thf(fact_8352_prod_Orelated,axiom,
% 5.52/5.87 ! [R2: complex > complex > $o,S3: set_complex,H2: complex > complex,G: complex > complex] :
% 5.52/5.87 ( ( R2 @ one_one_complex @ one_one_complex )
% 5.52/5.87 => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 5.52/5.87 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.87 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.87 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X22 @ Y23 ) ) )
% 5.52/5.87 => ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.87 => ( ! [X4: complex] :
% 5.52/5.87 ( ( member_complex @ X4 @ S3 )
% 5.52/5.87 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.87 => ( R2 @ ( groups3708469109370488835omplex @ H2 @ S3 ) @ ( groups3708469109370488835omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.related
% 5.52/5.87 thf(fact_8353_prod_Orelated,axiom,
% 5.52/5.87 ! [R2: complex > complex > $o,S3: set_Extended_enat,H2: extended_enat > complex,G: extended_enat > complex] :
% 5.52/5.87 ( ( R2 @ one_one_complex @ one_one_complex )
% 5.52/5.87 => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 5.52/5.87 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.87 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.87 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X22 @ Y23 ) ) )
% 5.52/5.87 => ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.87 => ( ! [X4: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ X4 @ S3 )
% 5.52/5.87 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.87 => ( R2 @ ( groups4622424608036095791omplex @ H2 @ S3 ) @ ( groups4622424608036095791omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.related
% 5.52/5.87 thf(fact_8354_prod_Orelated,axiom,
% 5.52/5.87 ! [R2: real > real > $o,S3: set_nat,H2: nat > real,G: nat > real] :
% 5.52/5.87 ( ( R2 @ one_one_real @ one_one_real )
% 5.52/5.87 => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 5.52/5.87 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.87 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.87 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X22 @ Y23 ) ) )
% 5.52/5.87 => ( ( finite_finite_nat @ S3 )
% 5.52/5.87 => ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ S3 )
% 5.52/5.87 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.87 => ( R2 @ ( groups129246275422532515t_real @ H2 @ S3 ) @ ( groups129246275422532515t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.related
% 5.52/5.87 thf(fact_8355_prod_Orelated,axiom,
% 5.52/5.87 ! [R2: real > real > $o,S3: set_int,H2: int > real,G: int > real] :
% 5.52/5.87 ( ( R2 @ one_one_real @ one_one_real )
% 5.52/5.87 => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 5.52/5.87 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.87 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.87 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X22 @ Y23 ) ) )
% 5.52/5.87 => ( ( finite_finite_int @ S3 )
% 5.52/5.87 => ( ! [X4: int] :
% 5.52/5.87 ( ( member_int @ X4 @ S3 )
% 5.52/5.87 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.87 => ( R2 @ ( groups2316167850115554303t_real @ H2 @ S3 ) @ ( groups2316167850115554303t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.related
% 5.52/5.87 thf(fact_8356_prod_Orelated,axiom,
% 5.52/5.87 ! [R2: real > real > $o,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.52/5.87 ( ( R2 @ one_one_real @ one_one_real )
% 5.52/5.87 => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 5.52/5.87 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.87 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.87 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X22 @ Y23 ) ) )
% 5.52/5.87 => ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.87 => ( ! [X4: complex] :
% 5.52/5.87 ( ( member_complex @ X4 @ S3 )
% 5.52/5.87 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.87 => ( R2 @ ( groups766887009212190081x_real @ H2 @ S3 ) @ ( groups766887009212190081x_real @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.related
% 5.52/5.87 thf(fact_8357_prod_Orelated,axiom,
% 5.52/5.87 ! [R2: real > real > $o,S3: set_Extended_enat,H2: extended_enat > real,G: extended_enat > real] :
% 5.52/5.87 ( ( R2 @ one_one_real @ one_one_real )
% 5.52/5.87 => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 5.52/5.87 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.87 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.87 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X22 @ Y23 ) ) )
% 5.52/5.87 => ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.87 => ( ! [X4: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ X4 @ S3 )
% 5.52/5.87 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.87 => ( R2 @ ( groups97031904164794029t_real @ H2 @ S3 ) @ ( groups97031904164794029t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.related
% 5.52/5.87 thf(fact_8358_prod_Orelated,axiom,
% 5.52/5.87 ! [R2: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 5.52/5.87 ( ( R2 @ one_one_rat @ one_one_rat )
% 5.52/5.87 => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 5.52/5.87 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.87 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.87 => ( R2 @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X22 @ Y23 ) ) )
% 5.52/5.87 => ( ( finite_finite_nat @ S3 )
% 5.52/5.87 => ( ! [X4: nat] :
% 5.52/5.87 ( ( member_nat @ X4 @ S3 )
% 5.52/5.87 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.87 => ( R2 @ ( groups73079841787564623at_rat @ H2 @ S3 ) @ ( groups73079841787564623at_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.related
% 5.52/5.87 thf(fact_8359_prod_Orelated,axiom,
% 5.52/5.87 ! [R2: rat > rat > $o,S3: set_int,H2: int > rat,G: int > rat] :
% 5.52/5.87 ( ( R2 @ one_one_rat @ one_one_rat )
% 5.52/5.87 => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 5.52/5.87 ( ( ( R2 @ X15 @ X22 )
% 5.52/5.87 & ( R2 @ Y15 @ Y23 ) )
% 5.52/5.87 => ( R2 @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X22 @ Y23 ) ) )
% 5.52/5.87 => ( ( finite_finite_int @ S3 )
% 5.52/5.87 => ( ! [X4: int] :
% 5.52/5.87 ( ( member_int @ X4 @ S3 )
% 5.52/5.87 => ( R2 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.52/5.87 => ( R2 @ ( groups1072433553688619179nt_rat @ H2 @ S3 ) @ ( groups1072433553688619179nt_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.related
% 5.52/5.87 thf(fact_8360_prod_Oinsert__if,axiom,
% 5.52/5.87 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.52/5.87 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.87 => ( ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.87 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.87 = ( groups2703838992350267259T_real @ G @ A2 ) ) )
% 5.52/5.87 & ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.87 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_real @ ( G @ X2 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert_if
% 5.52/5.87 thf(fact_8361_prod_Oinsert__if,axiom,
% 5.52/5.87 ! [A2: set_real,X2: real,G: real > real] :
% 5.52/5.87 ( ( finite_finite_real @ A2 )
% 5.52/5.87 => ( ( ( member_real @ X2 @ A2 )
% 5.52/5.87 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X2 @ A2 ) )
% 5.52/5.87 = ( groups1681761925125756287l_real @ G @ A2 ) ) )
% 5.52/5.87 & ( ~ ( member_real @ X2 @ A2 )
% 5.52/5.87 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_real @ ( G @ X2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert_if
% 5.52/5.87 thf(fact_8362_prod_Oinsert__if,axiom,
% 5.52/5.87 ! [A2: set_nat,X2: nat,G: nat > real] :
% 5.52/5.87 ( ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ( ( member_nat @ X2 @ A2 )
% 5.52/5.87 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.52/5.87 = ( groups129246275422532515t_real @ G @ A2 ) ) )
% 5.52/5.87 & ( ~ ( member_nat @ X2 @ A2 )
% 5.52/5.87 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_real @ ( G @ X2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert_if
% 5.52/5.87 thf(fact_8363_prod_Oinsert__if,axiom,
% 5.52/5.87 ! [A2: set_int,X2: int,G: int > real] :
% 5.52/5.87 ( ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( ( member_int @ X2 @ A2 )
% 5.52/5.87 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.87 = ( groups2316167850115554303t_real @ G @ A2 ) ) )
% 5.52/5.87 & ( ~ ( member_int @ X2 @ A2 )
% 5.52/5.87 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_real @ ( G @ X2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert_if
% 5.52/5.87 thf(fact_8364_prod_Oinsert__if,axiom,
% 5.52/5.87 ! [A2: set_complex,X2: complex,G: complex > real] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.87 => ( ( ( member_complex @ X2 @ A2 )
% 5.52/5.87 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.87 = ( groups766887009212190081x_real @ G @ A2 ) ) )
% 5.52/5.87 & ( ~ ( member_complex @ X2 @ A2 )
% 5.52/5.87 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_real @ ( G @ X2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert_if
% 5.52/5.87 thf(fact_8365_prod_Oinsert__if,axiom,
% 5.52/5.87 ! [A2: set_Extended_enat,X2: extended_enat,G: extended_enat > real] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.87 => ( ( ( member_Extended_enat @ X2 @ A2 )
% 5.52/5.87 => ( ( groups97031904164794029t_real @ G @ ( insert_Extended_enat @ X2 @ A2 ) )
% 5.52/5.87 = ( groups97031904164794029t_real @ G @ A2 ) ) )
% 5.52/5.87 & ( ~ ( member_Extended_enat @ X2 @ A2 )
% 5.52/5.87 => ( ( groups97031904164794029t_real @ G @ ( insert_Extended_enat @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_real @ ( G @ X2 ) @ ( groups97031904164794029t_real @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert_if
% 5.52/5.87 thf(fact_8366_prod_Oinsert__if,axiom,
% 5.52/5.87 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.52/5.87 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.87 => ( ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.87 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.87 = ( groups5726676334696518183BT_rat @ G @ A2 ) ) )
% 5.52/5.87 & ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.87 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_rat @ ( G @ X2 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert_if
% 5.52/5.87 thf(fact_8367_prod_Oinsert__if,axiom,
% 5.52/5.87 ! [A2: set_real,X2: real,G: real > rat] :
% 5.52/5.87 ( ( finite_finite_real @ A2 )
% 5.52/5.87 => ( ( ( member_real @ X2 @ A2 )
% 5.52/5.87 => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X2 @ A2 ) )
% 5.52/5.87 = ( groups4061424788464935467al_rat @ G @ A2 ) ) )
% 5.52/5.87 & ( ~ ( member_real @ X2 @ A2 )
% 5.52/5.87 => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_rat @ ( G @ X2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert_if
% 5.52/5.87 thf(fact_8368_prod_Oinsert__if,axiom,
% 5.52/5.87 ! [A2: set_nat,X2: nat,G: nat > rat] :
% 5.52/5.87 ( ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ( ( member_nat @ X2 @ A2 )
% 5.52/5.87 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.52/5.87 = ( groups73079841787564623at_rat @ G @ A2 ) ) )
% 5.52/5.87 & ( ~ ( member_nat @ X2 @ A2 )
% 5.52/5.87 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_rat @ ( G @ X2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert_if
% 5.52/5.87 thf(fact_8369_prod_Oinsert__if,axiom,
% 5.52/5.87 ! [A2: set_int,X2: int,G: int > rat] :
% 5.52/5.87 ( ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( ( member_int @ X2 @ A2 )
% 5.52/5.87 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.87 = ( groups1072433553688619179nt_rat @ G @ A2 ) ) )
% 5.52/5.87 & ( ~ ( member_int @ X2 @ A2 )
% 5.52/5.87 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.87 = ( times_times_rat @ ( G @ X2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.insert_if
% 5.52/5.87 thf(fact_8370_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.52/5.87 ! [S5: set_real,T5: set_real,S3: set_real,I: real > real,J: real > real,T6: set_real,G: real > complex,H2: real > complex] :
% 5.52/5.87 ( ( finite_finite_real @ S5 )
% 5.52/5.87 => ( ( finite_finite_real @ T5 )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.52/5.87 => ( ( I @ ( J @ A3 ) )
% 5.52/5.87 = A3 ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.52/5.87 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T6 @ T5 ) ) )
% 5.52/5.87 => ( ! [B2: real] :
% 5.52/5.87 ( ( member_real @ B2 @ ( minus_minus_set_real @ T6 @ T5 ) )
% 5.52/5.87 => ( ( J @ ( I @ B2 ) )
% 5.52/5.87 = B2 ) )
% 5.52/5.87 => ( ! [B2: real] :
% 5.52/5.87 ( ( member_real @ B2 @ ( minus_minus_set_real @ T6 @ T5 ) )
% 5.52/5.87 => ( member_real @ ( I @ B2 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ S5 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: real] :
% 5.52/5.87 ( ( member_real @ B2 @ T5 )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ S3 )
% 5.52/5.87 => ( ( H2 @ ( J @ A3 ) )
% 5.52/5.87 = ( G @ A3 ) ) )
% 5.52/5.87 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.52/5.87 = ( groups713298508707869441omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.reindex_bij_witness_not_neutral
% 5.52/5.87 thf(fact_8371_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.52/5.87 ! [S5: set_real,T5: set_nat,S3: set_real,I: nat > real,J: real > nat,T6: set_nat,G: real > complex,H2: nat > complex] :
% 5.52/5.87 ( ( finite_finite_real @ S5 )
% 5.52/5.87 => ( ( finite_finite_nat @ T5 )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.52/5.87 => ( ( I @ ( J @ A3 ) )
% 5.52/5.87 = A3 ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.52/5.87 => ( member_nat @ ( J @ A3 ) @ ( minus_minus_set_nat @ T6 @ T5 ) ) )
% 5.52/5.87 => ( ! [B2: nat] :
% 5.52/5.87 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ T6 @ T5 ) )
% 5.52/5.87 => ( ( J @ ( I @ B2 ) )
% 5.52/5.87 = B2 ) )
% 5.52/5.87 => ( ! [B2: nat] :
% 5.52/5.87 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ T6 @ T5 ) )
% 5.52/5.87 => ( member_real @ ( I @ B2 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ S5 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: nat] :
% 5.52/5.87 ( ( member_nat @ B2 @ T5 )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ S3 )
% 5.52/5.87 => ( ( H2 @ ( J @ A3 ) )
% 5.52/5.87 = ( G @ A3 ) ) )
% 5.52/5.87 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.52/5.87 = ( groups6464643781859351333omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.reindex_bij_witness_not_neutral
% 5.52/5.87 thf(fact_8372_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.52/5.87 ! [S5: set_real,T5: set_int,S3: set_real,I: int > real,J: real > int,T6: set_int,G: real > complex,H2: int > complex] :
% 5.52/5.87 ( ( finite_finite_real @ S5 )
% 5.52/5.87 => ( ( finite_finite_int @ T5 )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.52/5.87 => ( ( I @ ( J @ A3 ) )
% 5.52/5.87 = A3 ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.52/5.87 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T6 @ T5 ) ) )
% 5.52/5.87 => ( ! [B2: int] :
% 5.52/5.87 ( ( member_int @ B2 @ ( minus_minus_set_int @ T6 @ T5 ) )
% 5.52/5.87 => ( ( J @ ( I @ B2 ) )
% 5.52/5.87 = B2 ) )
% 5.52/5.87 => ( ! [B2: int] :
% 5.52/5.87 ( ( member_int @ B2 @ ( minus_minus_set_int @ T6 @ T5 ) )
% 5.52/5.87 => ( member_real @ ( I @ B2 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ S5 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: int] :
% 5.52/5.87 ( ( member_int @ B2 @ T5 )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ S3 )
% 5.52/5.87 => ( ( H2 @ ( J @ A3 ) )
% 5.52/5.87 = ( G @ A3 ) ) )
% 5.52/5.87 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.52/5.87 = ( groups7440179247065528705omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.reindex_bij_witness_not_neutral
% 5.52/5.87 thf(fact_8373_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.52/5.87 ! [S5: set_real,T5: set_complex,S3: set_real,I: complex > real,J: real > complex,T6: set_complex,G: real > complex,H2: complex > complex] :
% 5.52/5.87 ( ( finite_finite_real @ S5 )
% 5.52/5.87 => ( ( finite3207457112153483333omplex @ T5 )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.52/5.87 => ( ( I @ ( J @ A3 ) )
% 5.52/5.87 = A3 ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.52/5.87 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T6 @ T5 ) ) )
% 5.52/5.87 => ( ! [B2: complex] :
% 5.52/5.87 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T6 @ T5 ) )
% 5.52/5.87 => ( ( J @ ( I @ B2 ) )
% 5.52/5.87 = B2 ) )
% 5.52/5.87 => ( ! [B2: complex] :
% 5.52/5.87 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T6 @ T5 ) )
% 5.52/5.87 => ( member_real @ ( I @ B2 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ S5 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: complex] :
% 5.52/5.87 ( ( member_complex @ B2 @ T5 )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ S3 )
% 5.52/5.87 => ( ( H2 @ ( J @ A3 ) )
% 5.52/5.87 = ( G @ A3 ) ) )
% 5.52/5.87 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.52/5.87 = ( groups3708469109370488835omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.reindex_bij_witness_not_neutral
% 5.52/5.87 thf(fact_8374_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.52/5.87 ! [S5: set_real,T5: set_Extended_enat,S3: set_real,I: extended_enat > real,J: real > extended_enat,T6: set_Extended_enat,G: real > complex,H2: extended_enat > complex] :
% 5.52/5.87 ( ( finite_finite_real @ S5 )
% 5.52/5.87 => ( ( finite4001608067531595151d_enat @ T5 )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.52/5.87 => ( ( I @ ( J @ A3 ) )
% 5.52/5.87 = A3 ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.52/5.87 => ( member_Extended_enat @ ( J @ A3 ) @ ( minus_925952699566721837d_enat @ T6 @ T5 ) ) )
% 5.52/5.87 => ( ! [B2: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ T6 @ T5 ) )
% 5.52/5.87 => ( ( J @ ( I @ B2 ) )
% 5.52/5.87 = B2 ) )
% 5.52/5.87 => ( ! [B2: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ T6 @ T5 ) )
% 5.52/5.87 => ( member_real @ ( I @ B2 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ S5 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ B2 @ T5 )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ S3 )
% 5.52/5.87 => ( ( H2 @ ( J @ A3 ) )
% 5.52/5.87 = ( G @ A3 ) ) )
% 5.52/5.87 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.52/5.87 = ( groups4622424608036095791omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.reindex_bij_witness_not_neutral
% 5.52/5.87 thf(fact_8375_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.52/5.87 ! [S5: set_nat,T5: set_real,S3: set_nat,I: real > nat,J: nat > real,T6: set_real,G: nat > complex,H2: real > complex] :
% 5.52/5.87 ( ( finite_finite_nat @ S5 )
% 5.52/5.87 => ( ( finite_finite_real @ T5 )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ S3 @ S5 ) )
% 5.52/5.87 => ( ( I @ ( J @ A3 ) )
% 5.52/5.87 = A3 ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ S3 @ S5 ) )
% 5.52/5.87 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T6 @ T5 ) ) )
% 5.52/5.87 => ( ! [B2: real] :
% 5.52/5.87 ( ( member_real @ B2 @ ( minus_minus_set_real @ T6 @ T5 ) )
% 5.52/5.87 => ( ( J @ ( I @ B2 ) )
% 5.52/5.87 = B2 ) )
% 5.52/5.87 => ( ! [B2: real] :
% 5.52/5.87 ( ( member_real @ B2 @ ( minus_minus_set_real @ T6 @ T5 ) )
% 5.52/5.87 => ( member_nat @ ( I @ B2 ) @ ( minus_minus_set_nat @ S3 @ S5 ) ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ S5 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: real] :
% 5.52/5.87 ( ( member_real @ B2 @ T5 )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ S3 )
% 5.52/5.87 => ( ( H2 @ ( J @ A3 ) )
% 5.52/5.87 = ( G @ A3 ) ) )
% 5.52/5.87 => ( ( groups6464643781859351333omplex @ G @ S3 )
% 5.52/5.87 = ( groups713298508707869441omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.reindex_bij_witness_not_neutral
% 5.52/5.87 thf(fact_8376_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.52/5.87 ! [S5: set_nat,T5: set_nat,S3: set_nat,I: nat > nat,J: nat > nat,T6: set_nat,G: nat > complex,H2: nat > complex] :
% 5.52/5.87 ( ( finite_finite_nat @ S5 )
% 5.52/5.87 => ( ( finite_finite_nat @ T5 )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ S3 @ S5 ) )
% 5.52/5.87 => ( ( I @ ( J @ A3 ) )
% 5.52/5.87 = A3 ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ S3 @ S5 ) )
% 5.52/5.87 => ( member_nat @ ( J @ A3 ) @ ( minus_minus_set_nat @ T6 @ T5 ) ) )
% 5.52/5.87 => ( ! [B2: nat] :
% 5.52/5.87 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ T6 @ T5 ) )
% 5.52/5.87 => ( ( J @ ( I @ B2 ) )
% 5.52/5.87 = B2 ) )
% 5.52/5.87 => ( ! [B2: nat] :
% 5.52/5.87 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ T6 @ T5 ) )
% 5.52/5.87 => ( member_nat @ ( I @ B2 ) @ ( minus_minus_set_nat @ S3 @ S5 ) ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ S5 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: nat] :
% 5.52/5.87 ( ( member_nat @ B2 @ T5 )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ S3 )
% 5.52/5.87 => ( ( H2 @ ( J @ A3 ) )
% 5.52/5.87 = ( G @ A3 ) ) )
% 5.52/5.87 => ( ( groups6464643781859351333omplex @ G @ S3 )
% 5.52/5.87 = ( groups6464643781859351333omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.reindex_bij_witness_not_neutral
% 5.52/5.87 thf(fact_8377_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.52/5.87 ! [S5: set_nat,T5: set_int,S3: set_nat,I: int > nat,J: nat > int,T6: set_int,G: nat > complex,H2: int > complex] :
% 5.52/5.87 ( ( finite_finite_nat @ S5 )
% 5.52/5.87 => ( ( finite_finite_int @ T5 )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ S3 @ S5 ) )
% 5.52/5.87 => ( ( I @ ( J @ A3 ) )
% 5.52/5.87 = A3 ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ S3 @ S5 ) )
% 5.52/5.87 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T6 @ T5 ) ) )
% 5.52/5.87 => ( ! [B2: int] :
% 5.52/5.87 ( ( member_int @ B2 @ ( minus_minus_set_int @ T6 @ T5 ) )
% 5.52/5.87 => ( ( J @ ( I @ B2 ) )
% 5.52/5.87 = B2 ) )
% 5.52/5.87 => ( ! [B2: int] :
% 5.52/5.87 ( ( member_int @ B2 @ ( minus_minus_set_int @ T6 @ T5 ) )
% 5.52/5.87 => ( member_nat @ ( I @ B2 ) @ ( minus_minus_set_nat @ S3 @ S5 ) ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ S5 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: int] :
% 5.52/5.87 ( ( member_int @ B2 @ T5 )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ S3 )
% 5.52/5.87 => ( ( H2 @ ( J @ A3 ) )
% 5.52/5.87 = ( G @ A3 ) ) )
% 5.52/5.87 => ( ( groups6464643781859351333omplex @ G @ S3 )
% 5.52/5.87 = ( groups7440179247065528705omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.reindex_bij_witness_not_neutral
% 5.52/5.87 thf(fact_8378_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.52/5.87 ! [S5: set_nat,T5: set_complex,S3: set_nat,I: complex > nat,J: nat > complex,T6: set_complex,G: nat > complex,H2: complex > complex] :
% 5.52/5.87 ( ( finite_finite_nat @ S5 )
% 5.52/5.87 => ( ( finite3207457112153483333omplex @ T5 )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ S3 @ S5 ) )
% 5.52/5.87 => ( ( I @ ( J @ A3 ) )
% 5.52/5.87 = A3 ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ S3 @ S5 ) )
% 5.52/5.87 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T6 @ T5 ) ) )
% 5.52/5.87 => ( ! [B2: complex] :
% 5.52/5.87 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T6 @ T5 ) )
% 5.52/5.87 => ( ( J @ ( I @ B2 ) )
% 5.52/5.87 = B2 ) )
% 5.52/5.87 => ( ! [B2: complex] :
% 5.52/5.87 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T6 @ T5 ) )
% 5.52/5.87 => ( member_nat @ ( I @ B2 ) @ ( minus_minus_set_nat @ S3 @ S5 ) ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ S5 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: complex] :
% 5.52/5.87 ( ( member_complex @ B2 @ T5 )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ S3 )
% 5.52/5.87 => ( ( H2 @ ( J @ A3 ) )
% 5.52/5.87 = ( G @ A3 ) ) )
% 5.52/5.87 => ( ( groups6464643781859351333omplex @ G @ S3 )
% 5.52/5.87 = ( groups3708469109370488835omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.reindex_bij_witness_not_neutral
% 5.52/5.87 thf(fact_8379_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.52/5.87 ! [S5: set_nat,T5: set_Extended_enat,S3: set_nat,I: extended_enat > nat,J: nat > extended_enat,T6: set_Extended_enat,G: nat > complex,H2: extended_enat > complex] :
% 5.52/5.87 ( ( finite_finite_nat @ S5 )
% 5.52/5.87 => ( ( finite4001608067531595151d_enat @ T5 )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ S3 @ S5 ) )
% 5.52/5.87 => ( ( I @ ( J @ A3 ) )
% 5.52/5.87 = A3 ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ S3 @ S5 ) )
% 5.52/5.87 => ( member_Extended_enat @ ( J @ A3 ) @ ( minus_925952699566721837d_enat @ T6 @ T5 ) ) )
% 5.52/5.87 => ( ! [B2: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ T6 @ T5 ) )
% 5.52/5.87 => ( ( J @ ( I @ B2 ) )
% 5.52/5.87 = B2 ) )
% 5.52/5.87 => ( ! [B2: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ T6 @ T5 ) )
% 5.52/5.87 => ( member_nat @ ( I @ B2 ) @ ( minus_minus_set_nat @ S3 @ S5 ) ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ S5 )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ B2 @ T5 )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [A3: nat] :
% 5.52/5.87 ( ( member_nat @ A3 @ S3 )
% 5.52/5.87 => ( ( H2 @ ( J @ A3 ) )
% 5.52/5.87 = ( G @ A3 ) ) )
% 5.52/5.87 => ( ( groups6464643781859351333omplex @ G @ S3 )
% 5.52/5.87 = ( groups4622424608036095791omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.reindex_bij_witness_not_neutral
% 5.52/5.87 thf(fact_8380_prod_Osetdiff__irrelevant,axiom,
% 5.52/5.87 ! [A2: set_nat,G: nat > complex] :
% 5.52/5.87 ( ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ( groups6464643781859351333omplex @ G
% 5.52/5.87 @ ( minus_minus_set_nat @ A2
% 5.52/5.87 @ ( collect_nat
% 5.52/5.87 @ ^ [X: nat] :
% 5.52/5.87 ( ( G @ X )
% 5.52/5.87 = one_one_complex ) ) ) )
% 5.52/5.87 = ( groups6464643781859351333omplex @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.setdiff_irrelevant
% 5.52/5.87 thf(fact_8381_prod_Osetdiff__irrelevant,axiom,
% 5.52/5.87 ! [A2: set_int,G: int > complex] :
% 5.52/5.87 ( ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( groups7440179247065528705omplex @ G
% 5.52/5.87 @ ( minus_minus_set_int @ A2
% 5.52/5.87 @ ( collect_int
% 5.52/5.87 @ ^ [X: int] :
% 5.52/5.87 ( ( G @ X )
% 5.52/5.87 = one_one_complex ) ) ) )
% 5.52/5.87 = ( groups7440179247065528705omplex @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.setdiff_irrelevant
% 5.52/5.87 thf(fact_8382_prod_Osetdiff__irrelevant,axiom,
% 5.52/5.87 ! [A2: set_complex,G: complex > complex] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.87 => ( ( groups3708469109370488835omplex @ G
% 5.52/5.87 @ ( minus_811609699411566653omplex @ A2
% 5.52/5.87 @ ( collect_complex
% 5.52/5.87 @ ^ [X: complex] :
% 5.52/5.87 ( ( G @ X )
% 5.52/5.87 = one_one_complex ) ) ) )
% 5.52/5.87 = ( groups3708469109370488835omplex @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.setdiff_irrelevant
% 5.52/5.87 thf(fact_8383_prod_Osetdiff__irrelevant,axiom,
% 5.52/5.87 ! [A2: set_Extended_enat,G: extended_enat > complex] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.87 => ( ( groups4622424608036095791omplex @ G
% 5.52/5.87 @ ( minus_925952699566721837d_enat @ A2
% 5.52/5.87 @ ( collec4429806609662206161d_enat
% 5.52/5.87 @ ^ [X: extended_enat] :
% 5.52/5.87 ( ( G @ X )
% 5.52/5.87 = one_one_complex ) ) ) )
% 5.52/5.87 = ( groups4622424608036095791omplex @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.setdiff_irrelevant
% 5.52/5.87 thf(fact_8384_prod_Osetdiff__irrelevant,axiom,
% 5.52/5.87 ! [A2: set_nat,G: nat > real] :
% 5.52/5.87 ( ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ( groups129246275422532515t_real @ G
% 5.52/5.87 @ ( minus_minus_set_nat @ A2
% 5.52/5.87 @ ( collect_nat
% 5.52/5.87 @ ^ [X: nat] :
% 5.52/5.87 ( ( G @ X )
% 5.52/5.87 = one_one_real ) ) ) )
% 5.52/5.87 = ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.setdiff_irrelevant
% 5.52/5.87 thf(fact_8385_prod_Osetdiff__irrelevant,axiom,
% 5.52/5.87 ! [A2: set_int,G: int > real] :
% 5.52/5.87 ( ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( groups2316167850115554303t_real @ G
% 5.52/5.87 @ ( minus_minus_set_int @ A2
% 5.52/5.87 @ ( collect_int
% 5.52/5.87 @ ^ [X: int] :
% 5.52/5.87 ( ( G @ X )
% 5.52/5.87 = one_one_real ) ) ) )
% 5.52/5.87 = ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.setdiff_irrelevant
% 5.52/5.87 thf(fact_8386_prod_Osetdiff__irrelevant,axiom,
% 5.52/5.87 ! [A2: set_complex,G: complex > real] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.87 => ( ( groups766887009212190081x_real @ G
% 5.52/5.87 @ ( minus_811609699411566653omplex @ A2
% 5.52/5.87 @ ( collect_complex
% 5.52/5.87 @ ^ [X: complex] :
% 5.52/5.87 ( ( G @ X )
% 5.52/5.87 = one_one_real ) ) ) )
% 5.52/5.87 = ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.setdiff_irrelevant
% 5.52/5.87 thf(fact_8387_prod_Osetdiff__irrelevant,axiom,
% 5.52/5.87 ! [A2: set_Extended_enat,G: extended_enat > real] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.87 => ( ( groups97031904164794029t_real @ G
% 5.52/5.87 @ ( minus_925952699566721837d_enat @ A2
% 5.52/5.87 @ ( collec4429806609662206161d_enat
% 5.52/5.87 @ ^ [X: extended_enat] :
% 5.52/5.87 ( ( G @ X )
% 5.52/5.87 = one_one_real ) ) ) )
% 5.52/5.87 = ( groups97031904164794029t_real @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.setdiff_irrelevant
% 5.52/5.87 thf(fact_8388_prod_Osetdiff__irrelevant,axiom,
% 5.52/5.87 ! [A2: set_nat,G: nat > rat] :
% 5.52/5.87 ( ( finite_finite_nat @ A2 )
% 5.52/5.87 => ( ( groups73079841787564623at_rat @ G
% 5.52/5.87 @ ( minus_minus_set_nat @ A2
% 5.52/5.87 @ ( collect_nat
% 5.52/5.87 @ ^ [X: nat] :
% 5.52/5.87 ( ( G @ X )
% 5.52/5.87 = one_one_rat ) ) ) )
% 5.52/5.87 = ( groups73079841787564623at_rat @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.setdiff_irrelevant
% 5.52/5.87 thf(fact_8389_prod_Osetdiff__irrelevant,axiom,
% 5.52/5.87 ! [A2: set_int,G: int > rat] :
% 5.52/5.87 ( ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( groups1072433553688619179nt_rat @ G
% 5.52/5.87 @ ( minus_minus_set_int @ A2
% 5.52/5.87 @ ( collect_int
% 5.52/5.87 @ ^ [X: int] :
% 5.52/5.87 ( ( G @ X )
% 5.52/5.87 = one_one_rat ) ) ) )
% 5.52/5.87 = ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.setdiff_irrelevant
% 5.52/5.87 thf(fact_8390_prod_OatLeastAtMost__rev,axiom,
% 5.52/5.87 ! [G: nat > nat,N: nat,M: nat] :
% 5.52/5.87 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.52/5.87 = ( groups708209901874060359at_nat
% 5.52/5.87 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.52/5.87 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.atLeastAtMost_rev
% 5.52/5.87 thf(fact_8391_prod_OatLeastAtMost__rev,axiom,
% 5.52/5.87 ! [G: nat > int,N: nat,M: nat] :
% 5.52/5.87 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.52/5.87 = ( groups705719431365010083at_int
% 5.52/5.87 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.52/5.87 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.atLeastAtMost_rev
% 5.52/5.87 thf(fact_8392_less__1__prod2,axiom,
% 5.52/5.87 ! [I5: set_real,I: real,F: real > real] :
% 5.52/5.87 ( ( finite_finite_real @ I5 )
% 5.52/5.87 => ( ( member_real @ I @ I5 )
% 5.52/5.87 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.52/5.87 => ( ! [I2: real] :
% 5.52/5.87 ( ( member_real @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod2
% 5.52/5.87 thf(fact_8393_less__1__prod2,axiom,
% 5.52/5.87 ! [I5: set_nat,I: nat,F: nat > real] :
% 5.52/5.87 ( ( finite_finite_nat @ I5 )
% 5.52/5.87 => ( ( member_nat @ I @ I5 )
% 5.52/5.87 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.52/5.87 => ( ! [I2: nat] :
% 5.52/5.87 ( ( member_nat @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod2
% 5.52/5.87 thf(fact_8394_less__1__prod2,axiom,
% 5.52/5.87 ! [I5: set_int,I: int,F: int > real] :
% 5.52/5.87 ( ( finite_finite_int @ I5 )
% 5.52/5.87 => ( ( member_int @ I @ I5 )
% 5.52/5.87 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.52/5.87 => ( ! [I2: int] :
% 5.52/5.87 ( ( member_int @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod2
% 5.52/5.87 thf(fact_8395_less__1__prod2,axiom,
% 5.52/5.87 ! [I5: set_complex,I: complex,F: complex > real] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ I5 )
% 5.52/5.87 => ( ( member_complex @ I @ I5 )
% 5.52/5.87 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.52/5.87 => ( ! [I2: complex] :
% 5.52/5.87 ( ( member_complex @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod2
% 5.52/5.87 thf(fact_8396_less__1__prod2,axiom,
% 5.52/5.87 ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > real] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ I5 )
% 5.52/5.87 => ( ( member_Extended_enat @ I @ I5 )
% 5.52/5.87 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.52/5.87 => ( ! [I2: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( groups97031904164794029t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod2
% 5.52/5.87 thf(fact_8397_less__1__prod2,axiom,
% 5.52/5.87 ! [I5: set_real,I: real,F: real > rat] :
% 5.52/5.87 ( ( finite_finite_real @ I5 )
% 5.52/5.87 => ( ( member_real @ I @ I5 )
% 5.52/5.87 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.52/5.87 => ( ! [I2: real] :
% 5.52/5.87 ( ( member_real @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod2
% 5.52/5.87 thf(fact_8398_less__1__prod2,axiom,
% 5.52/5.87 ! [I5: set_nat,I: nat,F: nat > rat] :
% 5.52/5.87 ( ( finite_finite_nat @ I5 )
% 5.52/5.87 => ( ( member_nat @ I @ I5 )
% 5.52/5.87 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.52/5.87 => ( ! [I2: nat] :
% 5.52/5.87 ( ( member_nat @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod2
% 5.52/5.87 thf(fact_8399_less__1__prod2,axiom,
% 5.52/5.87 ! [I5: set_int,I: int,F: int > rat] :
% 5.52/5.87 ( ( finite_finite_int @ I5 )
% 5.52/5.87 => ( ( member_int @ I @ I5 )
% 5.52/5.87 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.52/5.87 => ( ! [I2: int] :
% 5.52/5.87 ( ( member_int @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod2
% 5.52/5.87 thf(fact_8400_less__1__prod2,axiom,
% 5.52/5.87 ! [I5: set_complex,I: complex,F: complex > rat] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ I5 )
% 5.52/5.87 => ( ( member_complex @ I @ I5 )
% 5.52/5.87 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.52/5.87 => ( ! [I2: complex] :
% 5.52/5.87 ( ( member_complex @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod2
% 5.52/5.87 thf(fact_8401_less__1__prod2,axiom,
% 5.52/5.87 ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > rat] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ I5 )
% 5.52/5.87 => ( ( member_Extended_enat @ I @ I5 )
% 5.52/5.87 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.52/5.87 => ( ! [I2: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( groups2245840878043517529at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod2
% 5.52/5.87 thf(fact_8402_less__1__prod,axiom,
% 5.52/5.87 ! [I5: set_real,F: real > real] :
% 5.52/5.87 ( ( finite_finite_real @ I5 )
% 5.52/5.87 => ( ( I5 != bot_bot_set_real )
% 5.52/5.87 => ( ! [I2: real] :
% 5.52/5.87 ( ( member_real @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod
% 5.52/5.87 thf(fact_8403_less__1__prod,axiom,
% 5.52/5.87 ! [I5: set_complex,F: complex > real] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ I5 )
% 5.52/5.87 => ( ( I5 != bot_bot_set_complex )
% 5.52/5.87 => ( ! [I2: complex] :
% 5.52/5.87 ( ( member_complex @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod
% 5.52/5.87 thf(fact_8404_less__1__prod,axiom,
% 5.52/5.87 ! [I5: set_nat,F: nat > real] :
% 5.52/5.87 ( ( finite_finite_nat @ I5 )
% 5.52/5.87 => ( ( I5 != bot_bot_set_nat )
% 5.52/5.87 => ( ! [I2: nat] :
% 5.52/5.87 ( ( member_nat @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod
% 5.52/5.87 thf(fact_8405_less__1__prod,axiom,
% 5.52/5.87 ! [I5: set_int,F: int > real] :
% 5.52/5.87 ( ( finite_finite_int @ I5 )
% 5.52/5.87 => ( ( I5 != bot_bot_set_int )
% 5.52/5.87 => ( ! [I2: int] :
% 5.52/5.87 ( ( member_int @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod
% 5.52/5.87 thf(fact_8406_less__1__prod,axiom,
% 5.52/5.87 ! [I5: set_Extended_enat,F: extended_enat > real] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ I5 )
% 5.52/5.87 => ( ( I5 != bot_bo7653980558646680370d_enat )
% 5.52/5.87 => ( ! [I2: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_real @ one_one_real @ ( groups97031904164794029t_real @ F @ I5 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod
% 5.52/5.87 thf(fact_8407_less__1__prod,axiom,
% 5.52/5.87 ! [I5: set_real,F: real > rat] :
% 5.52/5.87 ( ( finite_finite_real @ I5 )
% 5.52/5.87 => ( ( I5 != bot_bot_set_real )
% 5.52/5.87 => ( ! [I2: real] :
% 5.52/5.87 ( ( member_real @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod
% 5.52/5.87 thf(fact_8408_less__1__prod,axiom,
% 5.52/5.87 ! [I5: set_complex,F: complex > rat] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ I5 )
% 5.52/5.87 => ( ( I5 != bot_bot_set_complex )
% 5.52/5.87 => ( ! [I2: complex] :
% 5.52/5.87 ( ( member_complex @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod
% 5.52/5.87 thf(fact_8409_less__1__prod,axiom,
% 5.52/5.87 ! [I5: set_nat,F: nat > rat] :
% 5.52/5.87 ( ( finite_finite_nat @ I5 )
% 5.52/5.87 => ( ( I5 != bot_bot_set_nat )
% 5.52/5.87 => ( ! [I2: nat] :
% 5.52/5.87 ( ( member_nat @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod
% 5.52/5.87 thf(fact_8410_less__1__prod,axiom,
% 5.52/5.87 ! [I5: set_int,F: int > rat] :
% 5.52/5.87 ( ( finite_finite_int @ I5 )
% 5.52/5.87 => ( ( I5 != bot_bot_set_int )
% 5.52/5.87 => ( ! [I2: int] :
% 5.52/5.87 ( ( member_int @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod
% 5.52/5.87 thf(fact_8411_less__1__prod,axiom,
% 5.52/5.87 ! [I5: set_Extended_enat,F: extended_enat > rat] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ I5 )
% 5.52/5.87 => ( ( I5 != bot_bo7653980558646680370d_enat )
% 5.52/5.87 => ( ! [I2: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ I2 @ I5 )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.52/5.87 => ( ord_less_rat @ one_one_rat @ ( groups2245840878043517529at_rat @ F @ I5 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % less_1_prod
% 5.52/5.87 thf(fact_8412_prod_Osubset__diff,axiom,
% 5.52/5.87 ! [B4: set_int,A2: set_int,G: int > real] :
% 5.52/5.87 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.52/5.87 => ( ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.52/5.87 = ( times_times_real @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups2316167850115554303t_real @ G @ B4 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.subset_diff
% 5.52/5.87 thf(fact_8413_prod_Osubset__diff,axiom,
% 5.52/5.87 ! [B4: set_complex,A2: set_complex,G: complex > real] :
% 5.52/5.87 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.52/5.87 => ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.87 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.52/5.87 = ( times_times_real @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups766887009212190081x_real @ G @ B4 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.subset_diff
% 5.52/5.87 thf(fact_8414_prod_Osubset__diff,axiom,
% 5.52/5.87 ! [B4: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > real] :
% 5.52/5.87 ( ( ord_le7203529160286727270d_enat @ B4 @ A2 )
% 5.52/5.87 => ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.87 => ( ( groups97031904164794029t_real @ G @ A2 )
% 5.52/5.87 = ( times_times_real @ ( groups97031904164794029t_real @ G @ ( minus_925952699566721837d_enat @ A2 @ B4 ) ) @ ( groups97031904164794029t_real @ G @ B4 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.subset_diff
% 5.52/5.87 thf(fact_8415_prod_Osubset__diff,axiom,
% 5.52/5.87 ! [B4: set_int,A2: set_int,G: int > rat] :
% 5.52/5.87 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.52/5.87 => ( ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 5.52/5.87 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups1072433553688619179nt_rat @ G @ B4 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.subset_diff
% 5.52/5.87 thf(fact_8416_prod_Osubset__diff,axiom,
% 5.52/5.87 ! [B4: set_complex,A2: set_complex,G: complex > rat] :
% 5.52/5.87 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.52/5.87 => ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.87 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.52/5.87 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups225925009352817453ex_rat @ G @ B4 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.subset_diff
% 5.52/5.87 thf(fact_8417_prod_Osubset__diff,axiom,
% 5.52/5.87 ! [B4: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > rat] :
% 5.52/5.87 ( ( ord_le7203529160286727270d_enat @ B4 @ A2 )
% 5.52/5.87 => ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.87 => ( ( groups2245840878043517529at_rat @ G @ A2 )
% 5.52/5.87 = ( times_times_rat @ ( groups2245840878043517529at_rat @ G @ ( minus_925952699566721837d_enat @ A2 @ B4 ) ) @ ( groups2245840878043517529at_rat @ G @ B4 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.subset_diff
% 5.52/5.87 thf(fact_8418_prod_Osubset__diff,axiom,
% 5.52/5.87 ! [B4: set_int,A2: set_int,G: int > nat] :
% 5.52/5.87 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.52/5.87 => ( ( finite_finite_int @ A2 )
% 5.52/5.87 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 5.52/5.87 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups1707563613775114915nt_nat @ G @ B4 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.subset_diff
% 5.52/5.87 thf(fact_8419_prod_Osubset__diff,axiom,
% 5.52/5.87 ! [B4: set_complex,A2: set_complex,G: complex > nat] :
% 5.52/5.87 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.52/5.87 => ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.87 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 5.52/5.87 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups861055069439313189ex_nat @ G @ B4 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.subset_diff
% 5.52/5.87 thf(fact_8420_prod_Osubset__diff,axiom,
% 5.52/5.87 ! [B4: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > nat] :
% 5.52/5.87 ( ( ord_le7203529160286727270d_enat @ B4 @ A2 )
% 5.52/5.87 => ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.87 => ( ( groups2880970938130013265at_nat @ G @ A2 )
% 5.52/5.87 = ( times_times_nat @ ( groups2880970938130013265at_nat @ G @ ( minus_925952699566721837d_enat @ A2 @ B4 ) ) @ ( groups2880970938130013265at_nat @ G @ B4 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.subset_diff
% 5.52/5.87 thf(fact_8421_prod_Osubset__diff,axiom,
% 5.52/5.87 ! [B4: set_complex,A2: set_complex,G: complex > int] :
% 5.52/5.87 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.52/5.87 => ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.87 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 5.52/5.87 = ( times_times_int @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups858564598930262913ex_int @ G @ B4 ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.subset_diff
% 5.52/5.87 thf(fact_8422_prod_Osame__carrier,axiom,
% 5.52/5.87 ! [C4: set_real,A2: set_real,B4: set_real,G: real > complex,H2: real > complex] :
% 5.52/5.87 ( ( finite_finite_real @ C4 )
% 5.52/5.87 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.52/5.87 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: real] :
% 5.52/5.87 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ( ( groups713298508707869441omplex @ G @ A2 )
% 5.52/5.87 = ( groups713298508707869441omplex @ H2 @ B4 ) )
% 5.52/5.87 = ( ( groups713298508707869441omplex @ G @ C4 )
% 5.52/5.87 = ( groups713298508707869441omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.same_carrier
% 5.52/5.87 thf(fact_8423_prod_Osame__carrier,axiom,
% 5.52/5.87 ! [C4: set_int,A2: set_int,B4: set_int,G: int > complex,H2: int > complex] :
% 5.52/5.87 ( ( finite_finite_int @ C4 )
% 5.52/5.87 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.52/5.87 => ( ( ord_less_eq_set_int @ B4 @ C4 )
% 5.52/5.87 => ( ! [A3: int] :
% 5.52/5.87 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: int] :
% 5.52/5.87 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B4 ) )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.52/5.87 = ( groups7440179247065528705omplex @ H2 @ B4 ) )
% 5.52/5.87 = ( ( groups7440179247065528705omplex @ G @ C4 )
% 5.52/5.87 = ( groups7440179247065528705omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.same_carrier
% 5.52/5.87 thf(fact_8424_prod_Osame__carrier,axiom,
% 5.52/5.87 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > complex,H2: complex > complex] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ C4 )
% 5.52/5.87 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.52/5.87 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.52/5.87 => ( ! [A3: complex] :
% 5.52/5.87 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: complex] :
% 5.52/5.87 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.52/5.87 = ( groups3708469109370488835omplex @ H2 @ B4 ) )
% 5.52/5.87 = ( ( groups3708469109370488835omplex @ G @ C4 )
% 5.52/5.87 = ( groups3708469109370488835omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.same_carrier
% 5.52/5.87 thf(fact_8425_prod_Osame__carrier,axiom,
% 5.52/5.87 ! [C4: set_Extended_enat,A2: set_Extended_enat,B4: set_Extended_enat,G: extended_enat > complex,H2: extended_enat > complex] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ C4 )
% 5.52/5.87 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 5.52/5.87 => ( ( ord_le7203529160286727270d_enat @ B4 @ C4 )
% 5.52/5.87 => ( ! [A3: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ A3 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ! [B2: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ C4 @ B4 ) )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_complex ) )
% 5.52/5.87 => ( ( ( groups4622424608036095791omplex @ G @ A2 )
% 5.52/5.87 = ( groups4622424608036095791omplex @ H2 @ B4 ) )
% 5.52/5.87 = ( ( groups4622424608036095791omplex @ G @ C4 )
% 5.52/5.87 = ( groups4622424608036095791omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.same_carrier
% 5.52/5.87 thf(fact_8426_prod_Osame__carrier,axiom,
% 5.52/5.87 ! [C4: set_real,A2: set_real,B4: set_real,G: real > real,H2: real > real] :
% 5.52/5.87 ( ( finite_finite_real @ C4 )
% 5.52/5.87 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.52/5.87 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.52/5.87 => ( ! [A3: real] :
% 5.52/5.87 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_real ) )
% 5.52/5.87 => ( ! [B2: real] :
% 5.52/5.87 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_real ) )
% 5.52/5.87 => ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.52/5.87 = ( groups1681761925125756287l_real @ H2 @ B4 ) )
% 5.52/5.87 = ( ( groups1681761925125756287l_real @ G @ C4 )
% 5.52/5.87 = ( groups1681761925125756287l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.same_carrier
% 5.52/5.87 thf(fact_8427_prod_Osame__carrier,axiom,
% 5.52/5.87 ! [C4: set_int,A2: set_int,B4: set_int,G: int > real,H2: int > real] :
% 5.52/5.87 ( ( finite_finite_int @ C4 )
% 5.52/5.87 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.52/5.87 => ( ( ord_less_eq_set_int @ B4 @ C4 )
% 5.52/5.87 => ( ! [A3: int] :
% 5.52/5.87 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_real ) )
% 5.52/5.87 => ( ! [B2: int] :
% 5.52/5.87 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B4 ) )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_real ) )
% 5.52/5.87 => ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.52/5.87 = ( groups2316167850115554303t_real @ H2 @ B4 ) )
% 5.52/5.87 = ( ( groups2316167850115554303t_real @ G @ C4 )
% 5.52/5.87 = ( groups2316167850115554303t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.same_carrier
% 5.52/5.87 thf(fact_8428_prod_Osame__carrier,axiom,
% 5.52/5.87 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > real,H2: complex > real] :
% 5.52/5.87 ( ( finite3207457112153483333omplex @ C4 )
% 5.52/5.87 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.52/5.87 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.52/5.87 => ( ! [A3: complex] :
% 5.52/5.87 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_real ) )
% 5.52/5.87 => ( ! [B2: complex] :
% 5.52/5.87 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.52/5.87 => ( ( H2 @ B2 )
% 5.52/5.87 = one_one_real ) )
% 5.52/5.87 => ( ( ( groups766887009212190081x_real @ G @ A2 )
% 5.52/5.87 = ( groups766887009212190081x_real @ H2 @ B4 ) )
% 5.52/5.87 = ( ( groups766887009212190081x_real @ G @ C4 )
% 5.52/5.87 = ( groups766887009212190081x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.52/5.87
% 5.52/5.87 % prod.same_carrier
% 5.52/5.87 thf(fact_8429_prod_Osame__carrier,axiom,
% 5.52/5.87 ! [C4: set_Extended_enat,A2: set_Extended_enat,B4: set_Extended_enat,G: extended_enat > real,H2: extended_enat > real] :
% 5.52/5.87 ( ( finite4001608067531595151d_enat @ C4 )
% 5.52/5.87 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 5.52/5.87 => ( ( ord_le7203529160286727270d_enat @ B4 @ C4 )
% 5.52/5.87 => ( ! [A3: extended_enat] :
% 5.52/5.87 ( ( member_Extended_enat @ A3 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 5.52/5.87 => ( ( G @ A3 )
% 5.52/5.87 = one_one_real ) )
% 5.52/5.88 => ( ! [B2: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ( ( groups97031904164794029t_real @ G @ A2 )
% 5.52/5.88 = ( groups97031904164794029t_real @ H2 @ B4 ) )
% 5.52/5.88 = ( ( groups97031904164794029t_real @ G @ C4 )
% 5.52/5.88 = ( groups97031904164794029t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrier
% 5.52/5.88 thf(fact_8430_prod_Osame__carrier,axiom,
% 5.52/5.88 ! [C4: set_real,A2: set_real,B4: set_real,G: real > rat,H2: real > rat] :
% 5.52/5.88 ( ( finite_finite_real @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.52/5.88 => ( ! [A3: real] :
% 5.52/5.88 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.52/5.88 => ( ( G @ A3 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ! [B2: real] :
% 5.52/5.88 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.52/5.88 = ( groups4061424788464935467al_rat @ H2 @ B4 ) )
% 5.52/5.88 = ( ( groups4061424788464935467al_rat @ G @ C4 )
% 5.52/5.88 = ( groups4061424788464935467al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrier
% 5.52/5.88 thf(fact_8431_prod_Osame__carrier,axiom,
% 5.52/5.88 ! [C4: set_int,A2: set_int,B4: set_int,G: int > rat,H2: int > rat] :
% 5.52/5.88 ( ( finite_finite_int @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ B4 @ C4 )
% 5.52/5.88 => ( ! [A3: int] :
% 5.52/5.88 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.52/5.88 => ( ( G @ A3 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ! [B2: int] :
% 5.52/5.88 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 5.52/5.88 = ( groups1072433553688619179nt_rat @ H2 @ B4 ) )
% 5.52/5.88 = ( ( groups1072433553688619179nt_rat @ G @ C4 )
% 5.52/5.88 = ( groups1072433553688619179nt_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrier
% 5.52/5.88 thf(fact_8432_prod_Osame__carrierI,axiom,
% 5.52/5.88 ! [C4: set_real,A2: set_real,B4: set_real,G: real > complex,H2: real > complex] :
% 5.52/5.88 ( ( finite_finite_real @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.52/5.88 => ( ! [A3: real] :
% 5.52/5.88 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.52/5.88 => ( ( G @ A3 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ! [B2: real] :
% 5.52/5.88 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ( ( groups713298508707869441omplex @ G @ C4 )
% 5.52/5.88 = ( groups713298508707869441omplex @ H2 @ C4 ) )
% 5.52/5.88 => ( ( groups713298508707869441omplex @ G @ A2 )
% 5.52/5.88 = ( groups713298508707869441omplex @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrierI
% 5.52/5.88 thf(fact_8433_prod_Osame__carrierI,axiom,
% 5.52/5.88 ! [C4: set_int,A2: set_int,B4: set_int,G: int > complex,H2: int > complex] :
% 5.52/5.88 ( ( finite_finite_int @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ B4 @ C4 )
% 5.52/5.88 => ( ! [A3: int] :
% 5.52/5.88 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.52/5.88 => ( ( G @ A3 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ! [B2: int] :
% 5.52/5.88 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ( ( groups7440179247065528705omplex @ G @ C4 )
% 5.52/5.88 = ( groups7440179247065528705omplex @ H2 @ C4 ) )
% 5.52/5.88 => ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.52/5.88 = ( groups7440179247065528705omplex @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrierI
% 5.52/5.88 thf(fact_8434_prod_Osame__carrierI,axiom,
% 5.52/5.88 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > complex,H2: complex > complex] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ C4 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.52/5.88 => ( ! [A3: complex] :
% 5.52/5.88 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.52/5.88 => ( ( G @ A3 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ! [B2: complex] :
% 5.52/5.88 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ( ( groups3708469109370488835omplex @ G @ C4 )
% 5.52/5.88 = ( groups3708469109370488835omplex @ H2 @ C4 ) )
% 5.52/5.88 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.52/5.88 = ( groups3708469109370488835omplex @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrierI
% 5.52/5.88 thf(fact_8435_prod_Osame__carrierI,axiom,
% 5.52/5.88 ! [C4: set_Extended_enat,A2: set_Extended_enat,B4: set_Extended_enat,G: extended_enat > complex,H2: extended_enat > complex] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ C4 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ B4 @ C4 )
% 5.52/5.88 => ( ! [A3: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ A3 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 5.52/5.88 => ( ( G @ A3 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ! [B2: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ( ( groups4622424608036095791omplex @ G @ C4 )
% 5.52/5.88 = ( groups4622424608036095791omplex @ H2 @ C4 ) )
% 5.52/5.88 => ( ( groups4622424608036095791omplex @ G @ A2 )
% 5.52/5.88 = ( groups4622424608036095791omplex @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrierI
% 5.52/5.88 thf(fact_8436_prod_Osame__carrierI,axiom,
% 5.52/5.88 ! [C4: set_real,A2: set_real,B4: set_real,G: real > real,H2: real > real] :
% 5.52/5.88 ( ( finite_finite_real @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.52/5.88 => ( ! [A3: real] :
% 5.52/5.88 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.52/5.88 => ( ( G @ A3 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ! [B2: real] :
% 5.52/5.88 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ( ( groups1681761925125756287l_real @ G @ C4 )
% 5.52/5.88 = ( groups1681761925125756287l_real @ H2 @ C4 ) )
% 5.52/5.88 => ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.52/5.88 = ( groups1681761925125756287l_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrierI
% 5.52/5.88 thf(fact_8437_prod_Osame__carrierI,axiom,
% 5.52/5.88 ! [C4: set_int,A2: set_int,B4: set_int,G: int > real,H2: int > real] :
% 5.52/5.88 ( ( finite_finite_int @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ B4 @ C4 )
% 5.52/5.88 => ( ! [A3: int] :
% 5.52/5.88 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.52/5.88 => ( ( G @ A3 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ! [B2: int] :
% 5.52/5.88 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ( ( groups2316167850115554303t_real @ G @ C4 )
% 5.52/5.88 = ( groups2316167850115554303t_real @ H2 @ C4 ) )
% 5.52/5.88 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.52/5.88 = ( groups2316167850115554303t_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrierI
% 5.52/5.88 thf(fact_8438_prod_Osame__carrierI,axiom,
% 5.52/5.88 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > real,H2: complex > real] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ C4 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.52/5.88 => ( ! [A3: complex] :
% 5.52/5.88 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.52/5.88 => ( ( G @ A3 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ! [B2: complex] :
% 5.52/5.88 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ( ( groups766887009212190081x_real @ G @ C4 )
% 5.52/5.88 = ( groups766887009212190081x_real @ H2 @ C4 ) )
% 5.52/5.88 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.52/5.88 = ( groups766887009212190081x_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrierI
% 5.52/5.88 thf(fact_8439_prod_Osame__carrierI,axiom,
% 5.52/5.88 ! [C4: set_Extended_enat,A2: set_Extended_enat,B4: set_Extended_enat,G: extended_enat > real,H2: extended_enat > real] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ C4 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ B4 @ C4 )
% 5.52/5.88 => ( ! [A3: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ A3 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 5.52/5.88 => ( ( G @ A3 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ! [B2: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ( ( groups97031904164794029t_real @ G @ C4 )
% 5.52/5.88 = ( groups97031904164794029t_real @ H2 @ C4 ) )
% 5.52/5.88 => ( ( groups97031904164794029t_real @ G @ A2 )
% 5.52/5.88 = ( groups97031904164794029t_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrierI
% 5.52/5.88 thf(fact_8440_prod_Osame__carrierI,axiom,
% 5.52/5.88 ! [C4: set_real,A2: set_real,B4: set_real,G: real > rat,H2: real > rat] :
% 5.52/5.88 ( ( finite_finite_real @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.52/5.88 => ( ! [A3: real] :
% 5.52/5.88 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.52/5.88 => ( ( G @ A3 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ! [B2: real] :
% 5.52/5.88 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ( ( groups4061424788464935467al_rat @ G @ C4 )
% 5.52/5.88 = ( groups4061424788464935467al_rat @ H2 @ C4 ) )
% 5.52/5.88 => ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.52/5.88 = ( groups4061424788464935467al_rat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrierI
% 5.52/5.88 thf(fact_8441_prod_Osame__carrierI,axiom,
% 5.52/5.88 ! [C4: set_int,A2: set_int,B4: set_int,G: int > rat,H2: int > rat] :
% 5.52/5.88 ( ( finite_finite_int @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ B4 @ C4 )
% 5.52/5.88 => ( ! [A3: int] :
% 5.52/5.88 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.52/5.88 => ( ( G @ A3 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ! [B2: int] :
% 5.52/5.88 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B4 ) )
% 5.52/5.88 => ( ( H2 @ B2 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ( ( groups1072433553688619179nt_rat @ G @ C4 )
% 5.52/5.88 = ( groups1072433553688619179nt_rat @ H2 @ C4 ) )
% 5.52/5.88 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 5.52/5.88 = ( groups1072433553688619179nt_rat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.same_carrierI
% 5.52/5.88 thf(fact_8442_prod_Omono__neutral__left,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,G: int > complex] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ( groups7440179247065528705omplex @ G @ S3 )
% 5.52/5.88 = ( groups7440179247065528705omplex @ G @ T6 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_left
% 5.52/5.88 thf(fact_8443_prod_Omono__neutral__left,axiom,
% 5.52/5.88 ! [T6: set_complex,S3: set_complex,G: complex > complex] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ T6 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.52/5.88 = ( groups3708469109370488835omplex @ G @ T6 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_left
% 5.52/5.88 thf(fact_8444_prod_Omono__neutral__left,axiom,
% 5.52/5.88 ! [T6: set_Extended_enat,S3: set_Extended_enat,G: extended_enat > complex] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ T6 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ( groups4622424608036095791omplex @ G @ S3 )
% 5.52/5.88 = ( groups4622424608036095791omplex @ G @ T6 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_left
% 5.52/5.88 thf(fact_8445_prod_Omono__neutral__left,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,G: int > real] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ( groups2316167850115554303t_real @ G @ S3 )
% 5.52/5.88 = ( groups2316167850115554303t_real @ G @ T6 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_left
% 5.52/5.88 thf(fact_8446_prod_Omono__neutral__left,axiom,
% 5.52/5.88 ! [T6: set_complex,S3: set_complex,G: complex > real] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ T6 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ( groups766887009212190081x_real @ G @ S3 )
% 5.52/5.88 = ( groups766887009212190081x_real @ G @ T6 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_left
% 5.52/5.88 thf(fact_8447_prod_Omono__neutral__left,axiom,
% 5.52/5.88 ! [T6: set_Extended_enat,S3: set_Extended_enat,G: extended_enat > real] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ T6 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ( groups97031904164794029t_real @ G @ S3 )
% 5.52/5.88 = ( groups97031904164794029t_real @ G @ T6 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_left
% 5.52/5.88 thf(fact_8448_prod_Omono__neutral__left,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,G: int > rat] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ( groups1072433553688619179nt_rat @ G @ S3 )
% 5.52/5.88 = ( groups1072433553688619179nt_rat @ G @ T6 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_left
% 5.52/5.88 thf(fact_8449_prod_Omono__neutral__left,axiom,
% 5.52/5.88 ! [T6: set_complex,S3: set_complex,G: complex > rat] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ T6 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ( groups225925009352817453ex_rat @ G @ S3 )
% 5.52/5.88 = ( groups225925009352817453ex_rat @ G @ T6 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_left
% 5.52/5.88 thf(fact_8450_prod_Omono__neutral__left,axiom,
% 5.52/5.88 ! [T6: set_Extended_enat,S3: set_Extended_enat,G: extended_enat > rat] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ T6 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ( groups2245840878043517529at_rat @ G @ S3 )
% 5.52/5.88 = ( groups2245840878043517529at_rat @ G @ T6 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_left
% 5.52/5.88 thf(fact_8451_prod_Omono__neutral__left,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,G: int > nat] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_nat ) )
% 5.52/5.88 => ( ( groups1707563613775114915nt_nat @ G @ S3 )
% 5.52/5.88 = ( groups1707563613775114915nt_nat @ G @ T6 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_left
% 5.52/5.88 thf(fact_8452_prod_Omono__neutral__right,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,G: int > complex] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ( groups7440179247065528705omplex @ G @ T6 )
% 5.52/5.88 = ( groups7440179247065528705omplex @ G @ S3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_right
% 5.52/5.88 thf(fact_8453_prod_Omono__neutral__right,axiom,
% 5.52/5.88 ! [T6: set_complex,S3: set_complex,G: complex > complex] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ T6 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ( groups3708469109370488835omplex @ G @ T6 )
% 5.52/5.88 = ( groups3708469109370488835omplex @ G @ S3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_right
% 5.52/5.88 thf(fact_8454_prod_Omono__neutral__right,axiom,
% 5.52/5.88 ! [T6: set_Extended_enat,S3: set_Extended_enat,G: extended_enat > complex] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ T6 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ( groups4622424608036095791omplex @ G @ T6 )
% 5.52/5.88 = ( groups4622424608036095791omplex @ G @ S3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_right
% 5.52/5.88 thf(fact_8455_prod_Omono__neutral__right,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,G: int > real] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ( groups2316167850115554303t_real @ G @ T6 )
% 5.52/5.88 = ( groups2316167850115554303t_real @ G @ S3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_right
% 5.52/5.88 thf(fact_8456_prod_Omono__neutral__right,axiom,
% 5.52/5.88 ! [T6: set_complex,S3: set_complex,G: complex > real] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ T6 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ( groups766887009212190081x_real @ G @ T6 )
% 5.52/5.88 = ( groups766887009212190081x_real @ G @ S3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_right
% 5.52/5.88 thf(fact_8457_prod_Omono__neutral__right,axiom,
% 5.52/5.88 ! [T6: set_Extended_enat,S3: set_Extended_enat,G: extended_enat > real] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ T6 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ( groups97031904164794029t_real @ G @ T6 )
% 5.52/5.88 = ( groups97031904164794029t_real @ G @ S3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_right
% 5.52/5.88 thf(fact_8458_prod_Omono__neutral__right,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,G: int > rat] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ( groups1072433553688619179nt_rat @ G @ T6 )
% 5.52/5.88 = ( groups1072433553688619179nt_rat @ G @ S3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_right
% 5.52/5.88 thf(fact_8459_prod_Omono__neutral__right,axiom,
% 5.52/5.88 ! [T6: set_complex,S3: set_complex,G: complex > rat] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ T6 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ( groups225925009352817453ex_rat @ G @ T6 )
% 5.52/5.88 = ( groups225925009352817453ex_rat @ G @ S3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_right
% 5.52/5.88 thf(fact_8460_prod_Omono__neutral__right,axiom,
% 5.52/5.88 ! [T6: set_Extended_enat,S3: set_Extended_enat,G: extended_enat > rat] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ T6 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ( groups2245840878043517529at_rat @ G @ T6 )
% 5.52/5.88 = ( groups2245840878043517529at_rat @ G @ S3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_right
% 5.52/5.88 thf(fact_8461_prod_Omono__neutral__right,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,G: int > nat] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_nat ) )
% 5.52/5.88 => ( ( groups1707563613775114915nt_nat @ G @ T6 )
% 5.52/5.88 = ( groups1707563613775114915nt_nat @ G @ S3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_right
% 5.52/5.88 thf(fact_8462_prod_Omono__neutral__cong__left,axiom,
% 5.52/5.88 ! [T6: set_real,S3: set_real,H2: real > complex,G: real > complex] :
% 5.52/5.88 ( ( finite_finite_real @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: real] :
% 5.52/5.88 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.52/5.88 => ( ( H2 @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ! [X4: real] :
% 5.52/5.88 ( ( member_real @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.52/5.88 = ( groups713298508707869441omplex @ H2 @ T6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_left
% 5.52/5.88 thf(fact_8463_prod_Omono__neutral__cong__left,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,H2: int > complex,G: int > complex] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( H2 @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups7440179247065528705omplex @ G @ S3 )
% 5.52/5.88 = ( groups7440179247065528705omplex @ H2 @ T6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_left
% 5.52/5.88 thf(fact_8464_prod_Omono__neutral__cong__left,axiom,
% 5.52/5.88 ! [T6: set_complex,S3: set_complex,H2: complex > complex,G: complex > complex] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ T6 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.52/5.88 => ( ( H2 @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.52/5.88 = ( groups3708469109370488835omplex @ H2 @ T6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_left
% 5.52/5.88 thf(fact_8465_prod_Omono__neutral__cong__left,axiom,
% 5.52/5.88 ! [T6: set_Extended_enat,S3: set_Extended_enat,H2: extended_enat > complex,G: extended_enat > complex] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ T6 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T6 @ S3 ) )
% 5.52/5.88 => ( ( H2 @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups4622424608036095791omplex @ G @ S3 )
% 5.52/5.88 = ( groups4622424608036095791omplex @ H2 @ T6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_left
% 5.52/5.88 thf(fact_8466_prod_Omono__neutral__cong__left,axiom,
% 5.52/5.88 ! [T6: set_real,S3: set_real,H2: real > real,G: real > real] :
% 5.52/5.88 ( ( finite_finite_real @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: real] :
% 5.52/5.88 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.52/5.88 => ( ( H2 @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ! [X4: real] :
% 5.52/5.88 ( ( member_real @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups1681761925125756287l_real @ G @ S3 )
% 5.52/5.88 = ( groups1681761925125756287l_real @ H2 @ T6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_left
% 5.52/5.88 thf(fact_8467_prod_Omono__neutral__cong__left,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,H2: int > real,G: int > real] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( H2 @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups2316167850115554303t_real @ G @ S3 )
% 5.52/5.88 = ( groups2316167850115554303t_real @ H2 @ T6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_left
% 5.52/5.88 thf(fact_8468_prod_Omono__neutral__cong__left,axiom,
% 5.52/5.88 ! [T6: set_complex,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ T6 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.52/5.88 => ( ( H2 @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups766887009212190081x_real @ G @ S3 )
% 5.52/5.88 = ( groups766887009212190081x_real @ H2 @ T6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_left
% 5.52/5.88 thf(fact_8469_prod_Omono__neutral__cong__left,axiom,
% 5.52/5.88 ! [T6: set_Extended_enat,S3: set_Extended_enat,H2: extended_enat > real,G: extended_enat > real] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ T6 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T6 @ S3 ) )
% 5.52/5.88 => ( ( H2 @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups97031904164794029t_real @ G @ S3 )
% 5.52/5.88 = ( groups97031904164794029t_real @ H2 @ T6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_left
% 5.52/5.88 thf(fact_8470_prod_Omono__neutral__cong__left,axiom,
% 5.52/5.88 ! [T6: set_real,S3: set_real,H2: real > rat,G: real > rat] :
% 5.52/5.88 ( ( finite_finite_real @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: real] :
% 5.52/5.88 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.52/5.88 => ( ( H2 @ X4 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ! [X4: real] :
% 5.52/5.88 ( ( member_real @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups4061424788464935467al_rat @ G @ S3 )
% 5.52/5.88 = ( groups4061424788464935467al_rat @ H2 @ T6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_left
% 5.52/5.88 thf(fact_8471_prod_Omono__neutral__cong__left,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,H2: int > rat,G: int > rat] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( H2 @ X4 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups1072433553688619179nt_rat @ G @ S3 )
% 5.52/5.88 = ( groups1072433553688619179nt_rat @ H2 @ T6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_left
% 5.52/5.88 thf(fact_8472_prod_Omono__neutral__cong__right,axiom,
% 5.52/5.88 ! [T6: set_real,S3: set_real,G: real > complex,H2: real > complex] :
% 5.52/5.88 ( ( finite_finite_real @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: real] :
% 5.52/5.88 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ! [X4: real] :
% 5.52/5.88 ( ( member_real @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups713298508707869441omplex @ G @ T6 )
% 5.52/5.88 = ( groups713298508707869441omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_right
% 5.52/5.88 thf(fact_8473_prod_Omono__neutral__cong__right,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,G: int > complex,H2: int > complex] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups7440179247065528705omplex @ G @ T6 )
% 5.52/5.88 = ( groups7440179247065528705omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_right
% 5.52/5.88 thf(fact_8474_prod_Omono__neutral__cong__right,axiom,
% 5.52/5.88 ! [T6: set_complex,S3: set_complex,G: complex > complex,H2: complex > complex] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ T6 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups3708469109370488835omplex @ G @ T6 )
% 5.52/5.88 = ( groups3708469109370488835omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_right
% 5.52/5.88 thf(fact_8475_prod_Omono__neutral__cong__right,axiom,
% 5.52/5.88 ! [T6: set_Extended_enat,S3: set_Extended_enat,G: extended_enat > complex,H2: extended_enat > complex] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ T6 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_complex ) )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups4622424608036095791omplex @ G @ T6 )
% 5.52/5.88 = ( groups4622424608036095791omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_right
% 5.52/5.88 thf(fact_8476_prod_Omono__neutral__cong__right,axiom,
% 5.52/5.88 ! [T6: set_real,S3: set_real,G: real > real,H2: real > real] :
% 5.52/5.88 ( ( finite_finite_real @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: real] :
% 5.52/5.88 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ! [X4: real] :
% 5.52/5.88 ( ( member_real @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups1681761925125756287l_real @ G @ T6 )
% 5.52/5.88 = ( groups1681761925125756287l_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_right
% 5.52/5.88 thf(fact_8477_prod_Omono__neutral__cong__right,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,G: int > real,H2: int > real] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups2316167850115554303t_real @ G @ T6 )
% 5.52/5.88 = ( groups2316167850115554303t_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_right
% 5.52/5.88 thf(fact_8478_prod_Omono__neutral__cong__right,axiom,
% 5.52/5.88 ! [T6: set_complex,S3: set_complex,G: complex > real,H2: complex > real] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ T6 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ! [X4: complex] :
% 5.52/5.88 ( ( member_complex @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups766887009212190081x_real @ G @ T6 )
% 5.52/5.88 = ( groups766887009212190081x_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_right
% 5.52/5.88 thf(fact_8479_prod_Omono__neutral__cong__right,axiom,
% 5.52/5.88 ! [T6: set_Extended_enat,S3: set_Extended_enat,G: extended_enat > real,H2: extended_enat > real] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ T6 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_real ) )
% 5.52/5.88 => ( ! [X4: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups97031904164794029t_real @ G @ T6 )
% 5.52/5.88 = ( groups97031904164794029t_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_right
% 5.52/5.88 thf(fact_8480_prod_Omono__neutral__cong__right,axiom,
% 5.52/5.88 ! [T6: set_real,S3: set_real,G: real > rat,H2: real > rat] :
% 5.52/5.88 ( ( finite_finite_real @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: real] :
% 5.52/5.88 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ! [X4: real] :
% 5.52/5.88 ( ( member_real @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups4061424788464935467al_rat @ G @ T6 )
% 5.52/5.88 = ( groups4061424788464935467al_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_right
% 5.52/5.88 thf(fact_8481_prod_Omono__neutral__cong__right,axiom,
% 5.52/5.88 ! [T6: set_int,S3: set_int,G: int > rat,H2: int > rat] :
% 5.52/5.88 ( ( finite_finite_int @ T6 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = one_one_rat ) )
% 5.52/5.88 => ( ! [X4: int] :
% 5.52/5.88 ( ( member_int @ X4 @ S3 )
% 5.52/5.88 => ( ( G @ X4 )
% 5.52/5.88 = ( H2 @ X4 ) ) )
% 5.52/5.88 => ( ( groups1072433553688619179nt_rat @ G @ T6 )
% 5.52/5.88 = ( groups1072433553688619179nt_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.mono_neutral_cong_right
% 5.52/5.88 thf(fact_8482_prod_OatLeast0__atMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > real,N: nat] :
% 5.52/5.88 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atLeast0_atMost_Suc
% 5.52/5.88 thf(fact_8483_prod_OatLeast0__atMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > rat,N: nat] :
% 5.52/5.88 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atLeast0_atMost_Suc
% 5.52/5.88 thf(fact_8484_prod_OatLeast0__atMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > nat,N: nat] :
% 5.52/5.88 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atLeast0_atMost_Suc
% 5.52/5.88 thf(fact_8485_prod_OatLeast0__atMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > int,N: nat] :
% 5.52/5.88 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atLeast0_atMost_Suc
% 5.52/5.88 thf(fact_8486_prod_Onat__ivl__Suc_H,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > real] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.88 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_real @ ( G @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.nat_ivl_Suc'
% 5.52/5.88 thf(fact_8487_prod_Onat__ivl__Suc_H,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > rat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.88 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_rat @ ( G @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.nat_ivl_Suc'
% 5.52/5.88 thf(fact_8488_prod_Onat__ivl__Suc_H,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.88 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_nat @ ( G @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.nat_ivl_Suc'
% 5.52/5.88 thf(fact_8489_prod_Onat__ivl__Suc_H,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > int] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.52/5.88 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_int @ ( G @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.nat_ivl_Suc'
% 5.52/5.88 thf(fact_8490_prod_OatLeast__Suc__atMost,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > real] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.88 = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atLeast_Suc_atMost
% 5.52/5.88 thf(fact_8491_prod_OatLeast__Suc__atMost,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > rat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.88 = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atLeast_Suc_atMost
% 5.52/5.88 thf(fact_8492_prod_OatLeast__Suc__atMost,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.88 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atLeast_Suc_atMost
% 5.52/5.88 thf(fact_8493_prod_OatLeast__Suc__atMost,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > int] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.88 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atLeast_Suc_atMost
% 5.52/5.88 thf(fact_8494_prod_OlessThan__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > real,N: nat] :
% 5.52/5.88 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups129246275422532515t_real
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.lessThan_Suc_shift
% 5.52/5.88 thf(fact_8495_prod_OlessThan__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > rat,N: nat] :
% 5.52/5.88 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups73079841787564623at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.lessThan_Suc_shift
% 5.52/5.88 thf(fact_8496_prod_OlessThan__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > nat,N: nat] :
% 5.52/5.88 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.lessThan_Suc_shift
% 5.52/5.88 thf(fact_8497_prod_OlessThan__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > int,N: nat] :
% 5.52/5.88 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.lessThan_Suc_shift
% 5.52/5.88 thf(fact_8498_prod_OSuc__reindex__ivl,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > real] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_real @ ( G @ M )
% 5.52/5.88 @ ( groups129246275422532515t_real
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.Suc_reindex_ivl
% 5.52/5.88 thf(fact_8499_prod_OSuc__reindex__ivl,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > rat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_rat @ ( G @ M )
% 5.52/5.88 @ ( groups73079841787564623at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.Suc_reindex_ivl
% 5.52/5.88 thf(fact_8500_prod_OSuc__reindex__ivl,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_nat @ ( G @ M )
% 5.52/5.88 @ ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.Suc_reindex_ivl
% 5.52/5.88 thf(fact_8501_prod_OSuc__reindex__ivl,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > int] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_int @ ( G @ M )
% 5.52/5.88 @ ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.Suc_reindex_ivl
% 5.52/5.88 thf(fact_8502_fact__prod,axiom,
% 5.52/5.88 ( semiri1406184849735516958ct_int
% 5.52/5.88 = ( ^ [N3: nat] :
% 5.52/5.88 ( semiri1314217659103216013at_int
% 5.52/5.88 @ ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [X: nat] : X
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_prod
% 5.52/5.88 thf(fact_8503_fact__prod,axiom,
% 5.52/5.88 ( semiri773545260158071498ct_rat
% 5.52/5.88 = ( ^ [N3: nat] :
% 5.52/5.88 ( semiri681578069525770553at_rat
% 5.52/5.88 @ ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [X: nat] : X
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_prod
% 5.52/5.88 thf(fact_8504_fact__prod,axiom,
% 5.52/5.88 ( semiri4449623510593786356d_enat
% 5.52/5.88 = ( ^ [N3: nat] :
% 5.52/5.88 ( semiri4216267220026989637d_enat
% 5.52/5.88 @ ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [X: nat] : X
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_prod
% 5.52/5.88 thf(fact_8505_fact__prod,axiom,
% 5.52/5.88 ( semiri2265585572941072030t_real
% 5.52/5.88 = ( ^ [N3: nat] :
% 5.52/5.88 ( semiri5074537144036343181t_real
% 5.52/5.88 @ ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [X: nat] : X
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_prod
% 5.52/5.88 thf(fact_8506_fact__prod,axiom,
% 5.52/5.88 ( semiri1408675320244567234ct_nat
% 5.52/5.88 = ( ^ [N3: nat] :
% 5.52/5.88 ( semiri1316708129612266289at_nat
% 5.52/5.88 @ ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [X: nat] : X
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_prod
% 5.52/5.88 thf(fact_8507_prod__mono__strict,axiom,
% 5.52/5.88 ! [A2: set_real,F: real > real,G: real > real] :
% 5.52/5.88 ( ( finite_finite_real @ A2 )
% 5.52/5.88 => ( ! [I2: real] :
% 5.52/5.88 ( ( member_real @ I2 @ A2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.52/5.88 & ( ord_less_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.88 => ( ( A2 != bot_bot_set_real )
% 5.52/5.88 => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono_strict
% 5.52/5.88 thf(fact_8508_prod__mono__strict,axiom,
% 5.52/5.88 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ! [I2: complex] :
% 5.52/5.88 ( ( member_complex @ I2 @ A2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.52/5.88 & ( ord_less_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.88 => ( ( A2 != bot_bot_set_complex )
% 5.52/5.88 => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono_strict
% 5.52/5.88 thf(fact_8509_prod__mono__strict,axiom,
% 5.52/5.88 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.52/5.88 ( ( finite_finite_nat @ A2 )
% 5.52/5.88 => ( ! [I2: nat] :
% 5.52/5.88 ( ( member_nat @ I2 @ A2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.52/5.88 & ( ord_less_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.88 => ( ( A2 != bot_bot_set_nat )
% 5.52/5.88 => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono_strict
% 5.52/5.88 thf(fact_8510_prod__mono__strict,axiom,
% 5.52/5.88 ! [A2: set_int,F: int > real,G: int > real] :
% 5.52/5.88 ( ( finite_finite_int @ A2 )
% 5.52/5.88 => ( ! [I2: int] :
% 5.52/5.88 ( ( member_int @ I2 @ A2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.52/5.88 & ( ord_less_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.88 => ( ( A2 != bot_bot_set_int )
% 5.52/5.88 => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono_strict
% 5.52/5.88 thf(fact_8511_prod__mono__strict,axiom,
% 5.52/5.88 ! [A2: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.88 => ( ! [I2: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ I2 @ A2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.52/5.88 & ( ord_less_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.88 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 5.52/5.88 => ( ord_less_real @ ( groups97031904164794029t_real @ F @ A2 ) @ ( groups97031904164794029t_real @ G @ A2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono_strict
% 5.52/5.88 thf(fact_8512_prod__mono__strict,axiom,
% 5.52/5.88 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.52/5.88 ( ( finite_finite_real @ A2 )
% 5.52/5.88 => ( ! [I2: real] :
% 5.52/5.88 ( ( member_real @ I2 @ A2 )
% 5.52/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.52/5.88 & ( ord_less_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.88 => ( ( A2 != bot_bot_set_real )
% 5.52/5.88 => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono_strict
% 5.52/5.88 thf(fact_8513_prod__mono__strict,axiom,
% 5.52/5.88 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ! [I2: complex] :
% 5.52/5.88 ( ( member_complex @ I2 @ A2 )
% 5.52/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.52/5.88 & ( ord_less_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.88 => ( ( A2 != bot_bot_set_complex )
% 5.52/5.88 => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono_strict
% 5.52/5.88 thf(fact_8514_prod__mono__strict,axiom,
% 5.52/5.88 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.52/5.88 ( ( finite_finite_nat @ A2 )
% 5.52/5.88 => ( ! [I2: nat] :
% 5.52/5.88 ( ( member_nat @ I2 @ A2 )
% 5.52/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.52/5.88 & ( ord_less_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.88 => ( ( A2 != bot_bot_set_nat )
% 5.52/5.88 => ( ord_less_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono_strict
% 5.52/5.88 thf(fact_8515_prod__mono__strict,axiom,
% 5.52/5.88 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.52/5.88 ( ( finite_finite_int @ A2 )
% 5.52/5.88 => ( ! [I2: int] :
% 5.52/5.88 ( ( member_int @ I2 @ A2 )
% 5.52/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.52/5.88 & ( ord_less_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.88 => ( ( A2 != bot_bot_set_int )
% 5.52/5.88 => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono_strict
% 5.52/5.88 thf(fact_8516_prod__mono__strict,axiom,
% 5.52/5.88 ! [A2: set_Extended_enat,F: extended_enat > rat,G: extended_enat > rat] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.88 => ( ! [I2: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ I2 @ A2 )
% 5.52/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.52/5.88 & ( ord_less_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.52/5.88 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 5.52/5.88 => ( ord_less_rat @ ( groups2245840878043517529at_rat @ F @ A2 ) @ ( groups2245840878043517529at_rat @ G @ A2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono_strict
% 5.52/5.88 thf(fact_8517_even__prod__iff,axiom,
% 5.52/5.88 ! [A2: set_nat,F: nat > code_integer] :
% 5.52/5.88 ( ( finite_finite_nat @ A2 )
% 5.52/5.88 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3455450783089532116nteger @ F @ A2 ) )
% 5.52/5.88 = ( ? [X: nat] :
% 5.52/5.88 ( ( member_nat @ X @ A2 )
% 5.52/5.88 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % even_prod_iff
% 5.52/5.88 thf(fact_8518_even__prod__iff,axiom,
% 5.52/5.88 ! [A2: set_int,F: int > code_integer] :
% 5.52/5.88 ( ( finite_finite_int @ A2 )
% 5.52/5.88 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3827104343326376752nteger @ F @ A2 ) )
% 5.52/5.88 = ( ? [X: int] :
% 5.52/5.88 ( ( member_int @ X @ A2 )
% 5.52/5.88 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % even_prod_iff
% 5.52/5.88 thf(fact_8519_even__prod__iff,axiom,
% 5.52/5.88 ! [A2: set_complex,F: complex > code_integer] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups8682486955453173170nteger @ F @ A2 ) )
% 5.52/5.88 = ( ? [X: complex] :
% 5.52/5.88 ( ( member_complex @ X @ A2 )
% 5.52/5.88 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % even_prod_iff
% 5.52/5.88 thf(fact_8520_even__prod__iff,axiom,
% 5.52/5.88 ! [A2: set_Extended_enat,F: extended_enat > code_integer] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.88 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups845124408420398302nteger @ F @ A2 ) )
% 5.52/5.88 = ( ? [X: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X @ A2 )
% 5.52/5.88 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % even_prod_iff
% 5.52/5.88 thf(fact_8521_even__prod__iff,axiom,
% 5.52/5.88 ! [A2: set_int,F: int > nat] :
% 5.52/5.88 ( ( finite_finite_int @ A2 )
% 5.52/5.88 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 5.52/5.88 = ( ? [X: int] :
% 5.52/5.88 ( ( member_int @ X @ A2 )
% 5.52/5.88 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % even_prod_iff
% 5.52/5.88 thf(fact_8522_even__prod__iff,axiom,
% 5.52/5.88 ! [A2: set_complex,F: complex > nat] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 5.52/5.88 = ( ? [X: complex] :
% 5.52/5.88 ( ( member_complex @ X @ A2 )
% 5.52/5.88 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % even_prod_iff
% 5.52/5.88 thf(fact_8523_even__prod__iff,axiom,
% 5.52/5.88 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.88 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups2880970938130013265at_nat @ F @ A2 ) )
% 5.52/5.88 = ( ? [X: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X @ A2 )
% 5.52/5.88 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % even_prod_iff
% 5.52/5.88 thf(fact_8524_even__prod__iff,axiom,
% 5.52/5.88 ! [A2: set_complex,F: complex > int] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A2 ) )
% 5.52/5.88 = ( ? [X: complex] :
% 5.52/5.88 ( ( member_complex @ X @ A2 )
% 5.52/5.88 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % even_prod_iff
% 5.52/5.88 thf(fact_8525_even__prod__iff,axiom,
% 5.52/5.88 ! [A2: set_Extended_enat,F: extended_enat > int] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.88 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups2878480467620962989at_int @ F @ A2 ) )
% 5.52/5.88 = ( ? [X: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X @ A2 )
% 5.52/5.88 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % even_prod_iff
% 5.52/5.88 thf(fact_8526_even__prod__iff,axiom,
% 5.52/5.88 ! [A2: set_nat,F: nat > nat] :
% 5.52/5.88 ( ( finite_finite_nat @ A2 )
% 5.52/5.88 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.52/5.88 = ( ? [X: nat] :
% 5.52/5.88 ( ( member_nat @ X @ A2 )
% 5.52/5.88 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % even_prod_iff
% 5.52/5.88 thf(fact_8527_prod_Oinsert__remove,axiom,
% 5.52/5.88 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,X2: vEBT_VEBT] :
% 5.52/5.88 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.88 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.88 = ( times_times_real @ ( G @ X2 ) @ ( groups2703838992350267259T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.insert_remove
% 5.52/5.88 thf(fact_8528_prod_Oinsert__remove,axiom,
% 5.52/5.88 ! [A2: set_complex,G: complex > real,X2: complex] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.88 = ( times_times_real @ ( G @ X2 ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.insert_remove
% 5.52/5.88 thf(fact_8529_prod_Oinsert__remove,axiom,
% 5.52/5.88 ! [A2: set_nat,G: nat > real,X2: nat] :
% 5.52/5.88 ( ( finite_finite_nat @ A2 )
% 5.52/5.88 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.52/5.88 = ( times_times_real @ ( G @ X2 ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.insert_remove
% 5.52/5.88 thf(fact_8530_prod_Oinsert__remove,axiom,
% 5.52/5.88 ! [A2: set_int,G: int > real,X2: int] :
% 5.52/5.88 ( ( finite_finite_int @ A2 )
% 5.52/5.88 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.88 = ( times_times_real @ ( G @ X2 ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.insert_remove
% 5.52/5.88 thf(fact_8531_prod_Oinsert__remove,axiom,
% 5.52/5.88 ! [A2: set_Extended_enat,G: extended_enat > real,X2: extended_enat] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.88 => ( ( groups97031904164794029t_real @ G @ ( insert_Extended_enat @ X2 @ A2 ) )
% 5.52/5.88 = ( times_times_real @ ( G @ X2 ) @ ( groups97031904164794029t_real @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.insert_remove
% 5.52/5.88 thf(fact_8532_prod_Oinsert__remove,axiom,
% 5.52/5.88 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > rat,X2: vEBT_VEBT] :
% 5.52/5.88 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.88 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.52/5.88 = ( times_times_rat @ ( G @ X2 ) @ ( groups5726676334696518183BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.insert_remove
% 5.52/5.88 thf(fact_8533_prod_Oinsert__remove,axiom,
% 5.52/5.88 ! [A2: set_complex,G: complex > rat,X2: complex] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.52/5.88 = ( times_times_rat @ ( G @ X2 ) @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.insert_remove
% 5.52/5.88 thf(fact_8534_prod_Oinsert__remove,axiom,
% 5.52/5.88 ! [A2: set_nat,G: nat > rat,X2: nat] :
% 5.52/5.88 ( ( finite_finite_nat @ A2 )
% 5.52/5.88 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.52/5.88 = ( times_times_rat @ ( G @ X2 ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.insert_remove
% 5.52/5.88 thf(fact_8535_prod_Oinsert__remove,axiom,
% 5.52/5.88 ! [A2: set_int,G: int > rat,X2: int] :
% 5.52/5.88 ( ( finite_finite_int @ A2 )
% 5.52/5.88 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X2 @ A2 ) )
% 5.52/5.88 = ( times_times_rat @ ( G @ X2 ) @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.insert_remove
% 5.52/5.88 thf(fact_8536_prod_Oinsert__remove,axiom,
% 5.52/5.88 ! [A2: set_Extended_enat,G: extended_enat > rat,X2: extended_enat] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.88 => ( ( groups2245840878043517529at_rat @ G @ ( insert_Extended_enat @ X2 @ A2 ) )
% 5.52/5.88 = ( times_times_rat @ ( G @ X2 ) @ ( groups2245840878043517529at_rat @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.insert_remove
% 5.52/5.88 thf(fact_8537_prod_Oremove,axiom,
% 5.52/5.88 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.52/5.88 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.88 => ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.88 => ( ( groups2703838992350267259T_real @ G @ A2 )
% 5.52/5.88 = ( times_times_real @ ( G @ X2 ) @ ( groups2703838992350267259T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.remove
% 5.52/5.88 thf(fact_8538_prod_Oremove,axiom,
% 5.52/5.88 ! [A2: set_real,X2: real,G: real > real] :
% 5.52/5.88 ( ( finite_finite_real @ A2 )
% 5.52/5.88 => ( ( member_real @ X2 @ A2 )
% 5.52/5.88 => ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.52/5.88 = ( times_times_real @ ( G @ X2 ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.remove
% 5.52/5.88 thf(fact_8539_prod_Oremove,axiom,
% 5.52/5.88 ! [A2: set_complex,X2: complex,G: complex > real] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ( member_complex @ X2 @ A2 )
% 5.52/5.88 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.52/5.88 = ( times_times_real @ ( G @ X2 ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.remove
% 5.52/5.88 thf(fact_8540_prod_Oremove,axiom,
% 5.52/5.88 ! [A2: set_nat,X2: nat,G: nat > real] :
% 5.52/5.88 ( ( finite_finite_nat @ A2 )
% 5.52/5.88 => ( ( member_nat @ X2 @ A2 )
% 5.52/5.88 => ( ( groups129246275422532515t_real @ G @ A2 )
% 5.52/5.88 = ( times_times_real @ ( G @ X2 ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.remove
% 5.52/5.88 thf(fact_8541_prod_Oremove,axiom,
% 5.52/5.88 ! [A2: set_int,X2: int,G: int > real] :
% 5.52/5.88 ( ( finite_finite_int @ A2 )
% 5.52/5.88 => ( ( member_int @ X2 @ A2 )
% 5.52/5.88 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.52/5.88 = ( times_times_real @ ( G @ X2 ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.remove
% 5.52/5.88 thf(fact_8542_prod_Oremove,axiom,
% 5.52/5.88 ! [A2: set_Extended_enat,X2: extended_enat,G: extended_enat > real] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.88 => ( ( member_Extended_enat @ X2 @ A2 )
% 5.52/5.88 => ( ( groups97031904164794029t_real @ G @ A2 )
% 5.52/5.88 = ( times_times_real @ ( G @ X2 ) @ ( groups97031904164794029t_real @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.remove
% 5.52/5.88 thf(fact_8543_prod_Oremove,axiom,
% 5.52/5.88 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.52/5.88 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.88 => ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.52/5.88 => ( ( groups5726676334696518183BT_rat @ G @ A2 )
% 5.52/5.88 = ( times_times_rat @ ( G @ X2 ) @ ( groups5726676334696518183BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.remove
% 5.52/5.88 thf(fact_8544_prod_Oremove,axiom,
% 5.52/5.88 ! [A2: set_real,X2: real,G: real > rat] :
% 5.52/5.88 ( ( finite_finite_real @ A2 )
% 5.52/5.88 => ( ( member_real @ X2 @ A2 )
% 5.52/5.88 => ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.52/5.88 = ( times_times_rat @ ( G @ X2 ) @ ( groups4061424788464935467al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.remove
% 5.52/5.88 thf(fact_8545_prod_Oremove,axiom,
% 5.52/5.88 ! [A2: set_complex,X2: complex,G: complex > rat] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ( member_complex @ X2 @ A2 )
% 5.52/5.88 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.52/5.88 = ( times_times_rat @ ( G @ X2 ) @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.remove
% 5.52/5.88 thf(fact_8546_prod_Oremove,axiom,
% 5.52/5.88 ! [A2: set_nat,X2: nat,G: nat > rat] :
% 5.52/5.88 ( ( finite_finite_nat @ A2 )
% 5.52/5.88 => ( ( member_nat @ X2 @ A2 )
% 5.52/5.88 => ( ( groups73079841787564623at_rat @ G @ A2 )
% 5.52/5.88 = ( times_times_rat @ ( G @ X2 ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.remove
% 5.52/5.88 thf(fact_8547_prod_Oub__add__nat,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.52/5.88 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.52/5.88 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.ub_add_nat
% 5.52/5.88 thf(fact_8548_prod_Oub__add__nat,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > rat,P6: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.52/5.88 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.52/5.88 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.ub_add_nat
% 5.52/5.88 thf(fact_8549_prod_Oub__add__nat,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.52/5.88 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.52/5.88 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.ub_add_nat
% 5.52/5.88 thf(fact_8550_prod_Oub__add__nat,axiom,
% 5.52/5.88 ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.52/5.88 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.52/5.88 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.ub_add_nat
% 5.52/5.88 thf(fact_8551_arcsin__less__arcsin,axiom,
% 5.52/5.88 ! [X2: real,Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.88 => ( ( ord_less_real @ X2 @ Y2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.52/5.88 => ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arcsin_less_arcsin
% 5.52/5.88 thf(fact_8552_arcsin__less__mono,axiom,
% 5.52/5.88 ! [X2: real,Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.52/5.88 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.52/5.88 => ( ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y2 ) )
% 5.52/5.88 = ( ord_less_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arcsin_less_mono
% 5.52/5.88 thf(fact_8553_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.52/5.88 ( set_fo2584398358068434914at_nat
% 5.52/5.88 = ( ^ [F3: nat > nat > nat,A4: nat,B3: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B3 @ A4 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A4 @ one_one_nat ) @ B3 @ ( F3 @ A4 @ Acc2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fold_atLeastAtMost_nat.simps
% 5.52/5.88 thf(fact_8554_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.52/5.88 ! [X2: nat > nat > nat,Xa2: nat,Xb: nat,Xc: nat,Y2: nat] :
% 5.52/5.88 ( ( ( set_fo2584398358068434914at_nat @ X2 @ Xa2 @ Xb @ Xc )
% 5.52/5.88 = Y2 )
% 5.52/5.88 => ( ( ( ord_less_nat @ Xb @ Xa2 )
% 5.52/5.88 => ( Y2 = Xc ) )
% 5.52/5.88 & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 5.52/5.88 => ( Y2
% 5.52/5.88 = ( set_fo2584398358068434914at_nat @ X2 @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X2 @ Xa2 @ Xc ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fold_atLeastAtMost_nat.elims
% 5.52/5.88 thf(fact_8555_prod_Odelta__remove,axiom,
% 5.52/5.88 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 5.52/5.88 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.52/5.88 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.52/5.88 => ( ( groups2703838992350267259T_real
% 5.52/5.88 @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( times_times_real @ ( B @ A ) @ ( groups2703838992350267259T_real @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.52/5.88 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.52/5.88 => ( ( groups2703838992350267259T_real
% 5.52/5.88 @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( groups2703838992350267259T_real @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.delta_remove
% 5.52/5.88 thf(fact_8556_prod_Odelta__remove,axiom,
% 5.52/5.88 ! [S3: set_real,A: real,B: real > real,C: real > real] :
% 5.52/5.88 ( ( finite_finite_real @ S3 )
% 5.52/5.88 => ( ( ( member_real @ A @ S3 )
% 5.52/5.88 => ( ( groups1681761925125756287l_real
% 5.52/5.88 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( times_times_real @ ( B @ A ) @ ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.52/5.88 & ( ~ ( member_real @ A @ S3 )
% 5.52/5.88 => ( ( groups1681761925125756287l_real
% 5.52/5.88 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.delta_remove
% 5.52/5.88 thf(fact_8557_prod_Odelta__remove,axiom,
% 5.52/5.88 ! [S3: set_complex,A: complex,B: complex > real,C: complex > real] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.88 => ( ( ( member_complex @ A @ S3 )
% 5.52/5.88 => ( ( groups766887009212190081x_real
% 5.52/5.88 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( times_times_real @ ( B @ A ) @ ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.52/5.88 & ( ~ ( member_complex @ A @ S3 )
% 5.52/5.88 => ( ( groups766887009212190081x_real
% 5.52/5.88 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.delta_remove
% 5.52/5.88 thf(fact_8558_prod_Odelta__remove,axiom,
% 5.52/5.88 ! [S3: set_nat,A: nat,B: nat > real,C: nat > real] :
% 5.52/5.88 ( ( finite_finite_nat @ S3 )
% 5.52/5.88 => ( ( ( member_nat @ A @ S3 )
% 5.52/5.88 => ( ( groups129246275422532515t_real
% 5.52/5.88 @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( times_times_real @ ( B @ A ) @ ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 5.52/5.88 & ( ~ ( member_nat @ A @ S3 )
% 5.52/5.88 => ( ( groups129246275422532515t_real
% 5.52/5.88 @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.delta_remove
% 5.52/5.88 thf(fact_8559_prod_Odelta__remove,axiom,
% 5.52/5.88 ! [S3: set_int,A: int,B: int > real,C: int > real] :
% 5.52/5.88 ( ( finite_finite_int @ S3 )
% 5.52/5.88 => ( ( ( member_int @ A @ S3 )
% 5.52/5.88 => ( ( groups2316167850115554303t_real
% 5.52/5.88 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( times_times_real @ ( B @ A ) @ ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.52/5.88 & ( ~ ( member_int @ A @ S3 )
% 5.52/5.88 => ( ( groups2316167850115554303t_real
% 5.52/5.88 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.delta_remove
% 5.52/5.88 thf(fact_8560_prod_Odelta__remove,axiom,
% 5.52/5.88 ! [S3: set_Extended_enat,A: extended_enat,B: extended_enat > real,C: extended_enat > real] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ S3 )
% 5.52/5.88 => ( ( ( member_Extended_enat @ A @ S3 )
% 5.52/5.88 => ( ( groups97031904164794029t_real
% 5.52/5.88 @ ^ [K2: extended_enat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( times_times_real @ ( B @ A ) @ ( groups97031904164794029t_real @ C @ ( minus_925952699566721837d_enat @ S3 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 5.52/5.88 & ( ~ ( member_Extended_enat @ A @ S3 )
% 5.52/5.88 => ( ( groups97031904164794029t_real
% 5.52/5.88 @ ^ [K2: extended_enat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( groups97031904164794029t_real @ C @ ( minus_925952699566721837d_enat @ S3 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.delta_remove
% 5.52/5.88 thf(fact_8561_prod_Odelta__remove,axiom,
% 5.52/5.88 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C: vEBT_VEBT > rat] :
% 5.52/5.88 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.52/5.88 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.52/5.88 => ( ( groups5726676334696518183BT_rat
% 5.52/5.88 @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( times_times_rat @ ( B @ A ) @ ( groups5726676334696518183BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.52/5.88 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.52/5.88 => ( ( groups5726676334696518183BT_rat
% 5.52/5.88 @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( groups5726676334696518183BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.delta_remove
% 5.52/5.88 thf(fact_8562_prod_Odelta__remove,axiom,
% 5.52/5.88 ! [S3: set_real,A: real,B: real > rat,C: real > rat] :
% 5.52/5.88 ( ( finite_finite_real @ S3 )
% 5.52/5.88 => ( ( ( member_real @ A @ S3 )
% 5.52/5.88 => ( ( groups4061424788464935467al_rat
% 5.52/5.88 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( times_times_rat @ ( B @ A ) @ ( groups4061424788464935467al_rat @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.52/5.88 & ( ~ ( member_real @ A @ S3 )
% 5.52/5.88 => ( ( groups4061424788464935467al_rat
% 5.52/5.88 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( groups4061424788464935467al_rat @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.delta_remove
% 5.52/5.88 thf(fact_8563_prod_Odelta__remove,axiom,
% 5.52/5.88 ! [S3: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ S3 )
% 5.52/5.88 => ( ( ( member_complex @ A @ S3 )
% 5.52/5.88 => ( ( groups225925009352817453ex_rat
% 5.52/5.88 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( times_times_rat @ ( B @ A ) @ ( groups225925009352817453ex_rat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.52/5.88 & ( ~ ( member_complex @ A @ S3 )
% 5.52/5.88 => ( ( groups225925009352817453ex_rat
% 5.52/5.88 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( groups225925009352817453ex_rat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.delta_remove
% 5.52/5.88 thf(fact_8564_prod_Odelta__remove,axiom,
% 5.52/5.88 ! [S3: set_nat,A: nat,B: nat > rat,C: nat > rat] :
% 5.52/5.88 ( ( finite_finite_nat @ S3 )
% 5.52/5.88 => ( ( ( member_nat @ A @ S3 )
% 5.52/5.88 => ( ( groups73079841787564623at_rat
% 5.52/5.88 @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( times_times_rat @ ( B @ A ) @ ( groups73079841787564623at_rat @ C @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 5.52/5.88 & ( ~ ( member_nat @ A @ S3 )
% 5.52/5.88 => ( ( groups73079841787564623at_rat
% 5.52/5.88 @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.52/5.88 @ S3 )
% 5.52/5.88 = ( groups73079841787564623at_rat @ C @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.delta_remove
% 5.52/5.88 thf(fact_8565_fact__eq__fact__times,axiom,
% 5.52/5.88 ! [N: nat,M: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.88 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.52/5.88 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.52/5.88 @ ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [X: nat] : X
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_eq_fact_times
% 5.52/5.88 thf(fact_8566_prod__mono2,axiom,
% 5.52/5.88 ! [B4: set_real,A2: set_real,F: real > real] :
% 5.52/5.88 ( ( finite_finite_real @ B4 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.52/5.88 => ( ! [B2: real] :
% 5.52/5.88 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.52/5.88 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 5.52/5.88 => ( ! [A3: real] :
% 5.52/5.88 ( ( member_real @ A3 @ A2 )
% 5.52/5.88 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.52/5.88 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ F @ B4 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono2
% 5.52/5.88 thf(fact_8567_prod__mono2,axiom,
% 5.52/5.88 ! [B4: set_int,A2: set_int,F: int > real] :
% 5.52/5.88 ( ( finite_finite_int @ B4 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.52/5.88 => ( ! [B2: int] :
% 5.52/5.88 ( ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A2 ) )
% 5.52/5.88 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 5.52/5.88 => ( ! [A3: int] :
% 5.52/5.88 ( ( member_int @ A3 @ A2 )
% 5.52/5.88 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.52/5.88 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ F @ B4 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono2
% 5.52/5.88 thf(fact_8568_prod__mono2,axiom,
% 5.52/5.88 ! [B4: set_complex,A2: set_complex,F: complex > real] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ B4 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.52/5.88 => ( ! [B2: complex] :
% 5.52/5.88 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.52/5.88 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 5.52/5.88 => ( ! [A3: complex] :
% 5.52/5.88 ( ( member_complex @ A3 @ A2 )
% 5.52/5.88 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.52/5.88 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ F @ B4 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono2
% 5.52/5.88 thf(fact_8569_prod__mono2,axiom,
% 5.52/5.88 ! [B4: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > real] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ B4 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ A2 @ B4 )
% 5.52/5.88 => ( ! [B2: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ B4 @ A2 ) )
% 5.52/5.88 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 5.52/5.88 => ( ! [A3: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ A3 @ A2 )
% 5.52/5.88 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.52/5.88 => ( ord_less_eq_real @ ( groups97031904164794029t_real @ F @ A2 ) @ ( groups97031904164794029t_real @ F @ B4 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono2
% 5.52/5.88 thf(fact_8570_prod__mono2,axiom,
% 5.52/5.88 ! [B4: set_real,A2: set_real,F: real > rat] :
% 5.52/5.88 ( ( finite_finite_real @ B4 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.52/5.88 => ( ! [B2: real] :
% 5.52/5.88 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.52/5.88 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 5.52/5.88 => ( ! [A3: real] :
% 5.52/5.88 ( ( member_real @ A3 @ A2 )
% 5.52/5.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.52/5.88 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ F @ B4 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono2
% 5.52/5.88 thf(fact_8571_prod__mono2,axiom,
% 5.52/5.88 ! [B4: set_int,A2: set_int,F: int > rat] :
% 5.52/5.88 ( ( finite_finite_int @ B4 )
% 5.52/5.88 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.52/5.88 => ( ! [B2: int] :
% 5.52/5.88 ( ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A2 ) )
% 5.52/5.88 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 5.52/5.88 => ( ! [A3: int] :
% 5.52/5.88 ( ( member_int @ A3 @ A2 )
% 5.52/5.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.52/5.88 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ F @ B4 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono2
% 5.52/5.88 thf(fact_8572_prod__mono2,axiom,
% 5.52/5.88 ! [B4: set_complex,A2: set_complex,F: complex > rat] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ B4 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.52/5.88 => ( ! [B2: complex] :
% 5.52/5.88 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.52/5.88 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 5.52/5.88 => ( ! [A3: complex] :
% 5.52/5.88 ( ( member_complex @ A3 @ A2 )
% 5.52/5.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.52/5.88 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ F @ B4 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono2
% 5.52/5.88 thf(fact_8573_prod__mono2,axiom,
% 5.52/5.88 ! [B4: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > rat] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ B4 )
% 5.52/5.88 => ( ( ord_le7203529160286727270d_enat @ A2 @ B4 )
% 5.52/5.88 => ( ! [B2: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ B4 @ A2 ) )
% 5.52/5.88 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 5.52/5.88 => ( ! [A3: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ A3 @ A2 )
% 5.52/5.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.52/5.88 => ( ord_less_eq_rat @ ( groups2245840878043517529at_rat @ F @ A2 ) @ ( groups2245840878043517529at_rat @ F @ B4 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono2
% 5.52/5.88 thf(fact_8574_prod__mono2,axiom,
% 5.52/5.88 ! [B4: set_real,A2: set_real,F: real > int] :
% 5.52/5.88 ( ( finite_finite_real @ B4 )
% 5.52/5.88 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.52/5.88 => ( ! [B2: real] :
% 5.52/5.88 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.52/5.88 => ( ord_less_eq_int @ one_one_int @ ( F @ B2 ) ) )
% 5.52/5.88 => ( ! [A3: real] :
% 5.52/5.88 ( ( member_real @ A3 @ A2 )
% 5.52/5.88 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 5.52/5.88 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ F @ B4 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono2
% 5.52/5.88 thf(fact_8575_prod__mono2,axiom,
% 5.52/5.88 ! [B4: set_complex,A2: set_complex,F: complex > int] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ B4 )
% 5.52/5.88 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.52/5.88 => ( ! [B2: complex] :
% 5.52/5.88 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.52/5.88 => ( ord_less_eq_int @ one_one_int @ ( F @ B2 ) ) )
% 5.52/5.88 => ( ! [A3: complex] :
% 5.52/5.88 ( ( member_complex @ A3 @ A2 )
% 5.52/5.88 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 5.52/5.88 => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B4 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_mono2
% 5.52/5.88 thf(fact_8576_prod__diff1,axiom,
% 5.52/5.88 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > complex,A: vEBT_VEBT] :
% 5.52/5.88 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.88 => ( ( ( F @ A )
% 5.52/5.88 != zero_zero_complex )
% 5.52/5.88 => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 5.52/5.88 => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.52/5.88 = ( divide1717551699836669952omplex @ ( groups127312072573709053omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.52/5.88 & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 5.52/5.88 => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.52/5.88 = ( groups127312072573709053omplex @ F @ A2 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_diff1
% 5.52/5.88 thf(fact_8577_prod__diff1,axiom,
% 5.52/5.88 ! [A2: set_real,F: real > complex,A: real] :
% 5.52/5.88 ( ( finite_finite_real @ A2 )
% 5.52/5.88 => ( ( ( F @ A )
% 5.52/5.88 != zero_zero_complex )
% 5.52/5.88 => ( ( ( member_real @ A @ A2 )
% 5.52/5.88 => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.52/5.88 = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.52/5.88 & ( ~ ( member_real @ A @ A2 )
% 5.52/5.88 => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.52/5.88 = ( groups713298508707869441omplex @ F @ A2 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_diff1
% 5.52/5.88 thf(fact_8578_prod__diff1,axiom,
% 5.52/5.88 ! [A2: set_complex,F: complex > complex,A: complex] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ( ( F @ A )
% 5.52/5.88 != zero_zero_complex )
% 5.52/5.88 => ( ( ( member_complex @ A @ A2 )
% 5.52/5.88 => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.52/5.88 = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.52/5.88 & ( ~ ( member_complex @ A @ A2 )
% 5.52/5.88 => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.52/5.88 = ( groups3708469109370488835omplex @ F @ A2 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_diff1
% 5.52/5.88 thf(fact_8579_prod__diff1,axiom,
% 5.52/5.88 ! [A2: set_nat,F: nat > complex,A: nat] :
% 5.52/5.88 ( ( finite_finite_nat @ A2 )
% 5.52/5.88 => ( ( ( F @ A )
% 5.52/5.88 != zero_zero_complex )
% 5.52/5.88 => ( ( ( member_nat @ A @ A2 )
% 5.52/5.88 => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.52/5.88 = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.52/5.88 & ( ~ ( member_nat @ A @ A2 )
% 5.52/5.88 => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.52/5.88 = ( groups6464643781859351333omplex @ F @ A2 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_diff1
% 5.52/5.88 thf(fact_8580_prod__diff1,axiom,
% 5.52/5.88 ! [A2: set_int,F: int > complex,A: int] :
% 5.52/5.88 ( ( finite_finite_int @ A2 )
% 5.52/5.88 => ( ( ( F @ A )
% 5.52/5.88 != zero_zero_complex )
% 5.52/5.88 => ( ( ( member_int @ A @ A2 )
% 5.52/5.88 => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.52/5.88 = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.52/5.88 & ( ~ ( member_int @ A @ A2 )
% 5.52/5.88 => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.52/5.88 = ( groups7440179247065528705omplex @ F @ A2 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_diff1
% 5.52/5.88 thf(fact_8581_prod__diff1,axiom,
% 5.52/5.88 ! [A2: set_Extended_enat,F: extended_enat > complex,A: extended_enat] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.88 => ( ( ( F @ A )
% 5.52/5.88 != zero_zero_complex )
% 5.52/5.88 => ( ( ( member_Extended_enat @ A @ A2 )
% 5.52/5.88 => ( ( groups4622424608036095791omplex @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 5.52/5.88 = ( divide1717551699836669952omplex @ ( groups4622424608036095791omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.52/5.88 & ( ~ ( member_Extended_enat @ A @ A2 )
% 5.52/5.88 => ( ( groups4622424608036095791omplex @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 5.52/5.88 = ( groups4622424608036095791omplex @ F @ A2 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_diff1
% 5.52/5.88 thf(fact_8582_prod__diff1,axiom,
% 5.52/5.88 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real,A: vEBT_VEBT] :
% 5.52/5.88 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.52/5.88 => ( ( ( F @ A )
% 5.52/5.88 != zero_zero_real )
% 5.52/5.88 => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 5.52/5.88 => ( ( groups2703838992350267259T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.52/5.88 = ( divide_divide_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.52/5.88 & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 5.52/5.88 => ( ( groups2703838992350267259T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.52/5.88 = ( groups2703838992350267259T_real @ F @ A2 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_diff1
% 5.52/5.88 thf(fact_8583_prod__diff1,axiom,
% 5.52/5.88 ! [A2: set_real,F: real > real,A: real] :
% 5.52/5.88 ( ( finite_finite_real @ A2 )
% 5.52/5.88 => ( ( ( F @ A )
% 5.52/5.88 != zero_zero_real )
% 5.52/5.88 => ( ( ( member_real @ A @ A2 )
% 5.52/5.88 => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.52/5.88 = ( divide_divide_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.52/5.88 & ( ~ ( member_real @ A @ A2 )
% 5.52/5.88 => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.52/5.88 = ( groups1681761925125756287l_real @ F @ A2 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_diff1
% 5.52/5.88 thf(fact_8584_prod__diff1,axiom,
% 5.52/5.88 ! [A2: set_complex,F: complex > real,A: complex] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ( ( F @ A )
% 5.52/5.88 != zero_zero_real )
% 5.52/5.88 => ( ( ( member_complex @ A @ A2 )
% 5.52/5.88 => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.52/5.88 = ( divide_divide_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.52/5.88 & ( ~ ( member_complex @ A @ A2 )
% 5.52/5.88 => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.52/5.88 = ( groups766887009212190081x_real @ F @ A2 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_diff1
% 5.52/5.88 thf(fact_8585_prod__diff1,axiom,
% 5.52/5.88 ! [A2: set_nat,F: nat > real,A: nat] :
% 5.52/5.88 ( ( finite_finite_nat @ A2 )
% 5.52/5.88 => ( ( ( F @ A )
% 5.52/5.88 != zero_zero_real )
% 5.52/5.88 => ( ( ( member_nat @ A @ A2 )
% 5.52/5.88 => ( ( groups129246275422532515t_real @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.52/5.88 = ( divide_divide_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.52/5.88 & ( ~ ( member_nat @ A @ A2 )
% 5.52/5.88 => ( ( groups129246275422532515t_real @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.52/5.88 = ( groups129246275422532515t_real @ F @ A2 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_diff1
% 5.52/5.88 thf(fact_8586_cos__arcsin__nonzero,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.88 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.52/5.88 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.52/5.88 != zero_zero_real ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % cos_arcsin_nonzero
% 5.52/5.88 thf(fact_8587_pochhammer__Suc__prod,axiom,
% 5.52/5.88 ! [A: complex,N: nat] :
% 5.52/5.88 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.52/5.88 = ( groups6464643781859351333omplex
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_Suc_prod
% 5.52/5.88 thf(fact_8588_pochhammer__Suc__prod,axiom,
% 5.52/5.88 ! [A: real,N: nat] :
% 5.52/5.88 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.52/5.88 = ( groups129246275422532515t_real
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_Suc_prod
% 5.52/5.88 thf(fact_8589_pochhammer__Suc__prod,axiom,
% 5.52/5.88 ! [A: rat,N: nat] :
% 5.52/5.88 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.52/5.88 = ( groups73079841787564623at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_Suc_prod
% 5.52/5.88 thf(fact_8590_pochhammer__Suc__prod,axiom,
% 5.52/5.88 ! [A: extended_enat,N: nat] :
% 5.52/5.88 ( ( comm_s3181272606743183617d_enat @ A @ ( suc @ N ) )
% 5.52/5.88 = ( groups7961826882256487087d_enat
% 5.52/5.88 @ ^ [I4: nat] : ( plus_p3455044024723400733d_enat @ A @ ( semiri4216267220026989637d_enat @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_Suc_prod
% 5.52/5.88 thf(fact_8591_pochhammer__Suc__prod,axiom,
% 5.52/5.88 ! [A: nat,N: nat] :
% 5.52/5.88 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.52/5.88 = ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_Suc_prod
% 5.52/5.88 thf(fact_8592_pochhammer__Suc__prod,axiom,
% 5.52/5.88 ! [A: int,N: nat] :
% 5.52/5.88 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.52/5.88 = ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_Suc_prod
% 5.52/5.88 thf(fact_8593_pochhammer__prod__rev,axiom,
% 5.52/5.88 ( comm_s2602460028002588243omplex
% 5.52/5.88 = ( ^ [A4: complex,N3: nat] :
% 5.52/5.88 ( groups6464643781859351333omplex
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_prod_rev
% 5.52/5.88 thf(fact_8594_pochhammer__prod__rev,axiom,
% 5.52/5.88 ( comm_s7457072308508201937r_real
% 5.52/5.88 = ( ^ [A4: real,N3: nat] :
% 5.52/5.88 ( groups129246275422532515t_real
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_prod_rev
% 5.52/5.88 thf(fact_8595_pochhammer__prod__rev,axiom,
% 5.52/5.88 ( comm_s4028243227959126397er_rat
% 5.52/5.88 = ( ^ [A4: rat,N3: nat] :
% 5.52/5.88 ( groups73079841787564623at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_prod_rev
% 5.52/5.88 thf(fact_8596_pochhammer__prod__rev,axiom,
% 5.52/5.88 ( comm_s3181272606743183617d_enat
% 5.52/5.88 = ( ^ [A4: extended_enat,N3: nat] :
% 5.52/5.88 ( groups7961826882256487087d_enat
% 5.52/5.88 @ ^ [I4: nat] : ( plus_p3455044024723400733d_enat @ A4 @ ( semiri4216267220026989637d_enat @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_prod_rev
% 5.52/5.88 thf(fact_8597_pochhammer__prod__rev,axiom,
% 5.52/5.88 ( comm_s4663373288045622133er_nat
% 5.52/5.88 = ( ^ [A4: nat,N3: nat] :
% 5.52/5.88 ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_prod_rev
% 5.52/5.88 thf(fact_8598_pochhammer__prod__rev,axiom,
% 5.52/5.88 ( comm_s4660882817536571857er_int
% 5.52/5.88 = ( ^ [A4: int,N3: nat] :
% 5.52/5.88 ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_prod_rev
% 5.52/5.88 thf(fact_8599_fact__div__fact,axiom,
% 5.52/5.88 ! [N: nat,M: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.88 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.52/5.88 = ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [X: nat] : X
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_div_fact
% 5.52/5.88 thf(fact_8600_prod_Oin__pairs,axiom,
% 5.52/5.88 ! [G: nat > real,M: nat,N: nat] :
% 5.52/5.88 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.52/5.88 = ( groups129246275422532515t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.in_pairs
% 5.52/5.88 thf(fact_8601_prod_Oin__pairs,axiom,
% 5.52/5.88 ! [G: nat > rat,M: nat,N: nat] :
% 5.52/5.88 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.52/5.88 = ( groups73079841787564623at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.in_pairs
% 5.52/5.88 thf(fact_8602_prod_Oin__pairs,axiom,
% 5.52/5.88 ! [G: nat > nat,M: nat,N: nat] :
% 5.52/5.88 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.52/5.88 = ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.in_pairs
% 5.52/5.88 thf(fact_8603_prod_Oin__pairs,axiom,
% 5.52/5.88 ! [G: nat > int,M: nat,N: nat] :
% 5.52/5.88 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.52/5.88 = ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.in_pairs
% 5.52/5.88 thf(fact_8604_sum__atLeastAtMost__code,axiom,
% 5.52/5.88 ! [F: nat > complex,A: nat,B: nat] :
% 5.52/5.88 ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.52/5.88 = ( set_fo1517530859248394432omplex
% 5.52/5.88 @ ^ [A4: nat] : ( plus_plus_complex @ ( F @ A4 ) )
% 5.52/5.88 @ A
% 5.52/5.88 @ B
% 5.52/5.88 @ zero_zero_complex ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_atLeastAtMost_code
% 5.52/5.88 thf(fact_8605_sum__atLeastAtMost__code,axiom,
% 5.52/5.88 ! [F: nat > rat,A: nat,B: nat] :
% 5.52/5.88 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.52/5.88 = ( set_fo1949268297981939178at_rat
% 5.52/5.88 @ ^ [A4: nat] : ( plus_plus_rat @ ( F @ A4 ) )
% 5.52/5.88 @ A
% 5.52/5.88 @ B
% 5.52/5.88 @ zero_zero_rat ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_atLeastAtMost_code
% 5.52/5.88 thf(fact_8606_sum__atLeastAtMost__code,axiom,
% 5.52/5.88 ! [F: nat > int,A: nat,B: nat] :
% 5.52/5.88 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.52/5.88 = ( set_fo2581907887559384638at_int
% 5.52/5.88 @ ^ [A4: nat] : ( plus_plus_int @ ( F @ A4 ) )
% 5.52/5.88 @ A
% 5.52/5.88 @ B
% 5.52/5.88 @ zero_zero_int ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_atLeastAtMost_code
% 5.52/5.88 thf(fact_8607_sum__atLeastAtMost__code,axiom,
% 5.52/5.88 ! [F: nat > nat,A: nat,B: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.52/5.88 = ( set_fo2584398358068434914at_nat
% 5.52/5.88 @ ^ [A4: nat] : ( plus_plus_nat @ ( F @ A4 ) )
% 5.52/5.88 @ A
% 5.52/5.88 @ B
% 5.52/5.88 @ zero_zero_nat ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_atLeastAtMost_code
% 5.52/5.88 thf(fact_8608_sum__atLeastAtMost__code,axiom,
% 5.52/5.88 ! [F: nat > real,A: nat,B: nat] :
% 5.52/5.88 ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.52/5.88 = ( set_fo3111899725591712190t_real
% 5.52/5.88 @ ^ [A4: nat] : ( plus_plus_real @ ( F @ A4 ) )
% 5.52/5.88 @ A
% 5.52/5.88 @ B
% 5.52/5.88 @ zero_zero_real ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_atLeastAtMost_code
% 5.52/5.88 thf(fact_8609_pochhammer__Suc__prod__rev,axiom,
% 5.52/5.88 ! [A: complex,N: nat] :
% 5.52/5.88 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.52/5.88 = ( groups6464643781859351333omplex
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_Suc_prod_rev
% 5.52/5.88 thf(fact_8610_pochhammer__Suc__prod__rev,axiom,
% 5.52/5.88 ! [A: real,N: nat] :
% 5.52/5.88 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.52/5.88 = ( groups129246275422532515t_real
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_Suc_prod_rev
% 5.52/5.88 thf(fact_8611_pochhammer__Suc__prod__rev,axiom,
% 5.52/5.88 ! [A: rat,N: nat] :
% 5.52/5.88 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.52/5.88 = ( groups73079841787564623at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_Suc_prod_rev
% 5.52/5.88 thf(fact_8612_pochhammer__Suc__prod__rev,axiom,
% 5.52/5.88 ! [A: extended_enat,N: nat] :
% 5.52/5.88 ( ( comm_s3181272606743183617d_enat @ A @ ( suc @ N ) )
% 5.52/5.88 = ( groups7961826882256487087d_enat
% 5.52/5.88 @ ^ [I4: nat] : ( plus_p3455044024723400733d_enat @ A @ ( semiri4216267220026989637d_enat @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_Suc_prod_rev
% 5.52/5.88 thf(fact_8613_pochhammer__Suc__prod__rev,axiom,
% 5.52/5.88 ! [A: nat,N: nat] :
% 5.52/5.88 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.52/5.88 = ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_Suc_prod_rev
% 5.52/5.88 thf(fact_8614_pochhammer__Suc__prod__rev,axiom,
% 5.52/5.88 ! [A: int,N: nat] :
% 5.52/5.88 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.52/5.88 = ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_Suc_prod_rev
% 5.52/5.88 thf(fact_8615_arcsin__lt__bounded,axiom,
% 5.52/5.88 ! [Y2: real] :
% 5.52/5.88 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.52/5.88 => ( ( ord_less_real @ Y2 @ one_one_real )
% 5.52/5.88 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 5.52/5.88 & ( ord_less_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arcsin_lt_bounded
% 5.52/5.88 thf(fact_8616_arcsin__lbound,axiom,
% 5.52/5.88 ! [Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.52/5.88 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arcsin_lbound
% 5.52/5.88 thf(fact_8617_arcsin__ubound,axiom,
% 5.52/5.88 ! [Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.52/5.88 => ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arcsin_ubound
% 5.52/5.88 thf(fact_8618_arcsin__bounded,axiom,
% 5.52/5.88 ! [Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.52/5.88 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 5.52/5.88 & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arcsin_bounded
% 5.52/5.88 thf(fact_8619_arcsin__sin,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.88 => ( ( arcsin @ ( sin_real @ X2 ) )
% 5.52/5.88 = X2 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arcsin_sin
% 5.52/5.88 thf(fact_8620_fact__code,axiom,
% 5.52/5.88 ( semiri1406184849735516958ct_int
% 5.52/5.88 = ( ^ [N3: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_code
% 5.52/5.88 thf(fact_8621_fact__code,axiom,
% 5.52/5.88 ( semiri773545260158071498ct_rat
% 5.52/5.88 = ( ^ [N3: nat] : ( semiri681578069525770553at_rat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_code
% 5.52/5.88 thf(fact_8622_fact__code,axiom,
% 5.52/5.88 ( semiri4449623510593786356d_enat
% 5.52/5.88 = ( ^ [N3: nat] : ( semiri4216267220026989637d_enat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_code
% 5.52/5.88 thf(fact_8623_fact__code,axiom,
% 5.52/5.88 ( semiri2265585572941072030t_real
% 5.52/5.88 = ( ^ [N3: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_code
% 5.52/5.88 thf(fact_8624_fact__code,axiom,
% 5.52/5.88 ( semiri1408675320244567234ct_nat
% 5.52/5.88 = ( ^ [N3: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_code
% 5.52/5.88 thf(fact_8625_le__arcsin__iff,axiom,
% 5.52/5.88 ! [X2: real,Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.52/5.88 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.88 => ( ( ord_less_eq_real @ Y2 @ ( arcsin @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_real @ ( sin_real @ Y2 ) @ X2 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % le_arcsin_iff
% 5.52/5.88 thf(fact_8626_arcsin__le__iff,axiom,
% 5.52/5.88 ! [X2: real,Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.52/5.88 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.88 => ( ( ord_less_eq_real @ ( arcsin @ X2 ) @ Y2 )
% 5.52/5.88 = ( ord_less_eq_real @ X2 @ ( sin_real @ Y2 ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arcsin_le_iff
% 5.52/5.88 thf(fact_8627_arcsin__pi,axiom,
% 5.52/5.88 ! [Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.52/5.88 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 5.52/5.88 & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ pi )
% 5.52/5.88 & ( ( sin_real @ ( arcsin @ Y2 ) )
% 5.52/5.88 = Y2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arcsin_pi
% 5.52/5.88 thf(fact_8628_arcsin,axiom,
% 5.52/5.88 ! [Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.52/5.88 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 5.52/5.88 & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.88 & ( ( sin_real @ ( arcsin @ Y2 ) )
% 5.52/5.88 = Y2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arcsin
% 5.52/5.88 thf(fact_8629_sin__arccos__abs,axiom,
% 5.52/5.88 ! [Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.52/5.88 => ( ( sin_real @ ( arccos @ Y2 ) )
% 5.52/5.88 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sin_arccos_abs
% 5.52/5.88 thf(fact_8630_sin__arccos,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.52/5.88 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.52/5.88 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sin_arccos
% 5.52/5.88 thf(fact_8631_floor__log__nat__eq__powr__iff,axiom,
% 5.52/5.88 ! [B: nat,K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.52/5.88 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.88 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.52/5.88 = ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.88 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.52/5.88 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_log_nat_eq_powr_iff
% 5.52/5.88 thf(fact_8632_of__nat__code,axiom,
% 5.52/5.88 ( semiri8010041392384452111omplex
% 5.52/5.88 = ( ^ [N3: nat] :
% 5.52/5.88 ( semiri2816024913162550771omplex
% 5.52/5.88 @ ^ [I4: complex] : ( plus_plus_complex @ I4 @ one_one_complex )
% 5.52/5.88 @ N3
% 5.52/5.88 @ zero_zero_complex ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % of_nat_code
% 5.52/5.88 thf(fact_8633_of__nat__code,axiom,
% 5.52/5.88 ( semiri1314217659103216013at_int
% 5.52/5.88 = ( ^ [N3: nat] :
% 5.52/5.88 ( semiri8420488043553186161ux_int
% 5.52/5.88 @ ^ [I4: int] : ( plus_plus_int @ I4 @ one_one_int )
% 5.52/5.88 @ N3
% 5.52/5.88 @ zero_zero_int ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % of_nat_code
% 5.52/5.88 thf(fact_8634_of__nat__code,axiom,
% 5.52/5.88 ( semiri5074537144036343181t_real
% 5.52/5.88 = ( ^ [N3: nat] :
% 5.52/5.88 ( semiri7260567687927622513x_real
% 5.52/5.88 @ ^ [I4: real] : ( plus_plus_real @ I4 @ one_one_real )
% 5.52/5.88 @ N3
% 5.52/5.88 @ zero_zero_real ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % of_nat_code
% 5.52/5.88 thf(fact_8635_of__nat__code,axiom,
% 5.52/5.88 ( semiri1316708129612266289at_nat
% 5.52/5.88 = ( ^ [N3: nat] :
% 5.52/5.88 ( semiri8422978514062236437ux_nat
% 5.52/5.88 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ one_one_nat )
% 5.52/5.88 @ N3
% 5.52/5.88 @ zero_zero_nat ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % of_nat_code
% 5.52/5.88 thf(fact_8636_of__nat__code,axiom,
% 5.52/5.88 ( semiri681578069525770553at_rat
% 5.52/5.88 = ( ^ [N3: nat] :
% 5.52/5.88 ( semiri7787848453975740701ux_rat
% 5.52/5.88 @ ^ [I4: rat] : ( plus_plus_rat @ I4 @ one_one_rat )
% 5.52/5.88 @ N3
% 5.52/5.88 @ zero_zero_rat ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % of_nat_code
% 5.52/5.88 thf(fact_8637_of__nat__code,axiom,
% 5.52/5.88 ( semiri4216267220026989637d_enat
% 5.52/5.88 = ( ^ [N3: nat] :
% 5.52/5.88 ( semiri8563196900006977889d_enat
% 5.52/5.88 @ ^ [I4: extended_enat] : ( plus_p3455044024723400733d_enat @ I4 @ one_on7984719198319812577d_enat )
% 5.52/5.88 @ N3
% 5.52/5.88 @ zero_z5237406670263579293d_enat ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % of_nat_code
% 5.52/5.88 thf(fact_8638_gchoose__row__sum__weighted,axiom,
% 5.52/5.88 ! [R: complex,M: nat] :
% 5.52/5.88 ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_complex @ ( gbinomial_complex @ R @ K2 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K2 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.52/5.88 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R @ ( suc @ M ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gchoose_row_sum_weighted
% 5.52/5.88 thf(fact_8639_gchoose__row__sum__weighted,axiom,
% 5.52/5.88 ! [R: rat,M: nat] :
% 5.52/5.88 ( ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_rat @ ( gbinomial_rat @ R @ K2 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K2 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.52/5.88 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R @ ( suc @ M ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gchoose_row_sum_weighted
% 5.52/5.88 thf(fact_8640_gchoose__row__sum__weighted,axiom,
% 5.52/5.88 ! [R: real,M: nat] :
% 5.52/5.88 ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_real @ ( gbinomial_real @ R @ K2 ) @ ( minus_minus_real @ ( divide_divide_real @ R @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.52/5.88 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R @ ( suc @ M ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gchoose_row_sum_weighted
% 5.52/5.88 thf(fact_8641_of__int__floor__cancel,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.88 = X2 )
% 5.52/5.88 = ( ? [N3: int] :
% 5.52/5.88 ( X2
% 5.52/5.88 = ( ring_1_of_int_real @ N3 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % of_int_floor_cancel
% 5.52/5.88 thf(fact_8642_of__int__floor__cancel,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.52/5.88 = X2 )
% 5.52/5.88 = ( ? [N3: int] :
% 5.52/5.88 ( X2
% 5.52/5.88 = ( ring_1_of_int_rat @ N3 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % of_int_floor_cancel
% 5.52/5.88 thf(fact_8643_floor__numeral,axiom,
% 5.52/5.88 ! [V: num] :
% 5.52/5.88 ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 5.52/5.88 = ( numeral_numeral_int @ V ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_numeral
% 5.52/5.88 thf(fact_8644_floor__numeral,axiom,
% 5.52/5.88 ! [V: num] :
% 5.52/5.88 ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 5.52/5.88 = ( numeral_numeral_int @ V ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_numeral
% 5.52/5.88 thf(fact_8645_gbinomial__0_I1_J,axiom,
% 5.52/5.88 ! [A: complex] :
% 5.52/5.88 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.52/5.88 = one_one_complex ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_0(1)
% 5.52/5.88 thf(fact_8646_gbinomial__0_I1_J,axiom,
% 5.52/5.88 ! [A: real] :
% 5.52/5.88 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.52/5.88 = one_one_real ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_0(1)
% 5.52/5.88 thf(fact_8647_gbinomial__0_I1_J,axiom,
% 5.52/5.88 ! [A: rat] :
% 5.52/5.88 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 5.52/5.88 = one_one_rat ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_0(1)
% 5.52/5.88 thf(fact_8648_gbinomial__0_I1_J,axiom,
% 5.52/5.88 ! [A: nat] :
% 5.52/5.88 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.52/5.88 = one_one_nat ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_0(1)
% 5.52/5.88 thf(fact_8649_gbinomial__0_I1_J,axiom,
% 5.52/5.88 ! [A: int] :
% 5.52/5.88 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.52/5.88 = one_one_int ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_0(1)
% 5.52/5.88 thf(fact_8650_floor__one,axiom,
% 5.52/5.88 ( ( archim6058952711729229775r_real @ one_one_real )
% 5.52/5.88 = one_one_int ) ).
% 5.52/5.88
% 5.52/5.88 % floor_one
% 5.52/5.88 thf(fact_8651_floor__one,axiom,
% 5.52/5.88 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 5.52/5.88 = one_one_int ) ).
% 5.52/5.88
% 5.52/5.88 % floor_one
% 5.52/5.88 thf(fact_8652_prod__eq__1__iff,axiom,
% 5.52/5.88 ! [A2: set_int,F: int > nat] :
% 5.52/5.88 ( ( finite_finite_int @ A2 )
% 5.52/5.88 => ( ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 5.52/5.88 = one_one_nat )
% 5.52/5.88 = ( ! [X: int] :
% 5.52/5.88 ( ( member_int @ X @ A2 )
% 5.52/5.88 => ( ( F @ X )
% 5.52/5.88 = one_one_nat ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_eq_1_iff
% 5.52/5.88 thf(fact_8653_prod__eq__1__iff,axiom,
% 5.52/5.88 ! [A2: set_complex,F: complex > nat] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ( ( groups861055069439313189ex_nat @ F @ A2 )
% 5.52/5.88 = one_one_nat )
% 5.52/5.88 = ( ! [X: complex] :
% 5.52/5.88 ( ( member_complex @ X @ A2 )
% 5.52/5.88 => ( ( F @ X )
% 5.52/5.88 = one_one_nat ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_eq_1_iff
% 5.52/5.88 thf(fact_8654_prod__eq__1__iff,axiom,
% 5.52/5.88 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.88 => ( ( ( groups2880970938130013265at_nat @ F @ A2 )
% 5.52/5.88 = one_one_nat )
% 5.52/5.88 = ( ! [X: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X @ A2 )
% 5.52/5.88 => ( ( F @ X )
% 5.52/5.88 = one_one_nat ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_eq_1_iff
% 5.52/5.88 thf(fact_8655_prod__eq__1__iff,axiom,
% 5.52/5.88 ! [A2: set_nat,F: nat > nat] :
% 5.52/5.88 ( ( finite_finite_nat @ A2 )
% 5.52/5.88 => ( ( ( groups708209901874060359at_nat @ F @ A2 )
% 5.52/5.88 = one_one_nat )
% 5.52/5.88 = ( ! [X: nat] :
% 5.52/5.88 ( ( member_nat @ X @ A2 )
% 5.52/5.88 => ( ( F @ X )
% 5.52/5.88 = one_one_nat ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_eq_1_iff
% 5.52/5.88 thf(fact_8656_prod__pos__nat__iff,axiom,
% 5.52/5.88 ! [A2: set_int,F: int > nat] :
% 5.52/5.88 ( ( finite_finite_int @ A2 )
% 5.52/5.88 => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 5.52/5.88 = ( ! [X: int] :
% 5.52/5.88 ( ( member_int @ X @ A2 )
% 5.52/5.88 => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_pos_nat_iff
% 5.52/5.88 thf(fact_8657_prod__pos__nat__iff,axiom,
% 5.52/5.88 ! [A2: set_complex,F: complex > nat] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ A2 )
% 5.52/5.88 => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 5.52/5.88 = ( ! [X: complex] :
% 5.52/5.88 ( ( member_complex @ X @ A2 )
% 5.52/5.88 => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_pos_nat_iff
% 5.52/5.88 thf(fact_8658_prod__pos__nat__iff,axiom,
% 5.52/5.88 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.88 => ( ( ord_less_nat @ zero_zero_nat @ ( groups2880970938130013265at_nat @ F @ A2 ) )
% 5.52/5.88 = ( ! [X: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ X @ A2 )
% 5.52/5.88 => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_pos_nat_iff
% 5.52/5.88 thf(fact_8659_prod__pos__nat__iff,axiom,
% 5.52/5.88 ! [A2: set_nat,F: nat > nat] :
% 5.52/5.88 ( ( finite_finite_nat @ A2 )
% 5.52/5.88 => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.52/5.88 = ( ! [X: nat] :
% 5.52/5.88 ( ( member_nat @ X @ A2 )
% 5.52/5.88 => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_pos_nat_iff
% 5.52/5.88 thf(fact_8660_zero__le__floor,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % zero_le_floor
% 5.52/5.88 thf(fact_8661_zero__le__floor,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_rat @ zero_zero_rat @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % zero_le_floor
% 5.52/5.88 thf(fact_8662_floor__less__zero,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ zero_zero_int )
% 5.52/5.88 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_less_zero
% 5.52/5.88 thf(fact_8663_floor__less__zero,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 5.52/5.88 = ( ord_less_rat @ X2 @ zero_zero_rat ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_less_zero
% 5.52/5.88 thf(fact_8664_numeral__le__floor,axiom,
% 5.52/5.88 ! [V: num,X2: real] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % numeral_le_floor
% 5.52/5.88 thf(fact_8665_numeral__le__floor,axiom,
% 5.52/5.88 ! [V: num,X2: rat] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % numeral_le_floor
% 5.52/5.88 thf(fact_8666_zero__less__floor,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % zero_less_floor
% 5.52/5.88 thf(fact_8667_zero__less__floor,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % zero_less_floor
% 5.52/5.88 thf(fact_8668_floor__le__zero,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ zero_zero_int )
% 5.52/5.88 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_le_zero
% 5.52/5.88 thf(fact_8669_floor__le__zero,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 5.52/5.88 = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_le_zero
% 5.52/5.88 thf(fact_8670_floor__less__numeral,axiom,
% 5.52/5.88 ! [X2: real,V: num] :
% 5.52/5.88 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.88 = ( ord_less_real @ X2 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_less_numeral
% 5.52/5.88 thf(fact_8671_floor__less__numeral,axiom,
% 5.52/5.88 ! [X2: rat,V: num] :
% 5.52/5.88 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.88 = ( ord_less_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_less_numeral
% 5.52/5.88 thf(fact_8672_one__le__floor,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % one_le_floor
% 5.52/5.88 thf(fact_8673_one__le__floor,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % one_le_floor
% 5.52/5.88 thf(fact_8674_floor__less__one,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.52/5.88 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_less_one
% 5.52/5.88 thf(fact_8675_floor__less__one,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.52/5.88 = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_less_one
% 5.52/5.88 thf(fact_8676_floor__neg__numeral,axiom,
% 5.52/5.88 ! [V: num] :
% 5.52/5.88 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.88 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_neg_numeral
% 5.52/5.88 thf(fact_8677_floor__neg__numeral,axiom,
% 5.52/5.88 ! [V: num] :
% 5.52/5.88 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.88 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_neg_numeral
% 5.52/5.88 thf(fact_8678_floor__diff__numeral,axiom,
% 5.52/5.88 ! [X2: real,V: num] :
% 5.52/5.88 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.52/5.88 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_diff_numeral
% 5.52/5.88 thf(fact_8679_floor__diff__numeral,axiom,
% 5.52/5.88 ! [X2: rat,V: num] :
% 5.52/5.88 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.52/5.88 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_diff_numeral
% 5.52/5.88 thf(fact_8680_floor__diff__one,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ one_one_real ) )
% 5.52/5.88 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_diff_one
% 5.52/5.88 thf(fact_8681_floor__diff__one,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 5.52/5.88 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_diff_one
% 5.52/5.88 thf(fact_8682_floor__numeral__power,axiom,
% 5.52/5.88 ! [X2: num,N: nat] :
% 5.52/5.88 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.52/5.88 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_numeral_power
% 5.52/5.88 thf(fact_8683_floor__numeral__power,axiom,
% 5.52/5.88 ! [X2: num,N: nat] :
% 5.52/5.88 ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.52/5.88 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_numeral_power
% 5.52/5.88 thf(fact_8684_floor__divide__eq__div__numeral,axiom,
% 5.52/5.88 ! [A: num,B: num] :
% 5.52/5.88 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.52/5.88 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_divide_eq_div_numeral
% 5.52/5.88 thf(fact_8685_numeral__less__floor,axiom,
% 5.52/5.88 ! [V: num,X2: real] :
% 5.52/5.88 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % numeral_less_floor
% 5.52/5.88 thf(fact_8686_numeral__less__floor,axiom,
% 5.52/5.88 ! [V: num,X2: rat] :
% 5.52/5.88 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % numeral_less_floor
% 5.52/5.88 thf(fact_8687_floor__le__numeral,axiom,
% 5.52/5.88 ! [X2: real,V: num] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.88 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_le_numeral
% 5.52/5.88 thf(fact_8688_floor__le__numeral,axiom,
% 5.52/5.88 ! [X2: rat,V: num] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.52/5.88 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_le_numeral
% 5.52/5.88 thf(fact_8689_one__less__floor,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % one_less_floor
% 5.52/5.88 thf(fact_8690_one__less__floor,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % one_less_floor
% 5.52/5.88 thf(fact_8691_floor__le__one,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.52/5.88 = ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_le_one
% 5.52/5.88 thf(fact_8692_floor__le__one,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.52/5.88 = ( ord_less_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_le_one
% 5.52/5.88 thf(fact_8693_neg__numeral__le__floor,axiom,
% 5.52/5.88 ! [V: num,X2: real] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % neg_numeral_le_floor
% 5.52/5.88 thf(fact_8694_neg__numeral__le__floor,axiom,
% 5.52/5.88 ! [V: num,X2: rat] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % neg_numeral_le_floor
% 5.52/5.88 thf(fact_8695_floor__less__neg__numeral,axiom,
% 5.52/5.88 ! [X2: real,V: num] :
% 5.52/5.88 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.88 = ( ord_less_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_less_neg_numeral
% 5.52/5.88 thf(fact_8696_floor__less__neg__numeral,axiom,
% 5.52/5.88 ! [X2: rat,V: num] :
% 5.52/5.88 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.88 = ( ord_less_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_less_neg_numeral
% 5.52/5.88 thf(fact_8697_arccos__0,axiom,
% 5.52/5.88 ( ( arccos @ zero_zero_real )
% 5.52/5.88 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arccos_0
% 5.52/5.88 thf(fact_8698_floor__one__divide__eq__div__numeral,axiom,
% 5.52/5.88 ! [B: num] :
% 5.52/5.88 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.52/5.88 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_one_divide_eq_div_numeral
% 5.52/5.88 thf(fact_8699_floor__minus__divide__eq__div__numeral,axiom,
% 5.52/5.88 ! [A: num,B: num] :
% 5.52/5.88 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.52/5.88 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_minus_divide_eq_div_numeral
% 5.52/5.88 thf(fact_8700_neg__numeral__less__floor,axiom,
% 5.52/5.88 ! [V: num,X2: real] :
% 5.52/5.88 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % neg_numeral_less_floor
% 5.52/5.88 thf(fact_8701_neg__numeral__less__floor,axiom,
% 5.52/5.88 ! [V: num,X2: rat] :
% 5.52/5.88 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % neg_numeral_less_floor
% 5.52/5.88 thf(fact_8702_floor__le__neg__numeral,axiom,
% 5.52/5.88 ! [X2: real,V: num] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.88 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_le_neg_numeral
% 5.52/5.88 thf(fact_8703_floor__le__neg__numeral,axiom,
% 5.52/5.88 ! [X2: rat,V: num] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.52/5.88 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_le_neg_numeral
% 5.52/5.88 thf(fact_8704_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.52/5.88 ! [B: num] :
% 5.52/5.88 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.52/5.88 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_minus_one_divide_eq_div_numeral
% 5.52/5.88 thf(fact_8705_floor__mono,axiom,
% 5.52/5.88 ! [X2: real,Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.52/5.88 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y2 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_mono
% 5.52/5.88 thf(fact_8706_floor__mono,axiom,
% 5.52/5.88 ! [X2: rat,Y2: rat] :
% 5.52/5.88 ( ( ord_less_eq_rat @ X2 @ Y2 )
% 5.52/5.88 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y2 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_mono
% 5.52/5.88 thf(fact_8707_of__int__floor__le,axiom,
% 5.52/5.88 ! [X2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) @ X2 ) ).
% 5.52/5.88
% 5.52/5.88 % of_int_floor_le
% 5.52/5.88 thf(fact_8708_of__int__floor__le,axiom,
% 5.52/5.88 ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 ) ).
% 5.52/5.88
% 5.52/5.88 % of_int_floor_le
% 5.52/5.88 thf(fact_8709_floor__less__cancel,axiom,
% 5.52/5.88 ! [X2: real,Y2: real] :
% 5.52/5.88 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y2 ) )
% 5.52/5.88 => ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_less_cancel
% 5.52/5.88 thf(fact_8710_floor__less__cancel,axiom,
% 5.52/5.88 ! [X2: rat,Y2: rat] :
% 5.52/5.88 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y2 ) )
% 5.52/5.88 => ( ord_less_rat @ X2 @ Y2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_less_cancel
% 5.52/5.88 thf(fact_8711_le__floor__iff,axiom,
% 5.52/5.88 ! [Z: int,X2: real] :
% 5.52/5.88 ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % le_floor_iff
% 5.52/5.88 thf(fact_8712_le__floor__iff,axiom,
% 5.52/5.88 ! [Z: int,X2: rat] :
% 5.52/5.88 ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % le_floor_iff
% 5.52/5.88 thf(fact_8713_floor__less__iff,axiom,
% 5.52/5.88 ! [X2: real,Z: int] :
% 5.52/5.88 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.52/5.88 = ( ord_less_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_less_iff
% 5.52/5.88 thf(fact_8714_floor__less__iff,axiom,
% 5.52/5.88 ! [X2: rat,Z: int] :
% 5.52/5.88 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.52/5.88 = ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_less_iff
% 5.52/5.88 thf(fact_8715_le__floor__add,axiom,
% 5.52/5.88 ! [X2: real,Y2: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y2 ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ Y2 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % le_floor_add
% 5.52/5.88 thf(fact_8716_le__floor__add,axiom,
% 5.52/5.88 ! [X2: rat,Y2: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y2 ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y2 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % le_floor_add
% 5.52/5.88 thf(fact_8717_int__add__floor,axiom,
% 5.52/5.88 ! [Z: int,X2: real] :
% 5.52/5.88 ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.88 = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % int_add_floor
% 5.52/5.88 thf(fact_8718_int__add__floor,axiom,
% 5.52/5.88 ! [Z: int,X2: rat] :
% 5.52/5.88 ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.52/5.88 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % int_add_floor
% 5.52/5.88 thf(fact_8719_floor__add__int,axiom,
% 5.52/5.88 ! [X2: real,Z: int] :
% 5.52/5.88 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.52/5.88 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_add_int
% 5.52/5.88 thf(fact_8720_floor__add__int,axiom,
% 5.52/5.88 ! [X2: rat,Z: int] :
% 5.52/5.88 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.52/5.88 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_add_int
% 5.52/5.88 thf(fact_8721_floor__divide__of__int__eq,axiom,
% 5.52/5.88 ! [K: int,L: int] :
% 5.52/5.88 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 5.52/5.88 = ( divide_divide_int @ K @ L ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_divide_of_int_eq
% 5.52/5.88 thf(fact_8722_floor__divide__of__int__eq,axiom,
% 5.52/5.88 ! [K: int,L: int] :
% 5.52/5.88 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 5.52/5.88 = ( divide_divide_int @ K @ L ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_divide_of_int_eq
% 5.52/5.88 thf(fact_8723_floor__power,axiom,
% 5.52/5.88 ! [X2: real,N: nat] :
% 5.52/5.88 ( ( X2
% 5.52/5.88 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) )
% 5.52/5.88 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X2 @ N ) )
% 5.52/5.88 = ( power_power_int @ ( archim6058952711729229775r_real @ X2 ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_power
% 5.52/5.88 thf(fact_8724_floor__power,axiom,
% 5.52/5.88 ! [X2: rat,N: nat] :
% 5.52/5.88 ( ( X2
% 5.52/5.88 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) )
% 5.52/5.88 => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X2 @ N ) )
% 5.52/5.88 = ( power_power_int @ ( archim3151403230148437115or_rat @ X2 ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_power
% 5.52/5.88 thf(fact_8725_gbinomial__Suc__Suc,axiom,
% 5.52/5.88 ! [A: real,K: nat] :
% 5.52/5.88 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.52/5.88 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_Suc_Suc
% 5.52/5.88 thf(fact_8726_gbinomial__Suc__Suc,axiom,
% 5.52/5.88 ! [A: rat,K: nat] :
% 5.52/5.88 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.52/5.88 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_Suc_Suc
% 5.52/5.88 thf(fact_8727_gbinomial__Suc__Suc,axiom,
% 5.52/5.88 ! [A: complex,K: nat] :
% 5.52/5.88 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.52/5.88 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_Suc_Suc
% 5.52/5.88 thf(fact_8728_gbinomial__of__nat__symmetric,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 5.52/5.88 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_of_nat_symmetric
% 5.52/5.88 thf(fact_8729_gbinomial__of__nat__symmetric,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 5.52/5.88 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_of_nat_symmetric
% 5.52/5.88 thf(fact_8730_one__add__floor,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.52/5.88 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % one_add_floor
% 5.52/5.88 thf(fact_8731_one__add__floor,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.52/5.88 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % one_add_floor
% 5.52/5.88 thf(fact_8732_floor__divide__of__nat__eq,axiom,
% 5.52/5.88 ! [M: nat,N: nat] :
% 5.52/5.88 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.52/5.88 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_divide_of_nat_eq
% 5.52/5.88 thf(fact_8733_floor__divide__of__nat__eq,axiom,
% 5.52/5.88 ! [M: nat,N: nat] :
% 5.52/5.88 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 5.52/5.88 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_divide_of_nat_eq
% 5.52/5.88 thf(fact_8734_gbinomial__addition__formula,axiom,
% 5.52/5.88 ! [A: complex,K: nat] :
% 5.52/5.88 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.52/5.88 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_addition_formula
% 5.52/5.88 thf(fact_8735_gbinomial__addition__formula,axiom,
% 5.52/5.88 ! [A: real,K: nat] :
% 5.52/5.88 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.52/5.88 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_addition_formula
% 5.52/5.88 thf(fact_8736_gbinomial__addition__formula,axiom,
% 5.52/5.88 ! [A: rat,K: nat] :
% 5.52/5.88 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.52/5.88 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_addition_formula
% 5.52/5.88 thf(fact_8737_gbinomial__absorb__comp,axiom,
% 5.52/5.88 ! [A: complex,K: nat] :
% 5.52/5.88 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.52/5.88 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_absorb_comp
% 5.52/5.88 thf(fact_8738_gbinomial__absorb__comp,axiom,
% 5.52/5.88 ! [A: real,K: nat] :
% 5.52/5.88 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.52/5.88 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_absorb_comp
% 5.52/5.88 thf(fact_8739_gbinomial__absorb__comp,axiom,
% 5.52/5.88 ! [A: rat,K: nat] :
% 5.52/5.88 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.52/5.88 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_absorb_comp
% 5.52/5.88 thf(fact_8740_gbinomial__mult__1,axiom,
% 5.52/5.88 ! [A: complex,K: nat] :
% 5.52/5.88 ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 5.52/5.88 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_mult_1
% 5.52/5.88 thf(fact_8741_gbinomial__mult__1,axiom,
% 5.52/5.88 ! [A: real,K: nat] :
% 5.52/5.88 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.52/5.88 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_mult_1
% 5.52/5.88 thf(fact_8742_gbinomial__mult__1,axiom,
% 5.52/5.88 ! [A: rat,K: nat] :
% 5.52/5.88 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.52/5.88 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_mult_1
% 5.52/5.88 thf(fact_8743_gbinomial__mult__1_H,axiom,
% 5.52/5.88 ! [A: complex,K: nat] :
% 5.52/5.88 ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 5.52/5.88 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_mult_1'
% 5.52/5.88 thf(fact_8744_gbinomial__mult__1_H,axiom,
% 5.52/5.88 ! [A: real,K: nat] :
% 5.52/5.88 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.52/5.88 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_mult_1'
% 5.52/5.88 thf(fact_8745_gbinomial__mult__1_H,axiom,
% 5.52/5.88 ! [A: rat,K: nat] :
% 5.52/5.88 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.52/5.88 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_mult_1'
% 5.52/5.88 thf(fact_8746_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.52/5.88 ! [K: nat,A: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.52/5.88 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_ge_n_over_k_pow_k
% 5.52/5.88 thf(fact_8747_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.52/5.88 ! [K: nat,A: rat] :
% 5.52/5.88 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.52/5.88 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_ge_n_over_k_pow_k
% 5.52/5.88 thf(fact_8748_real__of__int__floor__add__one__gt,axiom,
% 5.52/5.88 ! [R: real] : ( ord_less_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 5.52/5.88
% 5.52/5.88 % real_of_int_floor_add_one_gt
% 5.52/5.88 thf(fact_8749_floor__eq,axiom,
% 5.52/5.88 ! [N: int,X2: real] :
% 5.52/5.88 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.52/5.88 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.52/5.88 => ( ( archim6058952711729229775r_real @ X2 )
% 5.52/5.88 = N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_eq
% 5.52/5.88 thf(fact_8750_real__of__int__floor__add__one__ge,axiom,
% 5.52/5.88 ! [R: real] : ( ord_less_eq_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 5.52/5.88
% 5.52/5.88 % real_of_int_floor_add_one_ge
% 5.52/5.88 thf(fact_8751_real__of__int__floor__gt__diff__one,axiom,
% 5.52/5.88 ! [R: real] : ( ord_less_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % real_of_int_floor_gt_diff_one
% 5.52/5.88 thf(fact_8752_real__of__int__floor__ge__diff__one,axiom,
% 5.52/5.88 ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % real_of_int_floor_ge_diff_one
% 5.52/5.88 thf(fact_8753_prod__int__plus__eq,axiom,
% 5.52/5.88 ! [I: nat,J: nat] :
% 5.52/5.88 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 5.52/5.88 = ( groups1705073143266064639nt_int
% 5.52/5.88 @ ^ [X: int] : X
% 5.52/5.88 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod_int_plus_eq
% 5.52/5.88 thf(fact_8754_floor__split,axiom,
% 5.52/5.88 ! [P: int > $o,T: real] :
% 5.52/5.88 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 5.52/5.88 = ( ! [I4: int] :
% 5.52/5.88 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I4 ) @ T )
% 5.52/5.88 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) ) )
% 5.52/5.88 => ( P @ I4 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_split
% 5.52/5.88 thf(fact_8755_floor__split,axiom,
% 5.52/5.88 ! [P: int > $o,T: rat] :
% 5.52/5.88 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 5.52/5.88 = ( ! [I4: int] :
% 5.52/5.88 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I4 ) @ T )
% 5.52/5.88 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) ) )
% 5.52/5.88 => ( P @ I4 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_split
% 5.52/5.88 thf(fact_8756_floor__eq__iff,axiom,
% 5.52/5.88 ! [X2: real,A: int] :
% 5.52/5.88 ( ( ( archim6058952711729229775r_real @ X2 )
% 5.52/5.88 = A )
% 5.52/5.88 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X2 )
% 5.52/5.88 & ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_eq_iff
% 5.52/5.88 thf(fact_8757_floor__eq__iff,axiom,
% 5.52/5.88 ! [X2: rat,A: int] :
% 5.52/5.88 ( ( ( archim3151403230148437115or_rat @ X2 )
% 5.52/5.88 = A )
% 5.52/5.88 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X2 )
% 5.52/5.88 & ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_eq_iff
% 5.52/5.88 thf(fact_8758_floor__unique,axiom,
% 5.52/5.88 ! [Z: int,X2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X2 )
% 5.52/5.88 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 5.52/5.88 => ( ( archim6058952711729229775r_real @ X2 )
% 5.52/5.88 = Z ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_unique
% 5.52/5.88 thf(fact_8759_floor__unique,axiom,
% 5.52/5.88 ! [Z: int,X2: rat] :
% 5.52/5.88 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X2 )
% 5.52/5.88 => ( ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 5.52/5.88 => ( ( archim3151403230148437115or_rat @ X2 )
% 5.52/5.88 = Z ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_unique
% 5.52/5.88 thf(fact_8760_le__mult__floor,axiom,
% 5.52/5.88 ! [A: real,B: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.52/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.52/5.88 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % le_mult_floor
% 5.52/5.88 thf(fact_8761_le__mult__floor,axiom,
% 5.52/5.88 ! [A: rat,B: rat] :
% 5.52/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.52/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.52/5.88 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % le_mult_floor
% 5.52/5.88 thf(fact_8762_less__floor__iff,axiom,
% 5.52/5.88 ! [Z: int,X2: real] :
% 5.52/5.88 ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % less_floor_iff
% 5.52/5.88 thf(fact_8763_less__floor__iff,axiom,
% 5.52/5.88 ! [Z: int,X2: rat] :
% 5.52/5.88 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.52/5.88 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % less_floor_iff
% 5.52/5.88 thf(fact_8764_floor__le__iff,axiom,
% 5.52/5.88 ! [X2: real,Z: int] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.52/5.88 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_le_iff
% 5.52/5.88 thf(fact_8765_floor__le__iff,axiom,
% 5.52/5.88 ! [X2: rat,Z: int] :
% 5.52/5.88 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.52/5.88 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_le_iff
% 5.52/5.88 thf(fact_8766_floor__correct,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) @ X2 )
% 5.52/5.88 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_correct
% 5.52/5.88 thf(fact_8767_floor__correct,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 )
% 5.52/5.88 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_correct
% 5.52/5.88 thf(fact_8768_arccos__less__arccos,axiom,
% 5.52/5.88 ! [X2: real,Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.88 => ( ( ord_less_real @ X2 @ Y2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.52/5.88 => ( ord_less_real @ ( arccos @ Y2 ) @ ( arccos @ X2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arccos_less_arccos
% 5.52/5.88 thf(fact_8769_arccos__less__mono,axiom,
% 5.52/5.88 ! [X2: real,Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.52/5.88 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.52/5.88 => ( ( ord_less_real @ ( arccos @ X2 ) @ ( arccos @ Y2 ) )
% 5.52/5.88 = ( ord_less_real @ Y2 @ X2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arccos_less_mono
% 5.52/5.88 thf(fact_8770_floor__eq2,axiom,
% 5.52/5.88 ! [N: int,X2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.52/5.88 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.52/5.88 => ( ( archim6058952711729229775r_real @ X2 )
% 5.52/5.88 = N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_eq2
% 5.52/5.88 thf(fact_8771_Suc__times__gbinomial,axiom,
% 5.52/5.88 ! [K: nat,A: complex] :
% 5.52/5.88 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.52/5.88 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % Suc_times_gbinomial
% 5.52/5.88 thf(fact_8772_Suc__times__gbinomial,axiom,
% 5.52/5.88 ! [K: nat,A: real] :
% 5.52/5.88 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.52/5.88 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % Suc_times_gbinomial
% 5.52/5.88 thf(fact_8773_Suc__times__gbinomial,axiom,
% 5.52/5.88 ! [K: nat,A: rat] :
% 5.52/5.88 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.52/5.88 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % Suc_times_gbinomial
% 5.52/5.88 thf(fact_8774_gbinomial__absorption,axiom,
% 5.52/5.88 ! [K: nat,A: complex] :
% 5.52/5.88 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.52/5.88 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_absorption
% 5.52/5.88 thf(fact_8775_gbinomial__absorption,axiom,
% 5.52/5.88 ! [K: nat,A: real] :
% 5.52/5.88 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.52/5.88 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_absorption
% 5.52/5.88 thf(fact_8776_gbinomial__absorption,axiom,
% 5.52/5.88 ! [K: nat,A: rat] :
% 5.52/5.88 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.52/5.88 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_absorption
% 5.52/5.88 thf(fact_8777_floor__divide__real__eq__div,axiom,
% 5.52/5.88 ! [B: int,A: real] :
% 5.52/5.88 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.52/5.88 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.52/5.88 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_divide_real_eq_div
% 5.52/5.88 thf(fact_8778_gbinomial__trinomial__revision,axiom,
% 5.52/5.88 ! [K: nat,M: nat,A: complex] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ M )
% 5.52/5.88 => ( ( times_times_complex @ ( gbinomial_complex @ A @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 5.52/5.88 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_trinomial_revision
% 5.52/5.88 thf(fact_8779_gbinomial__trinomial__revision,axiom,
% 5.52/5.88 ! [K: nat,M: nat,A: real] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ M )
% 5.52/5.88 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.52/5.88 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_trinomial_revision
% 5.52/5.88 thf(fact_8780_gbinomial__trinomial__revision,axiom,
% 5.52/5.88 ! [K: nat,M: nat,A: rat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ M )
% 5.52/5.88 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.52/5.88 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_trinomial_revision
% 5.52/5.88 thf(fact_8781_ln__prod,axiom,
% 5.52/5.88 ! [I5: set_option_nat,F: option_nat > real] :
% 5.52/5.88 ( ( finite5523153139673422903on_nat @ I5 )
% 5.52/5.88 => ( ! [I2: option_nat] :
% 5.52/5.88 ( ( member_option_nat @ I2 @ I5 )
% 5.52/5.88 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.88 => ( ( ln_ln_real @ ( groups6579596140936342515t_real @ F @ I5 ) )
% 5.52/5.88 = ( groups4518532050878116744t_real
% 5.52/5.88 @ ^ [X: option_nat] : ( ln_ln_real @ ( F @ X ) )
% 5.52/5.88 @ I5 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % ln_prod
% 5.52/5.88 thf(fact_8782_ln__prod,axiom,
% 5.52/5.88 ! [I5: set_real,F: real > real] :
% 5.52/5.88 ( ( finite_finite_real @ I5 )
% 5.52/5.88 => ( ! [I2: real] :
% 5.52/5.88 ( ( member_real @ I2 @ I5 )
% 5.52/5.88 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.88 => ( ( ln_ln_real @ ( groups1681761925125756287l_real @ F @ I5 ) )
% 5.52/5.88 = ( groups8097168146408367636l_real
% 5.52/5.88 @ ^ [X: real] : ( ln_ln_real @ ( F @ X ) )
% 5.52/5.88 @ I5 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % ln_prod
% 5.52/5.88 thf(fact_8783_ln__prod,axiom,
% 5.52/5.88 ! [I5: set_set_nat_rat,F: set_nat_rat > real] :
% 5.52/5.88 ( ( finite6430367030675640852at_rat @ I5 )
% 5.52/5.88 => ( ! [I2: set_nat_rat] :
% 5.52/5.88 ( ( member_set_nat_rat @ I2 @ I5 )
% 5.52/5.88 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.88 => ( ( ln_ln_real @ ( groups2125999189389939536t_real @ F @ I5 ) )
% 5.52/5.88 = ( groups4357547368389691109t_real
% 5.52/5.88 @ ^ [X: set_nat_rat] : ( ln_ln_real @ ( F @ X ) )
% 5.52/5.88 @ I5 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % ln_prod
% 5.52/5.88 thf(fact_8784_ln__prod,axiom,
% 5.52/5.88 ! [I5: set_int,F: int > real] :
% 5.52/5.88 ( ( finite_finite_int @ I5 )
% 5.52/5.88 => ( ! [I2: int] :
% 5.52/5.88 ( ( member_int @ I2 @ I5 )
% 5.52/5.88 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.88 => ( ( ln_ln_real @ ( groups2316167850115554303t_real @ F @ I5 ) )
% 5.52/5.88 = ( groups8778361861064173332t_real
% 5.52/5.88 @ ^ [X: int] : ( ln_ln_real @ ( F @ X ) )
% 5.52/5.88 @ I5 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % ln_prod
% 5.52/5.88 thf(fact_8785_ln__prod,axiom,
% 5.52/5.88 ! [I5: set_complex,F: complex > real] :
% 5.52/5.88 ( ( finite3207457112153483333omplex @ I5 )
% 5.52/5.88 => ( ! [I2: complex] :
% 5.52/5.88 ( ( member_complex @ I2 @ I5 )
% 5.52/5.88 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.88 => ( ( ln_ln_real @ ( groups766887009212190081x_real @ F @ I5 ) )
% 5.52/5.88 = ( groups5808333547571424918x_real
% 5.52/5.88 @ ^ [X: complex] : ( ln_ln_real @ ( F @ X ) )
% 5.52/5.88 @ I5 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % ln_prod
% 5.52/5.88 thf(fact_8786_ln__prod,axiom,
% 5.52/5.88 ! [I5: set_Extended_enat,F: extended_enat > real] :
% 5.52/5.88 ( ( finite4001608067531595151d_enat @ I5 )
% 5.52/5.88 => ( ! [I2: extended_enat] :
% 5.52/5.88 ( ( member_Extended_enat @ I2 @ I5 )
% 5.52/5.88 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.88 => ( ( ln_ln_real @ ( groups97031904164794029t_real @ F @ I5 ) )
% 5.52/5.88 = ( groups4148127829035722712t_real
% 5.52/5.88 @ ^ [X: extended_enat] : ( ln_ln_real @ ( F @ X ) )
% 5.52/5.88 @ I5 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % ln_prod
% 5.52/5.88 thf(fact_8787_ln__prod,axiom,
% 5.52/5.88 ! [I5: set_nat,F: nat > real] :
% 5.52/5.88 ( ( finite_finite_nat @ I5 )
% 5.52/5.88 => ( ! [I2: nat] :
% 5.52/5.88 ( ( member_nat @ I2 @ I5 )
% 5.52/5.88 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.52/5.88 => ( ( ln_ln_real @ ( groups129246275422532515t_real @ F @ I5 ) )
% 5.52/5.88 = ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [X: nat] : ( ln_ln_real @ ( F @ X ) )
% 5.52/5.88 @ I5 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % ln_prod
% 5.52/5.88 thf(fact_8788_floor__divide__lower,axiom,
% 5.52/5.88 ! [Q2: real,P6: real] :
% 5.52/5.88 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.52/5.88 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q2 ) ) ) @ Q2 ) @ P6 ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_divide_lower
% 5.52/5.88 thf(fact_8789_floor__divide__lower,axiom,
% 5.52/5.88 ! [Q2: rat,P6: rat] :
% 5.52/5.88 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.52/5.88 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q2 ) ) ) @ Q2 ) @ P6 ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_divide_lower
% 5.52/5.88 thf(fact_8790_arccos__lt__bounded,axiom,
% 5.52/5.88 ! [Y2: real] :
% 5.52/5.88 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.52/5.88 => ( ( ord_less_real @ Y2 @ one_one_real )
% 5.52/5.88 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 5.52/5.88 & ( ord_less_real @ ( arccos @ Y2 ) @ pi ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arccos_lt_bounded
% 5.52/5.88 thf(fact_8791_gbinomial__rec,axiom,
% 5.52/5.88 ! [A: complex,K: nat] :
% 5.52/5.88 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.52/5.88 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_rec
% 5.52/5.88 thf(fact_8792_gbinomial__rec,axiom,
% 5.52/5.88 ! [A: real,K: nat] :
% 5.52/5.88 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.52/5.88 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_rec
% 5.52/5.88 thf(fact_8793_gbinomial__rec,axiom,
% 5.52/5.88 ! [A: rat,K: nat] :
% 5.52/5.88 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.52/5.88 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_rec
% 5.52/5.88 thf(fact_8794_gbinomial__factors,axiom,
% 5.52/5.88 ! [A: complex,K: nat] :
% 5.52/5.88 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.52/5.88 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_factors
% 5.52/5.88 thf(fact_8795_gbinomial__factors,axiom,
% 5.52/5.88 ! [A: real,K: nat] :
% 5.52/5.88 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.52/5.88 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_factors
% 5.52/5.88 thf(fact_8796_gbinomial__factors,axiom,
% 5.52/5.88 ! [A: rat,K: nat] :
% 5.52/5.88 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.52/5.88 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_factors
% 5.52/5.88 thf(fact_8797_gbinomial__negated__upper,axiom,
% 5.52/5.88 ( gbinomial_complex
% 5.52/5.88 = ( ^ [A4: complex,K2: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K2 ) @ A4 ) @ one_one_complex ) @ K2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_negated_upper
% 5.52/5.88 thf(fact_8798_gbinomial__negated__upper,axiom,
% 5.52/5.88 ( gbinomial_real
% 5.52/5.88 = ( ^ [A4: real,K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K2 ) @ A4 ) @ one_one_real ) @ K2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_negated_upper
% 5.52/5.88 thf(fact_8799_gbinomial__negated__upper,axiom,
% 5.52/5.88 ( gbinomial_rat
% 5.52/5.88 = ( ^ [A4: rat,K2: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K2 ) @ A4 ) @ one_one_rat ) @ K2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_negated_upper
% 5.52/5.88 thf(fact_8800_gbinomial__index__swap,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 5.52/5.88 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_index_swap
% 5.52/5.88 thf(fact_8801_gbinomial__index__swap,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ K ) )
% 5.52/5.88 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_index_swap
% 5.52/5.88 thf(fact_8802_gbinomial__index__swap,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K ) )
% 5.52/5.88 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_index_swap
% 5.52/5.88 thf(fact_8803_sin__arccos__nonzero,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.88 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.52/5.88 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.52/5.88 != zero_zero_real ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sin_arccos_nonzero
% 5.52/5.88 thf(fact_8804_floor__divide__upper,axiom,
% 5.52/5.88 ! [Q2: real,P6: real] :
% 5.52/5.88 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.52/5.88 => ( ord_less_real @ P6 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_divide_upper
% 5.52/5.88 thf(fact_8805_floor__divide__upper,axiom,
% 5.52/5.88 ! [Q2: rat,P6: rat] :
% 5.52/5.88 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.52/5.88 => ( ord_less_rat @ P6 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_divide_upper
% 5.52/5.88 thf(fact_8806_round__def,axiom,
% 5.52/5.88 ( archim8280529875227126926d_real
% 5.52/5.88 = ( ^ [X: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % round_def
% 5.52/5.88 thf(fact_8807_round__def,axiom,
% 5.52/5.88 ( archim7778729529865785530nd_rat
% 5.52/5.88 = ( ^ [X: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % round_def
% 5.52/5.88 thf(fact_8808_gbinomial__minus,axiom,
% 5.52/5.88 ! [A: complex,K: nat] :
% 5.52/5.88 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.52/5.88 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_minus
% 5.52/5.88 thf(fact_8809_gbinomial__minus,axiom,
% 5.52/5.88 ! [A: real,K: nat] :
% 5.52/5.88 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.52/5.88 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_minus
% 5.52/5.88 thf(fact_8810_gbinomial__minus,axiom,
% 5.52/5.88 ! [A: rat,K: nat] :
% 5.52/5.88 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.52/5.88 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_minus
% 5.52/5.88 thf(fact_8811_gbinomial__reduce__nat,axiom,
% 5.52/5.88 ! [K: nat,A: complex] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.88 => ( ( gbinomial_complex @ A @ K )
% 5.52/5.88 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_reduce_nat
% 5.52/5.88 thf(fact_8812_gbinomial__reduce__nat,axiom,
% 5.52/5.88 ! [K: nat,A: real] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.88 => ( ( gbinomial_real @ A @ K )
% 5.52/5.88 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_reduce_nat
% 5.52/5.88 thf(fact_8813_gbinomial__reduce__nat,axiom,
% 5.52/5.88 ! [K: nat,A: rat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.88 => ( ( gbinomial_rat @ A @ K )
% 5.52/5.88 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_reduce_nat
% 5.52/5.88 thf(fact_8814_gbinomial__pochhammer,axiom,
% 5.52/5.88 ( gbinomial_complex
% 5.52/5.88 = ( ^ [A4: complex,K2: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A4 ) @ K2 ) ) @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_pochhammer
% 5.52/5.88 thf(fact_8815_gbinomial__pochhammer,axiom,
% 5.52/5.88 ( gbinomial_rat
% 5.52/5.88 = ( ^ [A4: rat,K2: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A4 ) @ K2 ) ) @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_pochhammer
% 5.52/5.88 thf(fact_8816_gbinomial__pochhammer,axiom,
% 5.52/5.88 ( gbinomial_real
% 5.52/5.88 = ( ^ [A4: real,K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A4 ) @ K2 ) ) @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_pochhammer
% 5.52/5.88 thf(fact_8817_gbinomial__pochhammer_H,axiom,
% 5.52/5.88 ( gbinomial_complex
% 5.52/5.88 = ( ^ [A4: complex,K2: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 ) @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_pochhammer'
% 5.52/5.88 thf(fact_8818_gbinomial__pochhammer_H,axiom,
% 5.52/5.88 ( gbinomial_rat
% 5.52/5.88 = ( ^ [A4: rat,K2: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A4 @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_pochhammer'
% 5.52/5.88 thf(fact_8819_gbinomial__pochhammer_H,axiom,
% 5.52/5.88 ( gbinomial_real
% 5.52/5.88 = ( ^ [A4: real,K2: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 ) @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_pochhammer'
% 5.52/5.88 thf(fact_8820_gbinomial__sum__up__index,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.52/5.88 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_sum_up_index
% 5.52/5.88 thf(fact_8821_gbinomial__sum__up__index,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.52/5.88 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_sum_up_index
% 5.52/5.88 thf(fact_8822_gbinomial__sum__up__index,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.52/5.88 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_sum_up_index
% 5.52/5.88 thf(fact_8823_gbinomial__Suc,axiom,
% 5.52/5.88 ! [A: complex,K: nat] :
% 5.52/5.88 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.52/5.88 = ( divide1717551699836669952omplex
% 5.52/5.88 @ ( groups6464643781859351333omplex
% 5.52/5.88 @ ^ [I4: nat] : ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.52/5.88 @ ( semiri5044797733671781792omplex @ ( suc @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_Suc
% 5.52/5.88 thf(fact_8824_gbinomial__Suc,axiom,
% 5.52/5.88 ! [A: rat,K: nat] :
% 5.52/5.88 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.52/5.88 = ( divide_divide_rat
% 5.52/5.88 @ ( groups73079841787564623at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.52/5.88 @ ( semiri773545260158071498ct_rat @ ( suc @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_Suc
% 5.52/5.88 thf(fact_8825_gbinomial__Suc,axiom,
% 5.52/5.88 ! [A: real,K: nat] :
% 5.52/5.88 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.52/5.88 = ( divide_divide_real
% 5.52/5.88 @ ( groups129246275422532515t_real
% 5.52/5.88 @ ^ [I4: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.52/5.88 @ ( semiri2265585572941072030t_real @ ( suc @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_Suc
% 5.52/5.88 thf(fact_8826_gbinomial__Suc,axiom,
% 5.52/5.88 ! [A: nat,K: nat] :
% 5.52/5.88 ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 5.52/5.88 = ( divide_divide_nat
% 5.52/5.88 @ ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.52/5.88 @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_Suc
% 5.52/5.88 thf(fact_8827_gbinomial__Suc,axiom,
% 5.52/5.88 ! [A: int,K: nat] :
% 5.52/5.88 ( ( gbinomial_int @ A @ ( suc @ K ) )
% 5.52/5.88 = ( divide_divide_int
% 5.52/5.88 @ ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [I4: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I4 ) )
% 5.52/5.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.52/5.88 @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_Suc
% 5.52/5.88 thf(fact_8828_floor__log__eq__powr__iff,axiom,
% 5.52/5.88 ! [X2: real,B: real,K: int] :
% 5.52/5.88 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.88 => ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.88 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X2 ) )
% 5.52/5.88 = K )
% 5.52/5.88 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X2 )
% 5.52/5.88 & ( ord_less_real @ X2 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_log_eq_powr_iff
% 5.52/5.88 thf(fact_8829_gbinomial__absorption_H,axiom,
% 5.52/5.88 ! [K: nat,A: complex] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.88 => ( ( gbinomial_complex @ A @ K )
% 5.52/5.88 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_absorption'
% 5.52/5.88 thf(fact_8830_gbinomial__absorption_H,axiom,
% 5.52/5.88 ! [K: nat,A: real] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.88 => ( ( gbinomial_real @ A @ K )
% 5.52/5.88 = ( times_times_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_absorption'
% 5.52/5.88 thf(fact_8831_gbinomial__absorption_H,axiom,
% 5.52/5.88 ! [K: nat,A: rat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.88 => ( ( gbinomial_rat @ A @ K )
% 5.52/5.88 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_absorption'
% 5.52/5.88 thf(fact_8832_arccos__le__pi2,axiom,
% 5.52/5.88 ! [Y2: real] :
% 5.52/5.88 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.88 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.52/5.88 => ( ord_less_eq_real @ ( arccos @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arccos_le_pi2
% 5.52/5.88 thf(fact_8833_floor__log2__div2,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.88 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.52/5.88 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_log2_div2
% 5.52/5.88 thf(fact_8834_floor__log__nat__eq__if,axiom,
% 5.52/5.88 ! [B: nat,N: nat,K: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.52/5.88 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.52/5.88 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.52/5.88 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.52/5.88 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % floor_log_nat_eq_if
% 5.52/5.88 thf(fact_8835_gbinomial__code,axiom,
% 5.52/5.88 ( gbinomial_complex
% 5.52/5.88 = ( ^ [A4: complex,K2: nat] :
% 5.52/5.88 ( if_complex @ ( K2 = zero_zero_nat ) @ one_one_complex
% 5.52/5.88 @ ( divide1717551699836669952omplex
% 5.52/5.88 @ ( set_fo1517530859248394432omplex
% 5.52/5.88 @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 5.52/5.88 @ zero_zero_nat
% 5.52/5.88 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 5.52/5.88 @ one_one_complex )
% 5.52/5.88 @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_code
% 5.52/5.88 thf(fact_8836_gbinomial__code,axiom,
% 5.52/5.88 ( gbinomial_rat
% 5.52/5.88 = ( ^ [A4: rat,K2: nat] :
% 5.52/5.88 ( if_rat @ ( K2 = zero_zero_nat ) @ one_one_rat
% 5.52/5.88 @ ( divide_divide_rat
% 5.52/5.88 @ ( set_fo1949268297981939178at_rat
% 5.52/5.88 @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A4 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 5.52/5.88 @ zero_zero_nat
% 5.52/5.88 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 5.52/5.88 @ one_one_rat )
% 5.52/5.88 @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_code
% 5.52/5.88 thf(fact_8837_gbinomial__code,axiom,
% 5.52/5.88 ( gbinomial_real
% 5.52/5.88 = ( ^ [A4: real,K2: nat] :
% 5.52/5.88 ( if_real @ ( K2 = zero_zero_nat ) @ one_one_real
% 5.52/5.88 @ ( divide_divide_real
% 5.52/5.88 @ ( set_fo3111899725591712190t_real
% 5.52/5.88 @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 5.52/5.88 @ zero_zero_nat
% 5.52/5.88 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 5.52/5.88 @ one_one_real )
% 5.52/5.88 @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_code
% 5.52/5.88 thf(fact_8838_arccos__cos__eq__abs__2pi,axiom,
% 5.52/5.88 ! [Theta: real] :
% 5.52/5.88 ~ ! [K3: int] :
% 5.52/5.88 ( ( arccos @ ( cos_real @ Theta ) )
% 5.52/5.88 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K3 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % arccos_cos_eq_abs_2pi
% 5.52/5.88 thf(fact_8839_gbinomial__partial__row__sum,axiom,
% 5.52/5.88 ! [A: complex,M: nat] :
% 5.52/5.88 ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K2 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ M ) )
% 5.52/5.88 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_partial_row_sum
% 5.52/5.88 thf(fact_8840_gbinomial__partial__row__sum,axiom,
% 5.52/5.88 ! [A: rat,M: nat] :
% 5.52/5.88 ( ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ M ) )
% 5.52/5.88 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_partial_row_sum
% 5.52/5.88 thf(fact_8841_gbinomial__partial__row__sum,axiom,
% 5.52/5.88 ! [A: real,M: nat] :
% 5.52/5.88 ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ M ) )
% 5.52/5.88 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_partial_row_sum
% 5.52/5.88 thf(fact_8842_binomial__code,axiom,
% 5.52/5.88 ( binomial
% 5.52/5.88 = ( ^ [N3: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N3 @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N3 @ ( minus_minus_nat @ N3 @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N3 @ K2 ) @ one_one_nat ) @ N3 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_code
% 5.52/5.88 thf(fact_8843_round__altdef,axiom,
% 5.52/5.88 ( archim8280529875227126926d_real
% 5.52/5.88 = ( ^ [X: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X ) ) @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % round_altdef
% 5.52/5.88 thf(fact_8844_round__altdef,axiom,
% 5.52/5.88 ( archim7778729529865785530nd_rat
% 5.52/5.88 = ( ^ [X: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X ) ) @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % round_altdef
% 5.52/5.88 thf(fact_8845_gbinomial__r__part__sum,axiom,
% 5.52/5.88 ! [M: nat] :
% 5.52/5.88 ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.52/5.88 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_r_part_sum
% 5.52/5.88 thf(fact_8846_gbinomial__r__part__sum,axiom,
% 5.52/5.88 ! [M: nat] :
% 5.52/5.88 ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.52/5.88 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_r_part_sum
% 5.52/5.88 thf(fact_8847_gbinomial__r__part__sum,axiom,
% 5.52/5.88 ! [M: nat] :
% 5.52/5.88 ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.52/5.88 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_r_part_sum
% 5.52/5.88 thf(fact_8848_central__binomial__lower__bound,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % central_binomial_lower_bound
% 5.52/5.88 thf(fact_8849_atMost__iff,axiom,
% 5.52/5.88 ! [I: real,K: real] :
% 5.52/5.88 ( ( member_real @ I @ ( set_ord_atMost_real @ K ) )
% 5.52/5.88 = ( ord_less_eq_real @ I @ K ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_iff
% 5.52/5.88 thf(fact_8850_atMost__iff,axiom,
% 5.52/5.88 ! [I: set_nat_rat,K: set_nat_rat] :
% 5.52/5.88 ( ( member_set_nat_rat @ I @ ( set_or3094126398206284534at_rat @ K ) )
% 5.52/5.88 = ( ord_le2679597024174929757at_rat @ I @ K ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_iff
% 5.52/5.88 thf(fact_8851_atMost__iff,axiom,
% 5.52/5.88 ! [I: set_nat,K: set_nat] :
% 5.52/5.88 ( ( member_set_nat @ I @ ( set_or4236626031148496127et_nat @ K ) )
% 5.52/5.88 = ( ord_less_eq_set_nat @ I @ K ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_iff
% 5.52/5.88 thf(fact_8852_atMost__iff,axiom,
% 5.52/5.88 ! [I: rat,K: rat] :
% 5.52/5.88 ( ( member_rat @ I @ ( set_ord_atMost_rat @ K ) )
% 5.52/5.88 = ( ord_less_eq_rat @ I @ K ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_iff
% 5.52/5.88 thf(fact_8853_atMost__iff,axiom,
% 5.52/5.88 ! [I: num,K: num] :
% 5.52/5.88 ( ( member_num @ I @ ( set_ord_atMost_num @ K ) )
% 5.52/5.88 = ( ord_less_eq_num @ I @ K ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_iff
% 5.52/5.88 thf(fact_8854_atMost__iff,axiom,
% 5.52/5.88 ! [I: int,K: int] :
% 5.52/5.88 ( ( member_int @ I @ ( set_ord_atMost_int @ K ) )
% 5.52/5.88 = ( ord_less_eq_int @ I @ K ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_iff
% 5.52/5.88 thf(fact_8855_atMost__iff,axiom,
% 5.52/5.88 ! [I: nat,K: nat] :
% 5.52/5.88 ( ( member_nat @ I @ ( set_ord_atMost_nat @ K ) )
% 5.52/5.88 = ( ord_less_eq_nat @ I @ K ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_iff
% 5.52/5.88 thf(fact_8856_binomial__n__n,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( binomial @ N @ N )
% 5.52/5.88 = one_one_nat ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_n_n
% 5.52/5.88 thf(fact_8857_atMost__subset__iff,axiom,
% 5.52/5.88 ! [X2: set_nat,Y2: set_nat] :
% 5.52/5.88 ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X2 ) @ ( set_or4236626031148496127et_nat @ Y2 ) )
% 5.52/5.88 = ( ord_less_eq_set_nat @ X2 @ Y2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_subset_iff
% 5.52/5.88 thf(fact_8858_atMost__subset__iff,axiom,
% 5.52/5.88 ! [X2: rat,Y2: rat] :
% 5.52/5.88 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X2 ) @ ( set_ord_atMost_rat @ Y2 ) )
% 5.52/5.88 = ( ord_less_eq_rat @ X2 @ Y2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_subset_iff
% 5.52/5.88 thf(fact_8859_atMost__subset__iff,axiom,
% 5.52/5.88 ! [X2: num,Y2: num] :
% 5.52/5.88 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X2 ) @ ( set_ord_atMost_num @ Y2 ) )
% 5.52/5.88 = ( ord_less_eq_num @ X2 @ Y2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_subset_iff
% 5.52/5.88 thf(fact_8860_atMost__subset__iff,axiom,
% 5.52/5.88 ! [X2: int,Y2: int] :
% 5.52/5.88 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X2 ) @ ( set_ord_atMost_int @ Y2 ) )
% 5.52/5.88 = ( ord_less_eq_int @ X2 @ Y2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_subset_iff
% 5.52/5.88 thf(fact_8861_atMost__subset__iff,axiom,
% 5.52/5.88 ! [X2: nat,Y2: nat] :
% 5.52/5.88 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X2 ) @ ( set_ord_atMost_nat @ Y2 ) )
% 5.52/5.88 = ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_subset_iff
% 5.52/5.88 thf(fact_8862_binomial__eq__0__iff,axiom,
% 5.52/5.88 ! [N: nat,K: nat] :
% 5.52/5.88 ( ( ( binomial @ N @ K )
% 5.52/5.88 = zero_zero_nat )
% 5.52/5.88 = ( ord_less_nat @ N @ K ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_eq_0_iff
% 5.52/5.88 thf(fact_8863_binomial__Suc__Suc,axiom,
% 5.52/5.88 ! [N: nat,K: nat] :
% 5.52/5.88 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.52/5.88 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_Suc_Suc
% 5.52/5.88 thf(fact_8864_binomial__n__0,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( binomial @ N @ zero_zero_nat )
% 5.52/5.88 = one_one_nat ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_n_0
% 5.52/5.88 thf(fact_8865_Icc__subset__Iic__iff,axiom,
% 5.52/5.88 ! [L: set_nat,H2: set_nat,H3: set_nat] :
% 5.52/5.88 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L @ H2 ) @ ( set_or4236626031148496127et_nat @ H3 ) )
% 5.52/5.88 = ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 5.52/5.88 | ( ord_less_eq_set_nat @ H2 @ H3 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % Icc_subset_Iic_iff
% 5.52/5.88 thf(fact_8866_Icc__subset__Iic__iff,axiom,
% 5.52/5.88 ! [L: rat,H2: rat,H3: rat] :
% 5.52/5.88 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H2 ) @ ( set_ord_atMost_rat @ H3 ) )
% 5.52/5.88 = ( ~ ( ord_less_eq_rat @ L @ H2 )
% 5.52/5.88 | ( ord_less_eq_rat @ H2 @ H3 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % Icc_subset_Iic_iff
% 5.52/5.88 thf(fact_8867_Icc__subset__Iic__iff,axiom,
% 5.52/5.88 ! [L: num,H2: num,H3: num] :
% 5.52/5.88 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 5.52/5.88 = ( ~ ( ord_less_eq_num @ L @ H2 )
% 5.52/5.88 | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % Icc_subset_Iic_iff
% 5.52/5.88 thf(fact_8868_Icc__subset__Iic__iff,axiom,
% 5.52/5.88 ! [L: nat,H2: nat,H3: nat] :
% 5.52/5.88 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 5.52/5.88 = ( ~ ( ord_less_eq_nat @ L @ H2 )
% 5.52/5.88 | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % Icc_subset_Iic_iff
% 5.52/5.88 thf(fact_8869_Icc__subset__Iic__iff,axiom,
% 5.52/5.88 ! [L: int,H2: int,H3: int] :
% 5.52/5.88 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 5.52/5.88 = ( ~ ( ord_less_eq_int @ L @ H2 )
% 5.52/5.88 | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % Icc_subset_Iic_iff
% 5.52/5.88 thf(fact_8870_Icc__subset__Iic__iff,axiom,
% 5.52/5.88 ! [L: real,H2: real,H3: real] :
% 5.52/5.88 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 5.52/5.88 = ( ~ ( ord_less_eq_real @ L @ H2 )
% 5.52/5.88 | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % Icc_subset_Iic_iff
% 5.52/5.88 thf(fact_8871_sum_OatMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > rat,N: nat] :
% 5.52/5.88 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_Suc
% 5.52/5.88 thf(fact_8872_sum_OatMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > int,N: nat] :
% 5.52/5.88 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_Suc
% 5.52/5.88 thf(fact_8873_sum_OatMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > complex,N: nat] :
% 5.52/5.88 ( ( groups2073611262835488442omplex @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_Suc
% 5.52/5.88 thf(fact_8874_sum_OatMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > nat,N: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_Suc
% 5.52/5.88 thf(fact_8875_sum_OatMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > real,N: nat] :
% 5.52/5.88 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_Suc
% 5.52/5.88 thf(fact_8876_zero__less__binomial__iff,axiom,
% 5.52/5.88 ! [N: nat,K: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.52/5.88 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.52/5.88
% 5.52/5.88 % zero_less_binomial_iff
% 5.52/5.88 thf(fact_8877_prod_OatMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > real,N: nat] :
% 5.52/5.88 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atMost_Suc
% 5.52/5.88 thf(fact_8878_prod_OatMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > rat,N: nat] :
% 5.52/5.88 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atMost_Suc
% 5.52/5.88 thf(fact_8879_prod_OatMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > nat,N: nat] :
% 5.52/5.88 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atMost_Suc
% 5.52/5.88 thf(fact_8880_prod_OatMost__Suc,axiom,
% 5.52/5.88 ! [G: nat > int,N: nat] :
% 5.52/5.88 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atMost_Suc
% 5.52/5.88 thf(fact_8881_choose__one,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( binomial @ N @ one_one_nat )
% 5.52/5.88 = N ) ).
% 5.52/5.88
% 5.52/5.88 % choose_one
% 5.52/5.88 thf(fact_8882_atMost__def,axiom,
% 5.52/5.88 ( set_or3094126398206284534at_rat
% 5.52/5.88 = ( ^ [U2: set_nat_rat] :
% 5.52/5.88 ( collect_set_nat_rat
% 5.52/5.88 @ ^ [X: set_nat_rat] : ( ord_le2679597024174929757at_rat @ X @ U2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_def
% 5.52/5.88 thf(fact_8883_atMost__def,axiom,
% 5.52/5.88 ( set_or5632376147039224640at_rat
% 5.52/5.88 = ( ^ [U2: nat > rat] :
% 5.52/5.88 ( collect_nat_rat
% 5.52/5.88 @ ^ [X: nat > rat] : ( ord_less_eq_nat_rat @ X @ U2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_def
% 5.52/5.88 thf(fact_8884_atMost__def,axiom,
% 5.52/5.88 ( set_or4236626031148496127et_nat
% 5.52/5.88 = ( ^ [U2: set_nat] :
% 5.52/5.88 ( collect_set_nat
% 5.52/5.88 @ ^ [X: set_nat] : ( ord_less_eq_set_nat @ X @ U2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_def
% 5.52/5.88 thf(fact_8885_atMost__def,axiom,
% 5.52/5.88 ( set_ord_atMost_rat
% 5.52/5.88 = ( ^ [U2: rat] :
% 5.52/5.88 ( collect_rat
% 5.52/5.88 @ ^ [X: rat] : ( ord_less_eq_rat @ X @ U2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_def
% 5.52/5.88 thf(fact_8886_atMost__def,axiom,
% 5.52/5.88 ( set_ord_atMost_num
% 5.52/5.88 = ( ^ [U2: num] :
% 5.52/5.88 ( collect_num
% 5.52/5.88 @ ^ [X: num] : ( ord_less_eq_num @ X @ U2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_def
% 5.52/5.88 thf(fact_8887_atMost__def,axiom,
% 5.52/5.88 ( set_ord_atMost_int
% 5.52/5.88 = ( ^ [U2: int] :
% 5.52/5.88 ( collect_int
% 5.52/5.88 @ ^ [X: int] : ( ord_less_eq_int @ X @ U2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_def
% 5.52/5.88 thf(fact_8888_atMost__def,axiom,
% 5.52/5.88 ( set_ord_atMost_nat
% 5.52/5.88 = ( ^ [U2: nat] :
% 5.52/5.88 ( collect_nat
% 5.52/5.88 @ ^ [X: nat] : ( ord_less_eq_nat @ X @ U2 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_def
% 5.52/5.88 thf(fact_8889_sum__choose__lower,axiom,
% 5.52/5.88 ! [R: nat,N: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R @ K2 ) @ K2 )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N ) ) @ N ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_choose_lower
% 5.52/5.88 thf(fact_8890_choose__rising__sum_I1_J,axiom,
% 5.52/5.88 ! [N: nat,M: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.52/5.88 @ ( set_ord_atMost_nat @ M ) )
% 5.52/5.88 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_rising_sum(1)
% 5.52/5.88 thf(fact_8891_choose__rising__sum_I2_J,axiom,
% 5.52/5.88 ! [N: nat,M: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.52/5.88 @ ( set_ord_atMost_nat @ M ) )
% 5.52/5.88 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_rising_sum(2)
% 5.52/5.88 thf(fact_8892_binomial__eq__0,axiom,
% 5.52/5.88 ! [N: nat,K: nat] :
% 5.52/5.88 ( ( ord_less_nat @ N @ K )
% 5.52/5.88 => ( ( binomial @ N @ K )
% 5.52/5.88 = zero_zero_nat ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_eq_0
% 5.52/5.88 thf(fact_8893_Suc__times__binomial,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 5.52/5.88 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % Suc_times_binomial
% 5.52/5.88 thf(fact_8894_Suc__times__binomial__eq,axiom,
% 5.52/5.88 ! [N: nat,K: nat] :
% 5.52/5.88 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 5.52/5.88 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % Suc_times_binomial_eq
% 5.52/5.88 thf(fact_8895_binomial__symmetric,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( binomial @ N @ K )
% 5.52/5.88 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_symmetric
% 5.52/5.88 thf(fact_8896_choose__mult__lemma,axiom,
% 5.52/5.88 ! [M: nat,R: nat,K: nat] :
% 5.52/5.88 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 5.52/5.88 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_mult_lemma
% 5.52/5.88 thf(fact_8897_binomial__le__pow,axiom,
% 5.52/5.88 ! [R: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ R @ N )
% 5.52/5.88 => ( ord_less_eq_nat @ ( binomial @ N @ R ) @ ( power_power_nat @ N @ R ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_le_pow
% 5.52/5.88 thf(fact_8898_sum__choose__diagonal,axiom,
% 5.52/5.88 ! [M: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N @ K2 ) @ ( minus_minus_nat @ M @ K2 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ M ) )
% 5.52/5.88 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_choose_diagonal
% 5.52/5.88 thf(fact_8899_vandermonde,axiom,
% 5.52/5.88 ! [M: nat,N: nat,R: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M @ K2 ) @ ( binomial @ N @ ( minus_minus_nat @ R @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ R ) )
% 5.52/5.88 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R ) ) ).
% 5.52/5.88
% 5.52/5.88 % vandermonde
% 5.52/5.88 thf(fact_8900_choose__row__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_row_sum
% 5.52/5.88 thf(fact_8901_binomial,axiom,
% 5.52/5.88 ! [A: nat,B: nat,N: nat] :
% 5.52/5.88 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.52/5.88 = ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial
% 5.52/5.88 thf(fact_8902_frac__ge__0,axiom,
% 5.52/5.88 ! [X2: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % frac_ge_0
% 5.52/5.88 thf(fact_8903_frac__ge__0,axiom,
% 5.52/5.88 ! [X2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % frac_ge_0
% 5.52/5.88 thf(fact_8904_frac__lt__1,axiom,
% 5.52/5.88 ! [X2: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X2 ) @ one_one_real ) ).
% 5.52/5.88
% 5.52/5.88 % frac_lt_1
% 5.52/5.88 thf(fact_8905_frac__lt__1,axiom,
% 5.52/5.88 ! [X2: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X2 ) @ one_one_rat ) ).
% 5.52/5.88
% 5.52/5.88 % frac_lt_1
% 5.52/5.88 thf(fact_8906_frac__1__eq,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X2 @ one_one_real ) )
% 5.52/5.88 = ( archim2898591450579166408c_real @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % frac_1_eq
% 5.52/5.88 thf(fact_8907_frac__1__eq,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) )
% 5.52/5.88 = ( archimedean_frac_rat @ X2 ) ) ).
% 5.52/5.88
% 5.52/5.88 % frac_1_eq
% 5.52/5.88 thf(fact_8908_zero__less__binomial,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % zero_less_binomial
% 5.52/5.88 thf(fact_8909_Suc__times__binomial__add,axiom,
% 5.52/5.88 ! [A: nat,B: nat] :
% 5.52/5.88 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.52/5.88 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % Suc_times_binomial_add
% 5.52/5.88 thf(fact_8910_binomial__Suc__Suc__eq__times,axiom,
% 5.52/5.88 ! [N: nat,K: nat] :
% 5.52/5.88 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.52/5.88 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_Suc_Suc_eq_times
% 5.52/5.88 thf(fact_8911_choose__mult,axiom,
% 5.52/5.88 ! [K: nat,M: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ M )
% 5.52/5.88 => ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 5.52/5.88 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_mult
% 5.52/5.88 thf(fact_8912_binomial__ring,axiom,
% 5.52/5.88 ! [A: complex,B: complex,N: nat] :
% 5.52/5.88 ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N )
% 5.52/5.88 = ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K2 ) ) @ ( power_power_complex @ A @ K2 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_ring
% 5.52/5.88 thf(fact_8913_binomial__ring,axiom,
% 5.52/5.88 ! [A: int,B: int,N: nat] :
% 5.52/5.88 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.52/5.88 = ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K2 ) ) @ ( power_power_int @ A @ K2 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_ring
% 5.52/5.88 thf(fact_8914_binomial__ring,axiom,
% 5.52/5.88 ! [A: rat,B: rat,N: nat] :
% 5.52/5.88 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 5.52/5.88 = ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K2 ) ) @ ( power_power_rat @ A @ K2 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_ring
% 5.52/5.88 thf(fact_8915_binomial__ring,axiom,
% 5.52/5.88 ! [A: extended_enat,B: extended_enat,N: nat] :
% 5.52/5.88 ( ( power_8040749407984259932d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ N )
% 5.52/5.88 = ( groups7108830773950497114d_enat
% 5.52/5.88 @ ^ [K2: nat] : ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ ( binomial @ N @ K2 ) ) @ ( power_8040749407984259932d_enat @ A @ K2 ) ) @ ( power_8040749407984259932d_enat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_ring
% 5.52/5.88 thf(fact_8916_binomial__ring,axiom,
% 5.52/5.88 ! [A: nat,B: nat,N: nat] :
% 5.52/5.88 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.52/5.88 = ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_ring
% 5.52/5.88 thf(fact_8917_binomial__ring,axiom,
% 5.52/5.88 ! [A: real,B: real,N: nat] :
% 5.52/5.88 ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N )
% 5.52/5.88 = ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K2 ) ) @ ( power_power_real @ A @ K2 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_ring
% 5.52/5.88 thf(fact_8918_binomial__absorb__comp,axiom,
% 5.52/5.88 ! [N: nat,K: nat] :
% 5.52/5.88 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 5.52/5.88 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_absorb_comp
% 5.52/5.88 thf(fact_8919_pochhammer__binomial__sum,axiom,
% 5.52/5.88 ! [A: complex,B: complex,N: nat] :
% 5.52/5.88 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ B ) @ N )
% 5.52/5.88 = ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K2 ) ) @ ( comm_s2602460028002588243omplex @ A @ K2 ) ) @ ( comm_s2602460028002588243omplex @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_binomial_sum
% 5.52/5.88 thf(fact_8920_pochhammer__binomial__sum,axiom,
% 5.52/5.88 ! [A: int,B: int,N: nat] :
% 5.52/5.88 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.52/5.88 = ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K2 ) ) @ ( comm_s4660882817536571857er_int @ A @ K2 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_binomial_sum
% 5.52/5.88 thf(fact_8921_pochhammer__binomial__sum,axiom,
% 5.52/5.88 ! [A: rat,B: rat,N: nat] :
% 5.52/5.88 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 5.52/5.88 = ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K2 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K2 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_binomial_sum
% 5.52/5.88 thf(fact_8922_pochhammer__binomial__sum,axiom,
% 5.52/5.88 ! [A: real,B: real,N: nat] :
% 5.52/5.88 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N )
% 5.52/5.88 = ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K2 ) ) @ ( comm_s7457072308508201937r_real @ A @ K2 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % pochhammer_binomial_sum
% 5.52/5.88 thf(fact_8923_choose__square__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [K2: nat] : ( power_power_nat @ ( binomial @ N @ K2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_square_sum
% 5.52/5.88 thf(fact_8924_atMost__nat__numeral,axiom,
% 5.52/5.88 ! [K: num] :
% 5.52/5.88 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.52/5.88 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % atMost_nat_numeral
% 5.52/5.88 thf(fact_8925_Iic__subset__Iio__iff,axiom,
% 5.52/5.88 ! [A: rat,B: rat] :
% 5.52/5.88 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 5.52/5.88 = ( ord_less_rat @ A @ B ) ) ).
% 5.52/5.88
% 5.52/5.88 % Iic_subset_Iio_iff
% 5.52/5.88 thf(fact_8926_Iic__subset__Iio__iff,axiom,
% 5.52/5.88 ! [A: num,B: num] :
% 5.52/5.88 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 5.52/5.88 = ( ord_less_num @ A @ B ) ) ).
% 5.52/5.88
% 5.52/5.88 % Iic_subset_Iio_iff
% 5.52/5.88 thf(fact_8927_Iic__subset__Iio__iff,axiom,
% 5.52/5.88 ! [A: int,B: int] :
% 5.52/5.88 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 5.52/5.88 = ( ord_less_int @ A @ B ) ) ).
% 5.52/5.88
% 5.52/5.88 % Iic_subset_Iio_iff
% 5.52/5.88 thf(fact_8928_Iic__subset__Iio__iff,axiom,
% 5.52/5.88 ! [A: nat,B: nat] :
% 5.52/5.88 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 5.52/5.88 = ( ord_less_nat @ A @ B ) ) ).
% 5.52/5.88
% 5.52/5.88 % Iic_subset_Iio_iff
% 5.52/5.88 thf(fact_8929_Iic__subset__Iio__iff,axiom,
% 5.52/5.88 ! [A: real,B: real] :
% 5.52/5.88 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 5.52/5.88 = ( ord_less_real @ A @ B ) ) ).
% 5.52/5.88
% 5.52/5.88 % Iic_subset_Iio_iff
% 5.52/5.88 thf(fact_8930_choose__alternating__linear__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( N != one_one_nat )
% 5.52/5.88 => ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I4 ) @ ( semiri8010041392384452111omplex @ I4 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_complex ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_alternating_linear_sum
% 5.52/5.88 thf(fact_8931_choose__alternating__linear__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( N != one_one_nat )
% 5.52/5.88 => ( ( groups7501900531339628137nteger
% 5.52/5.88 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I4 ) @ ( semiri4939895301339042750nteger @ I4 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_alternating_linear_sum
% 5.52/5.88 thf(fact_8932_choose__alternating__linear__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( N != one_one_nat )
% 5.52/5.88 => ( ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I4 ) @ ( semiri1314217659103216013at_int @ I4 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_int ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_alternating_linear_sum
% 5.52/5.88 thf(fact_8933_choose__alternating__linear__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( N != one_one_nat )
% 5.52/5.88 => ( ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I4 ) @ ( semiri681578069525770553at_rat @ I4 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_rat ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_alternating_linear_sum
% 5.52/5.88 thf(fact_8934_choose__alternating__linear__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( N != one_one_nat )
% 5.52/5.88 => ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( semiri5074537144036343181t_real @ I4 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_real ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_alternating_linear_sum
% 5.52/5.88 thf(fact_8935_binomial__absorption,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 5.52/5.88 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_absorption
% 5.52/5.88 thf(fact_8936_binomial__r__part__sum,axiom,
% 5.52/5.88 ! [M: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.52/5.88 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_r_part_sum
% 5.52/5.88 thf(fact_8937_choose__linear__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_linear_sum
% 5.52/5.88 thf(fact_8938_binomial__fact__lemma,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.52/5.88 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_fact_lemma
% 5.52/5.88 thf(fact_8939_choose__alternating__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I4 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_complex ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_alternating_sum
% 5.52/5.88 thf(fact_8940_choose__alternating__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( groups7501900531339628137nteger
% 5.52/5.88 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I4 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_z3403309356797280102nteger ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_alternating_sum
% 5.52/5.88 thf(fact_8941_choose__alternating__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I4 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_int ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_alternating_sum
% 5.52/5.88 thf(fact_8942_choose__alternating__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I4 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_rat ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_alternating_sum
% 5.52/5.88 thf(fact_8943_choose__alternating__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_real ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_alternating_sum
% 5.52/5.88 thf(fact_8944_sum_OatMost__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > rat,N: nat] :
% 5.52/5.88 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_Suc_shift
% 5.52/5.88 thf(fact_8945_sum_OatMost__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > int,N: nat] :
% 5.52/5.88 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_Suc_shift
% 5.52/5.88 thf(fact_8946_sum_OatMost__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > complex,N: nat] :
% 5.52/5.88 ( ( groups2073611262835488442omplex @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( plus_plus_complex @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_Suc_shift
% 5.52/5.88 thf(fact_8947_sum_OatMost__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > nat,N: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_Suc_shift
% 5.52/5.88 thf(fact_8948_sum_OatMost__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > real,N: nat] :
% 5.52/5.88 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_Suc_shift
% 5.52/5.88 thf(fact_8949_polyfun__eq__coeffs,axiom,
% 5.52/5.88 ! [C: nat > complex,N: nat,D2: nat > complex] :
% 5.52/5.88 ( ( ! [X: complex] :
% 5.52/5.88 ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( D2 @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) )
% 5.52/5.88 = ( ! [I4: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ I4 @ N )
% 5.52/5.88 => ( ( C @ I4 )
% 5.52/5.88 = ( D2 @ I4 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_eq_coeffs
% 5.52/5.88 thf(fact_8950_polyfun__eq__coeffs,axiom,
% 5.52/5.88 ! [C: nat > real,N: nat,D2: nat > real] :
% 5.52/5.88 ( ( ! [X: real] :
% 5.52/5.88 ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( D2 @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) )
% 5.52/5.88 = ( ! [I4: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ I4 @ N )
% 5.52/5.88 => ( ( C @ I4 )
% 5.52/5.88 = ( D2 @ I4 ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_eq_coeffs
% 5.52/5.88 thf(fact_8951_bounded__imp__summable,axiom,
% 5.52/5.88 ! [A: nat > int,B4: int] :
% 5.52/5.88 ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N2 ) )
% 5.52/5.88 => ( ! [N2: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N2 ) ) @ B4 )
% 5.52/5.88 => ( summable_int @ A ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % bounded_imp_summable
% 5.52/5.88 thf(fact_8952_bounded__imp__summable,axiom,
% 5.52/5.88 ! [A: nat > nat,B4: nat] :
% 5.52/5.88 ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N2 ) )
% 5.52/5.88 => ( ! [N2: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N2 ) ) @ B4 )
% 5.52/5.88 => ( summable_nat @ A ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % bounded_imp_summable
% 5.52/5.88 thf(fact_8953_bounded__imp__summable,axiom,
% 5.52/5.88 ! [A: nat > real,B4: real] :
% 5.52/5.88 ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.52/5.88 => ( ! [N2: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N2 ) ) @ B4 )
% 5.52/5.88 => ( summable_real @ A ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % bounded_imp_summable
% 5.52/5.88 thf(fact_8954_prod_OatMost__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > real,N: nat] :
% 5.52/5.88 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups129246275422532515t_real
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atMost_Suc_shift
% 5.52/5.88 thf(fact_8955_prod_OatMost__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > rat,N: nat] :
% 5.52/5.88 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups73079841787564623at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atMost_Suc_shift
% 5.52/5.88 thf(fact_8956_prod_OatMost__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > nat,N: nat] :
% 5.52/5.88 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atMost_Suc_shift
% 5.52/5.88 thf(fact_8957_prod_OatMost__Suc__shift,axiom,
% 5.52/5.88 ! [G: nat > int,N: nat] :
% 5.52/5.88 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.52/5.88 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atMost_Suc_shift
% 5.52/5.88 thf(fact_8958_binomial__ge__n__over__k__pow__k,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_ge_n_over_k_pow_k
% 5.52/5.88 thf(fact_8959_binomial__ge__n__over__k__pow__k,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_ge_n_over_k_pow_k
% 5.52/5.88 thf(fact_8960_binomial__maximum_H,axiom,
% 5.52/5.88 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_maximum'
% 5.52/5.88 thf(fact_8961_binomial__mono,axiom,
% 5.52/5.88 ! [K: nat,K6: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ K6 )
% 5.52/5.88 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.52/5.88 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_mono
% 5.52/5.88 thf(fact_8962_binomial__antimono,axiom,
% 5.52/5.88 ! [K: nat,K6: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ K6 )
% 5.52/5.88 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.52/5.88 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.52/5.88 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_antimono
% 5.52/5.88 thf(fact_8963_binomial__maximum,axiom,
% 5.52/5.88 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_maximum
% 5.52/5.88 thf(fact_8964_binomial__le__pow2,axiom,
% 5.52/5.88 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_le_pow2
% 5.52/5.88 thf(fact_8965_choose__reduce__nat,axiom,
% 5.52/5.88 ! [N: nat,K: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.88 => ( ( binomial @ N @ K )
% 5.52/5.88 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_reduce_nat
% 5.52/5.88 thf(fact_8966_times__binomial__minus1__eq,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.52/5.88 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.52/5.88 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % times_binomial_minus1_eq
% 5.52/5.88 thf(fact_8967_binomial__altdef__nat,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( binomial @ N @ K )
% 5.52/5.88 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_altdef_nat
% 5.52/5.88 thf(fact_8968_frac__eq,axiom,
% 5.52/5.88 ! [X2: real] :
% 5.52/5.88 ( ( ( archim2898591450579166408c_real @ X2 )
% 5.52/5.88 = X2 )
% 5.52/5.88 = ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.88 & ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % frac_eq
% 5.52/5.88 thf(fact_8969_frac__eq,axiom,
% 5.52/5.88 ! [X2: rat] :
% 5.52/5.88 ( ( ( archimedean_frac_rat @ X2 )
% 5.52/5.88 = X2 )
% 5.52/5.88 = ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.52/5.88 & ( ord_less_rat @ X2 @ one_one_rat ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % frac_eq
% 5.52/5.88 thf(fact_8970_polyfun__eq__0,axiom,
% 5.52/5.88 ! [C: nat > complex,N: nat] :
% 5.52/5.88 ( ( ! [X: complex] :
% 5.52/5.88 ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_complex ) )
% 5.52/5.88 = ( ! [I4: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ I4 @ N )
% 5.52/5.88 => ( ( C @ I4 )
% 5.52/5.88 = zero_zero_complex ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_eq_0
% 5.52/5.88 thf(fact_8971_polyfun__eq__0,axiom,
% 5.52/5.88 ! [C: nat > real,N: nat] :
% 5.52/5.88 ( ( ! [X: real] :
% 5.52/5.88 ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_real ) )
% 5.52/5.88 = ( ! [I4: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ I4 @ N )
% 5.52/5.88 => ( ( C @ I4 )
% 5.52/5.88 = zero_zero_real ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_eq_0
% 5.52/5.88 thf(fact_8972_zero__polynom__imp__zero__coeffs,axiom,
% 5.52/5.88 ! [C: nat > complex,N: nat,K: nat] :
% 5.52/5.88 ( ! [W3: complex] :
% 5.52/5.88 ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ W3 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_complex )
% 5.52/5.88 => ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( C @ K )
% 5.52/5.88 = zero_zero_complex ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % zero_polynom_imp_zero_coeffs
% 5.52/5.88 thf(fact_8973_zero__polynom__imp__zero__coeffs,axiom,
% 5.52/5.88 ! [C: nat > real,N: nat,K: nat] :
% 5.52/5.88 ( ! [W3: real] :
% 5.52/5.88 ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ W3 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_real )
% 5.52/5.88 => ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( C @ K )
% 5.52/5.88 = zero_zero_real ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % zero_polynom_imp_zero_coeffs
% 5.52/5.88 thf(fact_8974_frac__add,axiom,
% 5.52/5.88 ! [X2: real,Y2: real] :
% 5.52/5.88 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real )
% 5.52/5.88 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.52/5.88 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y2 ) ) ) )
% 5.52/5.88 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real )
% 5.52/5.88 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.52/5.88 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % frac_add
% 5.52/5.88 thf(fact_8975_frac__add,axiom,
% 5.52/5.88 ! [X2: rat,Y2: rat] :
% 5.52/5.88 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat )
% 5.52/5.88 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ Y2 ) )
% 5.52/5.88 = ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y2 ) ) ) )
% 5.52/5.88 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat )
% 5.52/5.88 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ Y2 ) )
% 5.52/5.88 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % frac_add
% 5.52/5.88 thf(fact_8976_sum_OatMost__shift,axiom,
% 5.52/5.88 ! [G: nat > rat,N: nat] :
% 5.52/5.88 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_shift
% 5.52/5.88 thf(fact_8977_sum_OatMost__shift,axiom,
% 5.52/5.88 ! [G: nat > int,N: nat] :
% 5.52/5.88 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_shift
% 5.52/5.88 thf(fact_8978_sum_OatMost__shift,axiom,
% 5.52/5.88 ! [G: nat > complex,N: nat] :
% 5.52/5.88 ( ( groups2073611262835488442omplex @ G @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( plus_plus_complex @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_shift
% 5.52/5.88 thf(fact_8979_sum_OatMost__shift,axiom,
% 5.52/5.88 ! [G: nat > nat,N: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_shift
% 5.52/5.88 thf(fact_8980_sum_OatMost__shift,axiom,
% 5.52/5.88 ! [G: nat > real,N: nat] :
% 5.52/5.88 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.atMost_shift
% 5.52/5.88 thf(fact_8981_sum__up__index__split,axiom,
% 5.52/5.88 ! [F: nat > rat,M: nat,N: nat] :
% 5.52/5.88 ( ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.52/5.88 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_up_index_split
% 5.52/5.88 thf(fact_8982_sum__up__index__split,axiom,
% 5.52/5.88 ! [F: nat > int,M: nat,N: nat] :
% 5.52/5.88 ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.52/5.88 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_up_index_split
% 5.52/5.88 thf(fact_8983_sum__up__index__split,axiom,
% 5.52/5.88 ! [F: nat > complex,M: nat,N: nat] :
% 5.52/5.88 ( ( groups2073611262835488442omplex @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.52/5.88 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_up_index_split
% 5.52/5.88 thf(fact_8984_sum__up__index__split,axiom,
% 5.52/5.88 ! [F: nat > nat,M: nat,N: nat] :
% 5.52/5.88 ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.52/5.88 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_up_index_split
% 5.52/5.88 thf(fact_8985_sum__up__index__split,axiom,
% 5.52/5.88 ! [F: nat > real,M: nat,N: nat] :
% 5.52/5.88 ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.52/5.88 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_up_index_split
% 5.52/5.88 thf(fact_8986_prod_OatMost__shift,axiom,
% 5.52/5.88 ! [G: nat > real,N: nat] :
% 5.52/5.88 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups129246275422532515t_real
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atMost_shift
% 5.52/5.88 thf(fact_8987_prod_OatMost__shift,axiom,
% 5.52/5.88 ! [G: nat > rat,N: nat] :
% 5.52/5.88 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups73079841787564623at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atMost_shift
% 5.52/5.88 thf(fact_8988_prod_OatMost__shift,axiom,
% 5.52/5.88 ! [G: nat > nat,N: nat] :
% 5.52/5.88 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atMost_shift
% 5.52/5.88 thf(fact_8989_prod_OatMost__shift,axiom,
% 5.52/5.88 ! [G: nat > int,N: nat] :
% 5.52/5.88 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.52/5.88 @ ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.atMost_shift
% 5.52/5.88 thf(fact_8990_gbinomial__parallel__sum,axiom,
% 5.52/5.88 ! [A: complex,N: nat] :
% 5.52/5.88 ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [K2: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ K2 )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ N ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_parallel_sum
% 5.52/5.88 thf(fact_8991_gbinomial__parallel__sum,axiom,
% 5.52/5.88 ! [A: rat,N: nat] :
% 5.52/5.88 ( ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [K2: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ K2 )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ N ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_parallel_sum
% 5.52/5.88 thf(fact_8992_gbinomial__parallel__sum,axiom,
% 5.52/5.88 ! [A: real,N: nat] :
% 5.52/5.88 ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [K2: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ K2 )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ N ) ) ).
% 5.52/5.88
% 5.52/5.88 % gbinomial_parallel_sum
% 5.52/5.88 thf(fact_8993_sum_Otriangle__reindex__eq,axiom,
% 5.52/5.88 ! [G: nat > nat > nat,N: nat] :
% 5.52/5.88 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.52/5.88 @ ( collec3392354462482085612at_nat
% 5.52/5.88 @ ( produc6081775807080527818_nat_o
% 5.52/5.88 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.52/5.88 = ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [K2: nat] :
% 5.52/5.88 ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K2 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ K2 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.triangle_reindex_eq
% 5.52/5.88 thf(fact_8994_sum_Otriangle__reindex__eq,axiom,
% 5.52/5.88 ! [G: nat > nat > real,N: nat] :
% 5.52/5.88 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.52/5.88 @ ( collec3392354462482085612at_nat
% 5.52/5.88 @ ( produc6081775807080527818_nat_o
% 5.52/5.88 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.52/5.88 = ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [K2: nat] :
% 5.52/5.88 ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K2 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ K2 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.triangle_reindex_eq
% 5.52/5.88 thf(fact_8995_prod_Otriangle__reindex__eq,axiom,
% 5.52/5.88 ! [G: nat > nat > nat,N: nat] :
% 5.52/5.88 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.52/5.88 @ ( collec3392354462482085612at_nat
% 5.52/5.88 @ ( produc6081775807080527818_nat_o
% 5.52/5.88 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.52/5.88 = ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [K2: nat] :
% 5.52/5.88 ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K2 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ K2 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.triangle_reindex_eq
% 5.52/5.88 thf(fact_8996_prod_Otriangle__reindex__eq,axiom,
% 5.52/5.88 ! [G: nat > nat > int,N: nat] :
% 5.52/5.88 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 5.52/5.88 @ ( collec3392354462482085612at_nat
% 5.52/5.88 @ ( produc6081775807080527818_nat_o
% 5.52/5.88 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.52/5.88 = ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [K2: nat] :
% 5.52/5.88 ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K2 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ K2 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.triangle_reindex_eq
% 5.52/5.88 thf(fact_8997_binomial__less__binomial__Suc,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.88 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_less_binomial_Suc
% 5.52/5.88 thf(fact_8998_binomial__strict__antimono,axiom,
% 5.52/5.88 ! [K: nat,K6: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ K @ K6 )
% 5.52/5.88 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.52/5.88 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.52/5.88 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_strict_antimono
% 5.52/5.88 thf(fact_8999_binomial__strict__mono,axiom,
% 5.52/5.88 ! [K: nat,K6: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ K @ K6 )
% 5.52/5.88 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.52/5.88 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_strict_mono
% 5.52/5.88 thf(fact_9000_central__binomial__odd,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.88 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.88 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % central_binomial_odd
% 5.52/5.88 thf(fact_9001_binomial__addition__formula,axiom,
% 5.52/5.88 ! [N: nat,K: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( binomial @ N @ ( suc @ K ) )
% 5.52/5.88 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_addition_formula
% 5.52/5.88 thf(fact_9002_choose__even__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.52/5.88 @ ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) @ zero_zero_complex )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.88 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_even_sum
% 5.52/5.88 thf(fact_9003_choose__even__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.52/5.88 @ ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [I4: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) @ zero_zero_int )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.88 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_even_sum
% 5.52/5.88 thf(fact_9004_choose__even__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.52/5.88 @ ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) @ zero_zero_rat )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.88 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_even_sum
% 5.52/5.88 thf(fact_9005_choose__even__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.52/5.88 @ ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) @ zero_zero_real )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.88 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_even_sum
% 5.52/5.88 thf(fact_9006_choose__odd__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.52/5.88 @ ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] :
% 5.52/5.88 ( if_complex
% 5.52/5.88 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.52/5.88 @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) )
% 5.52/5.88 @ zero_zero_complex )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.88 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_odd_sum
% 5.52/5.88 thf(fact_9007_choose__odd__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.52/5.88 @ ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [I4: nat] :
% 5.52/5.88 ( if_int
% 5.52/5.88 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.52/5.88 @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) )
% 5.52/5.88 @ zero_zero_int )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.88 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_odd_sum
% 5.52/5.88 thf(fact_9008_choose__odd__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.52/5.88 @ ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [I4: nat] :
% 5.52/5.88 ( if_rat
% 5.52/5.88 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.52/5.88 @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) )
% 5.52/5.88 @ zero_zero_rat )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.88 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_odd_sum
% 5.52/5.88 thf(fact_9009_choose__odd__sum,axiom,
% 5.52/5.88 ! [N: nat] :
% 5.52/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.88 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.52/5.88 @ ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] :
% 5.52/5.88 ( if_real
% 5.52/5.88 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.52/5.88 @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) )
% 5.52/5.88 @ zero_zero_real )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.88 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % choose_odd_sum
% 5.52/5.88 thf(fact_9010_fact__binomial,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) ) )
% 5.52/5.88 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_binomial
% 5.52/5.88 thf(fact_9011_fact__binomial,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) )
% 5.52/5.88 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_binomial
% 5.52/5.88 thf(fact_9012_fact__binomial,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) )
% 5.52/5.88 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % fact_binomial
% 5.52/5.88 thf(fact_9013_binomial__fact,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.52/5.88 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_fact
% 5.52/5.88 thf(fact_9014_binomial__fact,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 5.52/5.88 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_fact
% 5.52/5.88 thf(fact_9015_binomial__fact,axiom,
% 5.52/5.88 ! [K: nat,N: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.52/5.88 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % binomial_fact
% 5.52/5.88 thf(fact_9016_sum__gp__basic,axiom,
% 5.52/5.88 ! [X2: complex,N: nat] :
% 5.52/5.88 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.88 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_gp_basic
% 5.52/5.88 thf(fact_9017_sum__gp__basic,axiom,
% 5.52/5.88 ! [X2: rat,N: nat] :
% 5.52/5.88 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.88 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_gp_basic
% 5.52/5.88 thf(fact_9018_sum__gp__basic,axiom,
% 5.52/5.88 ! [X2: int,N: nat] :
% 5.52/5.88 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.88 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_gp_basic
% 5.52/5.88 thf(fact_9019_sum__gp__basic,axiom,
% 5.52/5.88 ! [X2: real,N: nat] :
% 5.52/5.88 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.88 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( suc @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_gp_basic
% 5.52/5.88 thf(fact_9020_polyfun__finite__roots,axiom,
% 5.52/5.88 ! [C: nat > complex,N: nat] :
% 5.52/5.88 ( ( finite3207457112153483333omplex
% 5.52/5.88 @ ( collect_complex
% 5.52/5.88 @ ^ [X: complex] :
% 5.52/5.88 ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_complex ) ) )
% 5.52/5.88 = ( ? [I4: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ I4 @ N )
% 5.52/5.88 & ( ( C @ I4 )
% 5.52/5.88 != zero_zero_complex ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_finite_roots
% 5.52/5.88 thf(fact_9021_polyfun__finite__roots,axiom,
% 5.52/5.88 ! [C: nat > real,N: nat] :
% 5.52/5.88 ( ( finite_finite_real
% 5.52/5.88 @ ( collect_real
% 5.52/5.88 @ ^ [X: real] :
% 5.52/5.88 ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_real ) ) )
% 5.52/5.88 = ( ? [I4: nat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ I4 @ N )
% 5.52/5.88 & ( ( C @ I4 )
% 5.52/5.88 != zero_zero_real ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_finite_roots
% 5.52/5.88 thf(fact_9022_polyfun__roots__finite,axiom,
% 5.52/5.88 ! [C: nat > complex,K: nat,N: nat] :
% 5.52/5.88 ( ( ( C @ K )
% 5.52/5.88 != zero_zero_complex )
% 5.52/5.88 => ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( finite3207457112153483333omplex
% 5.52/5.88 @ ( collect_complex
% 5.52/5.88 @ ^ [Z2: complex] :
% 5.52/5.88 ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z2 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_complex ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_roots_finite
% 5.52/5.88 thf(fact_9023_polyfun__roots__finite,axiom,
% 5.52/5.88 ! [C: nat > real,K: nat,N: nat] :
% 5.52/5.88 ( ( ( C @ K )
% 5.52/5.88 != zero_zero_real )
% 5.52/5.88 => ( ( ord_less_eq_nat @ K @ N )
% 5.52/5.88 => ( finite_finite_real
% 5.52/5.88 @ ( collect_real
% 5.52/5.88 @ ^ [Z2: real] :
% 5.52/5.88 ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z2 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_real ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_roots_finite
% 5.52/5.88 thf(fact_9024_polyfun__linear__factor__root,axiom,
% 5.52/5.88 ! [C: nat > complex,A: complex,N: nat] :
% 5.52/5.88 ( ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ A @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_complex )
% 5.52/5.88 => ~ ! [B2: nat > complex] :
% 5.52/5.88 ~ ! [Z5: complex] :
% 5.52/5.88 ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( times_times_complex @ ( minus_minus_complex @ Z5 @ A )
% 5.52/5.88 @ ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( B2 @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_linear_factor_root
% 5.52/5.88 thf(fact_9025_polyfun__linear__factor__root,axiom,
% 5.52/5.88 ! [C: nat > rat,A: rat,N: nat] :
% 5.52/5.88 ( ( ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ A @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_rat )
% 5.52/5.88 => ~ ! [B2: nat > rat] :
% 5.52/5.88 ~ ! [Z5: rat] :
% 5.52/5.88 ( ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( times_times_rat @ ( minus_minus_rat @ Z5 @ A )
% 5.52/5.88 @ ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_rat @ ( B2 @ I4 ) @ ( power_power_rat @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_linear_factor_root
% 5.52/5.88 thf(fact_9026_polyfun__linear__factor__root,axiom,
% 5.52/5.88 ! [C: nat > int,A: int,N: nat] :
% 5.52/5.88 ( ( ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ A @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_int )
% 5.52/5.88 => ~ ! [B2: nat > int] :
% 5.52/5.88 ~ ! [Z5: int] :
% 5.52/5.88 ( ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( times_times_int @ ( minus_minus_int @ Z5 @ A )
% 5.52/5.88 @ ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_int @ ( B2 @ I4 ) @ ( power_power_int @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_linear_factor_root
% 5.52/5.88 thf(fact_9027_polyfun__linear__factor__root,axiom,
% 5.52/5.88 ! [C: nat > real,A: real,N: nat] :
% 5.52/5.88 ( ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ A @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = zero_zero_real )
% 5.52/5.88 => ~ ! [B2: nat > real] :
% 5.52/5.88 ~ ! [Z5: real] :
% 5.52/5.88 ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( times_times_real @ ( minus_minus_real @ Z5 @ A )
% 5.52/5.88 @ ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( B2 @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_linear_factor_root
% 5.52/5.88 thf(fact_9028_polyfun__linear__factor,axiom,
% 5.52/5.88 ! [C: nat > complex,N: nat,A: complex] :
% 5.52/5.88 ? [B2: nat > complex] :
% 5.52/5.88 ! [Z5: complex] :
% 5.52/5.88 ( ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( plus_plus_complex
% 5.52/5.88 @ ( times_times_complex @ ( minus_minus_complex @ Z5 @ A )
% 5.52/5.88 @ ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( B2 @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.52/5.88 @ ( groups2073611262835488442omplex
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ A @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_linear_factor
% 5.52/5.88 thf(fact_9029_polyfun__linear__factor,axiom,
% 5.52/5.88 ! [C: nat > rat,N: nat,A: rat] :
% 5.52/5.88 ? [B2: nat > rat] :
% 5.52/5.88 ! [Z5: rat] :
% 5.52/5.88 ( ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( plus_plus_rat
% 5.52/5.88 @ ( times_times_rat @ ( minus_minus_rat @ Z5 @ A )
% 5.52/5.88 @ ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_rat @ ( B2 @ I4 ) @ ( power_power_rat @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.52/5.88 @ ( groups2906978787729119204at_rat
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ A @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_linear_factor
% 5.52/5.88 thf(fact_9030_polyfun__linear__factor,axiom,
% 5.52/5.88 ! [C: nat > int,N: nat,A: int] :
% 5.52/5.88 ? [B2: nat > int] :
% 5.52/5.88 ! [Z5: int] :
% 5.52/5.88 ( ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( plus_plus_int
% 5.52/5.88 @ ( times_times_int @ ( minus_minus_int @ Z5 @ A )
% 5.52/5.88 @ ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_int @ ( B2 @ I4 ) @ ( power_power_int @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.52/5.88 @ ( groups3539618377306564664at_int
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ A @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_linear_factor
% 5.52/5.88 thf(fact_9031_polyfun__linear__factor,axiom,
% 5.52/5.88 ! [C: nat > real,N: nat,A: real] :
% 5.52/5.88 ? [B2: nat > real] :
% 5.52/5.88 ! [Z5: real] :
% 5.52/5.88 ( ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.88 = ( plus_plus_real
% 5.52/5.88 @ ( times_times_real @ ( minus_minus_real @ Z5 @ A )
% 5.52/5.88 @ ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( B2 @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.52/5.88 @ ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ A @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % polyfun_linear_factor
% 5.52/5.88 thf(fact_9032_sum__power__shift,axiom,
% 5.52/5.88 ! [M: nat,N: nat,X2: complex] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.88 = ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_power_shift
% 5.52/5.88 thf(fact_9033_sum__power__shift,axiom,
% 5.52/5.88 ! [M: nat,N: nat,X2: rat] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.88 = ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_power_shift
% 5.52/5.88 thf(fact_9034_sum__power__shift,axiom,
% 5.52/5.88 ! [M: nat,N: nat,X2: int] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.88 = ( times_times_int @ ( power_power_int @ X2 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_power_shift
% 5.52/5.88 thf(fact_9035_sum__power__shift,axiom,
% 5.52/5.88 ! [M: nat,N: nat,X2: real] :
% 5.52/5.88 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.88 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.52/5.88 = ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum_power_shift
% 5.52/5.88 thf(fact_9036_sum_Otriangle__reindex,axiom,
% 5.52/5.88 ! [G: nat > nat > nat,N: nat] :
% 5.52/5.88 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.52/5.88 @ ( collec3392354462482085612at_nat
% 5.52/5.88 @ ( produc6081775807080527818_nat_o
% 5.52/5.88 @ ^ [I4: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.52/5.88 = ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [K2: nat] :
% 5.52/5.88 ( groups3542108847815614940at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K2 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ K2 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.triangle_reindex
% 5.52/5.88 thf(fact_9037_sum_Otriangle__reindex,axiom,
% 5.52/5.88 ! [G: nat > nat > real,N: nat] :
% 5.52/5.88 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.52/5.88 @ ( collec3392354462482085612at_nat
% 5.52/5.88 @ ( produc6081775807080527818_nat_o
% 5.52/5.88 @ ^ [I4: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.52/5.88 = ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [K2: nat] :
% 5.52/5.88 ( groups6591440286371151544t_real
% 5.52/5.88 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K2 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ K2 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % sum.triangle_reindex
% 5.52/5.88 thf(fact_9038_prod_Otriangle__reindex,axiom,
% 5.52/5.88 ! [G: nat > nat > nat,N: nat] :
% 5.52/5.88 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.52/5.88 @ ( collec3392354462482085612at_nat
% 5.52/5.88 @ ( produc6081775807080527818_nat_o
% 5.52/5.88 @ ^ [I4: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.52/5.88 = ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [K2: nat] :
% 5.52/5.88 ( groups708209901874060359at_nat
% 5.52/5.88 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K2 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ K2 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.triangle_reindex
% 5.52/5.88 thf(fact_9039_prod_Otriangle__reindex,axiom,
% 5.52/5.88 ! [G: nat > nat > int,N: nat] :
% 5.52/5.88 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 5.52/5.88 @ ( collec3392354462482085612at_nat
% 5.52/5.88 @ ( produc6081775807080527818_nat_o
% 5.52/5.88 @ ^ [I4: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.52/5.88 = ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [K2: nat] :
% 5.52/5.88 ( groups705719431365010083at_int
% 5.52/5.88 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K2 @ I4 ) )
% 5.52/5.88 @ ( set_ord_atMost_nat @ K2 ) )
% 5.52/5.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.52/5.88
% 5.52/5.88 % prod.triangle_reindex
% 5.52/5.88 thf(fact_9040_summable__Cauchy__product,axiom,
% 5.52/5.88 ! [A: nat > complex,B: nat > complex] :
% 5.52/5.88 ( ( summable_real
% 5.52/5.88 @ ^ [K2: nat] : ( real_V1022390504157884413omplex @ ( A @ K2 ) ) )
% 5.52/5.88 => ( ( summable_real
% 5.52/5.88 @ ^ [K2: nat] : ( real_V1022390504157884413omplex @ ( B @ K2 ) ) )
% 5.52/5.89 => ( summable_complex
% 5.52/5.89 @ ^ [K2: nat] :
% 5.52/5.89 ( groups2073611262835488442omplex
% 5.52/5.89 @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( B @ ( minus_minus_nat @ K2 @ I4 ) ) )
% 5.52/5.89 @ ( set_ord_atMost_nat @ K2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % summable_Cauchy_product
% 5.52/5.89 thf(fact_9041_summable__Cauchy__product,axiom,
% 5.52/5.89 ! [A: nat > real,B: nat > real] :
% 5.52/5.89 ( ( summable_real
% 5.52/5.89 @ ^ [K2: nat] : ( real_V7735802525324610683m_real @ ( A @ K2 ) ) )
% 5.52/5.89 => ( ( summable_real
% 5.52/5.89 @ ^ [K2: nat] : ( real_V7735802525324610683m_real @ ( B @ K2 ) ) )
% 5.52/5.89 => ( summable_real
% 5.52/5.89 @ ^ [K2: nat] :
% 5.52/5.89 ( groups6591440286371151544t_real
% 5.52/5.89 @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( B @ ( minus_minus_nat @ K2 @ I4 ) ) )
% 5.52/5.89 @ ( set_ord_atMost_nat @ K2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % summable_Cauchy_product
% 5.52/5.89 thf(fact_9042_Cauchy__product,axiom,
% 5.52/5.89 ! [A: nat > complex,B: nat > complex] :
% 5.52/5.89 ( ( summable_real
% 5.52/5.89 @ ^ [K2: nat] : ( real_V1022390504157884413omplex @ ( A @ K2 ) ) )
% 5.52/5.89 => ( ( summable_real
% 5.52/5.89 @ ^ [K2: nat] : ( real_V1022390504157884413omplex @ ( B @ K2 ) ) )
% 5.52/5.89 => ( ( times_times_complex @ ( suminf_complex @ A ) @ ( suminf_complex @ B ) )
% 5.52/5.89 = ( suminf_complex
% 5.52/5.89 @ ^ [K2: nat] :
% 5.52/5.89 ( groups2073611262835488442omplex
% 5.52/5.89 @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( B @ ( minus_minus_nat @ K2 @ I4 ) ) )
% 5.52/5.89 @ ( set_ord_atMost_nat @ K2 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Cauchy_product
% 5.52/5.89 thf(fact_9043_Cauchy__product,axiom,
% 5.52/5.89 ! [A: nat > real,B: nat > real] :
% 5.52/5.89 ( ( summable_real
% 5.52/5.89 @ ^ [K2: nat] : ( real_V7735802525324610683m_real @ ( A @ K2 ) ) )
% 5.52/5.89 => ( ( summable_real
% 5.52/5.89 @ ^ [K2: nat] : ( real_V7735802525324610683m_real @ ( B @ K2 ) ) )
% 5.52/5.89 => ( ( times_times_real @ ( suminf_real @ A ) @ ( suminf_real @ B ) )
% 5.52/5.89 = ( suminf_real
% 5.52/5.89 @ ^ [K2: nat] :
% 5.52/5.89 ( groups6591440286371151544t_real
% 5.52/5.89 @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( B @ ( minus_minus_nat @ K2 @ I4 ) ) )
% 5.52/5.89 @ ( set_ord_atMost_nat @ K2 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Cauchy_product
% 5.52/5.89 thf(fact_9044_choose__two,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.89 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % choose_two
% 5.52/5.89 thf(fact_9045_polynomial__product__nat,axiom,
% 5.52/5.89 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X2: nat] :
% 5.52/5.89 ( ! [I2: nat] :
% 5.52/5.89 ( ( ord_less_nat @ M @ I2 )
% 5.52/5.89 => ( ( A @ I2 )
% 5.52/5.89 = zero_zero_nat ) )
% 5.52/5.89 => ( ! [J2: nat] :
% 5.52/5.89 ( ( ord_less_nat @ N @ J2 )
% 5.52/5.89 => ( ( B @ J2 )
% 5.52/5.89 = zero_zero_nat ) )
% 5.52/5.89 => ( ( times_times_nat
% 5.52/5.89 @ ( groups3542108847815614940at_nat
% 5.52/5.89 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( power_power_nat @ X2 @ I4 ) )
% 5.52/5.89 @ ( set_ord_atMost_nat @ M ) )
% 5.52/5.89 @ ( groups3542108847815614940at_nat
% 5.52/5.89 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X2 @ J3 ) )
% 5.52/5.89 @ ( set_ord_atMost_nat @ N ) ) )
% 5.52/5.89 = ( groups3542108847815614940at_nat
% 5.52/5.89 @ ^ [R5: nat] :
% 5.52/5.89 ( times_times_nat
% 5.52/5.89 @ ( groups3542108847815614940at_nat
% 5.52/5.89 @ ^ [K2: nat] : ( times_times_nat @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 5.52/5.89 @ ( set_ord_atMost_nat @ R5 ) )
% 5.52/5.89 @ ( power_power_nat @ X2 @ R5 ) )
% 5.52/5.89 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % polynomial_product_nat
% 5.52/5.89 thf(fact_9046_Maclaurin__sin__bound,axiom,
% 5.52/5.89 ! [X2: real,N: nat] :
% 5.52/5.89 ( ord_less_eq_real
% 5.52/5.89 @ ( abs_abs_real
% 5.52/5.89 @ ( minus_minus_real @ ( sin_real @ X2 )
% 5.52/5.89 @ ( groups6591440286371151544t_real
% 5.52/5.89 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.89 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.52/5.89 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X2 ) @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Maclaurin_sin_bound
% 5.52/5.89 thf(fact_9047_of__nat__id,axiom,
% 5.52/5.89 ( semiri1316708129612266289at_nat
% 5.52/5.89 = ( ^ [N3: nat] : N3 ) ) ).
% 5.52/5.89
% 5.52/5.89 % of_nat_id
% 5.52/5.89 thf(fact_9048_real__sqrt__inverse,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( sqrt @ ( inverse_inverse_real @ X2 ) )
% 5.52/5.89 = ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_sqrt_inverse
% 5.52/5.89 thf(fact_9049_divide__real__def,axiom,
% 5.52/5.89 ( divide_divide_real
% 5.52/5.89 = ( ^ [X: real,Y: real] : ( times_times_real @ X @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % divide_real_def
% 5.52/5.89 thf(fact_9050_forall__pos__mono__1,axiom,
% 5.52/5.89 ! [P: real > $o,E: real] :
% 5.52/5.89 ( ! [D3: real,E2: real] :
% 5.52/5.89 ( ( ord_less_real @ D3 @ E2 )
% 5.52/5.89 => ( ( P @ D3 )
% 5.52/5.89 => ( P @ E2 ) ) )
% 5.52/5.89 => ( ! [N2: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 5.52/5.89 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.52/5.89 => ( P @ E ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % forall_pos_mono_1
% 5.52/5.89 thf(fact_9051_real__arch__inverse,axiom,
% 5.52/5.89 ! [E: real] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ E )
% 5.52/5.89 = ( ? [N3: nat] :
% 5.52/5.89 ( ( N3 != zero_zero_nat )
% 5.52/5.89 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 5.52/5.89 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) @ E ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_arch_inverse
% 5.52/5.89 thf(fact_9052_forall__pos__mono,axiom,
% 5.52/5.89 ! [P: real > $o,E: real] :
% 5.52/5.89 ( ! [D3: real,E2: real] :
% 5.52/5.89 ( ( ord_less_real @ D3 @ E2 )
% 5.52/5.89 => ( ( P @ D3 )
% 5.52/5.89 => ( P @ E2 ) ) )
% 5.52/5.89 => ( ! [N2: nat] :
% 5.52/5.89 ( ( N2 != zero_zero_nat )
% 5.52/5.89 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) )
% 5.52/5.89 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.52/5.89 => ( P @ E ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % forall_pos_mono
% 5.52/5.89 thf(fact_9053_sqrt__divide__self__eq,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( divide_divide_real @ ( sqrt @ X2 ) @ X2 )
% 5.52/5.89 = ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sqrt_divide_self_eq
% 5.52/5.89 thf(fact_9054_ln__inverse,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( ln_ln_real @ ( inverse_inverse_real @ X2 ) )
% 5.52/5.89 = ( uminus_uminus_real @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % ln_inverse
% 5.52/5.89 thf(fact_9055_log__inverse,axiom,
% 5.52/5.89 ! [A: real,X2: real] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.89 => ( ( A != one_one_real )
% 5.52/5.89 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( log @ A @ ( inverse_inverse_real @ X2 ) )
% 5.52/5.89 = ( uminus_uminus_real @ ( log @ A @ X2 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % log_inverse
% 5.52/5.89 thf(fact_9056_exp__plus__inverse__exp,axiom,
% 5.52/5.89 ! [X2: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % exp_plus_inverse_exp
% 5.52/5.89 thf(fact_9057_plus__inverse__ge__2,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % plus_inverse_ge_2
% 5.52/5.89 thf(fact_9058_real__inv__sqrt__pow2,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.89 = ( inverse_inverse_real @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_inv_sqrt_pow2
% 5.52/5.89 thf(fact_9059_tan__cot,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) )
% 5.52/5.89 = ( inverse_inverse_real @ ( tan_real @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % tan_cot
% 5.52/5.89 thf(fact_9060_real__le__x__sinh,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ord_less_eq_real @ X2 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_le_x_sinh
% 5.52/5.89 thf(fact_9061_real__le__abs__sinh,axiom,
% 5.52/5.89 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_le_abs_sinh
% 5.52/5.89 thf(fact_9062_complex__unimodular__polar,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.52/5.89 = one_one_real )
% 5.52/5.89 => ~ ! [T4: real] :
% 5.52/5.89 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.52/5.89 => ( ( ord_less_real @ T4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.52/5.89 => ( Z
% 5.52/5.89 != ( complex2 @ ( cos_real @ T4 ) @ ( sin_real @ T4 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_unimodular_polar
% 5.52/5.89 thf(fact_9063_cot__less__zero,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.52/5.89 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.52/5.89 => ( ord_less_real @ ( cot_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % cot_less_zero
% 5.52/5.89 thf(fact_9064_sinh__real__less__iff,axiom,
% 5.52/5.89 ! [X2: real,Y2: real] :
% 5.52/5.89 ( ( ord_less_real @ ( sinh_real @ X2 ) @ ( sinh_real @ Y2 ) )
% 5.52/5.89 = ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % sinh_real_less_iff
% 5.52/5.89 thf(fact_9065_sinh__real__pos__iff,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X2 ) )
% 5.52/5.89 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % sinh_real_pos_iff
% 5.52/5.89 thf(fact_9066_sinh__real__neg__iff,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( ord_less_real @ ( sinh_real @ X2 ) @ zero_zero_real )
% 5.52/5.89 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.52/5.89
% 5.52/5.89 % sinh_real_neg_iff
% 5.52/5.89 thf(fact_9067_cot__periodic,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( cot_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.52/5.89 = ( cot_real @ X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % cot_periodic
% 5.52/5.89 thf(fact_9068_sinh__less__cosh__real,axiom,
% 5.52/5.89 ! [X2: real] : ( ord_less_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % sinh_less_cosh_real
% 5.52/5.89 thf(fact_9069_cosh__real__pos,axiom,
% 5.52/5.89 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % cosh_real_pos
% 5.52/5.89 thf(fact_9070_cosh__real__nonpos__less__iff,axiom,
% 5.52/5.89 ! [X2: real,Y2: real] :
% 5.52/5.89 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.52/5.89 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.52/5.89 => ( ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y2 ) )
% 5.52/5.89 = ( ord_less_real @ Y2 @ X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % cosh_real_nonpos_less_iff
% 5.52/5.89 thf(fact_9071_cosh__real__nonneg__less__iff,axiom,
% 5.52/5.89 ! [X2: real,Y2: real] :
% 5.52/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.89 => ( ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y2 ) )
% 5.52/5.89 = ( ord_less_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % cosh_real_nonneg_less_iff
% 5.52/5.89 thf(fact_9072_cosh__real__strict__mono,axiom,
% 5.52/5.89 ! [X2: real,Y2: real] :
% 5.52/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( ord_less_real @ X2 @ Y2 )
% 5.52/5.89 => ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % cosh_real_strict_mono
% 5.52/5.89 thf(fact_9073_complex__inverse,axiom,
% 5.52/5.89 ! [A: real,B: real] :
% 5.52/5.89 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.52/5.89 = ( complex2 @ ( divide_divide_real @ A @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ B ) @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_inverse
% 5.52/5.89 thf(fact_9074_complex__norm,axiom,
% 5.52/5.89 ! [X2: real,Y2: real] :
% 5.52/5.89 ( ( real_V1022390504157884413omplex @ ( complex2 @ X2 @ Y2 ) )
% 5.52/5.89 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_norm
% 5.52/5.89 thf(fact_9075_cosh__ln__real,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( cosh_real @ ( ln_ln_real @ X2 ) )
% 5.52/5.89 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % cosh_ln_real
% 5.52/5.89 thf(fact_9076_cot__gt__zero,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.89 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % cot_gt_zero
% 5.52/5.89 thf(fact_9077_sinh__ln__real,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( sinh_real @ ( ln_ln_real @ X2 ) )
% 5.52/5.89 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sinh_ln_real
% 5.52/5.89 thf(fact_9078_tan__cot_H,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) )
% 5.52/5.89 = ( cot_real @ X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % tan_cot'
% 5.52/5.89 thf(fact_9079_arctan__def,axiom,
% 5.52/5.89 ( arctan
% 5.52/5.89 = ( ^ [Y: real] :
% 5.52/5.89 ( the_real
% 5.52/5.89 @ ^ [X: real] :
% 5.52/5.89 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.52/5.89 & ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.89 & ( ( tan_real @ X )
% 5.52/5.89 = Y ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % arctan_def
% 5.52/5.89 thf(fact_9080_arcsin__def,axiom,
% 5.52/5.89 ( arcsin
% 5.52/5.89 = ( ^ [Y: real] :
% 5.52/5.89 ( the_real
% 5.52/5.89 @ ^ [X: real] :
% 5.52/5.89 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.52/5.89 & ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.89 & ( ( sin_real @ X )
% 5.52/5.89 = Y ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % arcsin_def
% 5.52/5.89 thf(fact_9081_modulo__int__unfold,axiom,
% 5.52/5.89 ! [L: int,K: int,N: nat,M: nat] :
% 5.52/5.89 ( ( ( ( ( sgn_sgn_int @ L )
% 5.52/5.89 = zero_zero_int )
% 5.52/5.89 | ( ( sgn_sgn_int @ K )
% 5.52/5.89 = zero_zero_int )
% 5.52/5.89 | ( N = zero_zero_nat ) )
% 5.52/5.89 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.52/5.89 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.52/5.89 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.52/5.89 = zero_zero_int )
% 5.52/5.89 | ( ( sgn_sgn_int @ K )
% 5.52/5.89 = zero_zero_int )
% 5.52/5.89 | ( N = zero_zero_nat ) )
% 5.52/5.89 => ( ( ( ( sgn_sgn_int @ K )
% 5.52/5.89 = ( sgn_sgn_int @ L ) )
% 5.52/5.89 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.52/5.89 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 5.52/5.89 & ( ( ( sgn_sgn_int @ K )
% 5.52/5.89 != ( sgn_sgn_int @ L ) )
% 5.52/5.89 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.52/5.89 = ( times_times_int @ ( sgn_sgn_int @ L )
% 5.52/5.89 @ ( minus_minus_int
% 5.52/5.89 @ ( semiri1314217659103216013at_int
% 5.52/5.89 @ ( times_times_nat @ N
% 5.52/5.89 @ ( zero_n2687167440665602831ol_nat
% 5.52/5.89 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 5.52/5.89 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % modulo_int_unfold
% 5.52/5.89 thf(fact_9082_powr__int,axiom,
% 5.52/5.89 ! [X2: real,I: int] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.52/5.89 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I ) )
% 5.52/5.89 = ( power_power_real @ X2 @ ( nat2 @ I ) ) ) )
% 5.52/5.89 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 5.52/5.89 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I ) )
% 5.52/5.89 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % powr_int
% 5.52/5.89 thf(fact_9083_nat__numeral,axiom,
% 5.52/5.89 ! [K: num] :
% 5.52/5.89 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.52/5.89 = ( numeral_numeral_nat @ K ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_numeral
% 5.52/5.89 thf(fact_9084_zless__nat__conj,axiom,
% 5.52/5.89 ! [W: int,Z: int] :
% 5.52/5.89 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.52/5.89 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.52/5.89 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % zless_nat_conj
% 5.52/5.89 thf(fact_9085_nat__neg__numeral,axiom,
% 5.52/5.89 ! [K: num] :
% 5.52/5.89 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.52/5.89 = zero_zero_nat ) ).
% 5.52/5.89
% 5.52/5.89 % nat_neg_numeral
% 5.52/5.89 thf(fact_9086_zero__less__nat__eq,axiom,
% 5.52/5.89 ! [Z: int] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.52/5.89 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.52/5.89
% 5.52/5.89 % zero_less_nat_eq
% 5.52/5.89 thf(fact_9087_diff__nat__numeral,axiom,
% 5.52/5.89 ! [V: num,V3: num] :
% 5.52/5.89 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.52/5.89 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % diff_nat_numeral
% 5.52/5.89 thf(fact_9088_nat__eq__numeral__power__cancel__iff,axiom,
% 5.52/5.89 ! [Y2: int,X2: num,N: nat] :
% 5.52/5.89 ( ( ( nat2 @ Y2 )
% 5.52/5.89 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.52/5.89 = ( Y2
% 5.52/5.89 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_eq_numeral_power_cancel_iff
% 5.52/5.89 thf(fact_9089_numeral__power__eq__nat__cancel__iff,axiom,
% 5.52/5.89 ! [X2: num,N: nat,Y2: int] :
% 5.52/5.89 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.52/5.89 = ( nat2 @ Y2 ) )
% 5.52/5.89 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.52/5.89 = Y2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % numeral_power_eq_nat_cancel_iff
% 5.52/5.89 thf(fact_9090_nat__ceiling__le__eq,axiom,
% 5.52/5.89 ! [X2: real,A: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) @ A )
% 5.52/5.89 = ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_ceiling_le_eq
% 5.52/5.89 thf(fact_9091_one__less__nat__eq,axiom,
% 5.52/5.89 ! [Z: int] :
% 5.52/5.89 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.52/5.89 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.52/5.89
% 5.52/5.89 % one_less_nat_eq
% 5.52/5.89 thf(fact_9092_nat__numeral__diff__1,axiom,
% 5.52/5.89 ! [V: num] :
% 5.52/5.89 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.52/5.89 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_numeral_diff_1
% 5.52/5.89 thf(fact_9093_nat__less__numeral__power__cancel__iff,axiom,
% 5.52/5.89 ! [A: int,X2: num,N: nat] :
% 5.52/5.89 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.52/5.89 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_less_numeral_power_cancel_iff
% 5.52/5.89 thf(fact_9094_numeral__power__less__nat__cancel__iff,axiom,
% 5.52/5.89 ! [X2: num,N: nat,A: int] :
% 5.52/5.89 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A ) )
% 5.52/5.89 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.52/5.89
% 5.52/5.89 % numeral_power_less_nat_cancel_iff
% 5.52/5.89 thf(fact_9095_numeral__power__le__nat__cancel__iff,axiom,
% 5.52/5.89 ! [X2: num,N: nat,A: int] :
% 5.52/5.89 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A ) )
% 5.52/5.89 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.52/5.89
% 5.52/5.89 % numeral_power_le_nat_cancel_iff
% 5.52/5.89 thf(fact_9096_nat__le__numeral__power__cancel__iff,axiom,
% 5.52/5.89 ! [A: int,X2: num,N: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.52/5.89 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_le_numeral_power_cancel_iff
% 5.52/5.89 thf(fact_9097_nat__numeral__as__int,axiom,
% 5.52/5.89 ( numeral_numeral_nat
% 5.52/5.89 = ( ^ [I4: num] : ( nat2 @ ( numeral_numeral_int @ I4 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_numeral_as_int
% 5.52/5.89 thf(fact_9098_nat__mono,axiom,
% 5.52/5.89 ! [X2: int,Y2: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ X2 @ Y2 )
% 5.52/5.89 => ( ord_less_eq_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_mono
% 5.52/5.89 thf(fact_9099_nat__one__as__int,axiom,
% 5.52/5.89 ( one_one_nat
% 5.52/5.89 = ( nat2 @ one_one_int ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_one_as_int
% 5.52/5.89 thf(fact_9100_div__eq__sgn__abs,axiom,
% 5.52/5.89 ! [K: int,L: int] :
% 5.52/5.89 ( ( ( sgn_sgn_int @ K )
% 5.52/5.89 = ( sgn_sgn_int @ L ) )
% 5.52/5.89 => ( ( divide_divide_int @ K @ L )
% 5.52/5.89 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % div_eq_sgn_abs
% 5.52/5.89 thf(fact_9101_unset__bit__nat__def,axiom,
% 5.52/5.89 ( bit_se4205575877204974255it_nat
% 5.52/5.89 = ( ^ [M3: nat,N3: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M3 @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % unset_bit_nat_def
% 5.52/5.89 thf(fact_9102_nat__mask__eq,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.52/5.89 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_mask_eq
% 5.52/5.89 thf(fact_9103_nat__mono__iff,axiom,
% 5.52/5.89 ! [Z: int,W: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.52/5.89 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.52/5.89 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_mono_iff
% 5.52/5.89 thf(fact_9104_zless__nat__eq__int__zless,axiom,
% 5.52/5.89 ! [M: nat,Z: int] :
% 5.52/5.89 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.52/5.89 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.52/5.89
% 5.52/5.89 % zless_nat_eq_int_zless
% 5.52/5.89 thf(fact_9105_nat__le__iff,axiom,
% 5.52/5.89 ! [X2: int,N: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ ( nat2 @ X2 ) @ N )
% 5.52/5.89 = ( ord_less_eq_int @ X2 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_le_iff
% 5.52/5.89 thf(fact_9106_nat__int__add,axiom,
% 5.52/5.89 ! [A: nat,B: nat] :
% 5.52/5.89 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.52/5.89 = ( plus_plus_nat @ A @ B ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_int_add
% 5.52/5.89 thf(fact_9107_sgn__mod,axiom,
% 5.52/5.89 ! [L: int,K: int] :
% 5.52/5.89 ( ( L != zero_zero_int )
% 5.52/5.89 => ( ~ ( dvd_dvd_int @ L @ K )
% 5.52/5.89 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 5.52/5.89 = ( sgn_sgn_int @ L ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sgn_mod
% 5.52/5.89 thf(fact_9108_nat__abs__mult__distrib,axiom,
% 5.52/5.89 ! [W: int,Z: int] :
% 5.52/5.89 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.52/5.89 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_abs_mult_distrib
% 5.52/5.89 thf(fact_9109_real__nat__ceiling__ge,axiom,
% 5.52/5.89 ! [X2: real] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_nat_ceiling_ge
% 5.52/5.89 thf(fact_9110_and__nat__def,axiom,
% 5.52/5.89 ( bit_se727722235901077358nd_nat
% 5.52/5.89 = ( ^ [M3: nat,N3: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_nat_def
% 5.52/5.89 thf(fact_9111_nat__plus__as__int,axiom,
% 5.52/5.89 ( plus_plus_nat
% 5.52/5.89 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_plus_as_int
% 5.52/5.89 thf(fact_9112_nat__times__as__int,axiom,
% 5.52/5.89 ( times_times_nat
% 5.52/5.89 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_times_as_int
% 5.52/5.89 thf(fact_9113_nat__div__as__int,axiom,
% 5.52/5.89 ( divide_divide_nat
% 5.52/5.89 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_div_as_int
% 5.52/5.89 thf(fact_9114_zsgn__def,axiom,
% 5.52/5.89 ( sgn_sgn_int
% 5.52/5.89 = ( ^ [I4: int] : ( if_int @ ( I4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % zsgn_def
% 5.52/5.89 thf(fact_9115_nat__less__eq__zless,axiom,
% 5.52/5.89 ! [W: int,Z: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.52/5.89 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.52/5.89 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_less_eq_zless
% 5.52/5.89 thf(fact_9116_nat__le__eq__zle,axiom,
% 5.52/5.89 ! [W: int,Z: int] :
% 5.52/5.89 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.52/5.89 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.52/5.89 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.52/5.89 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_le_eq_zle
% 5.52/5.89 thf(fact_9117_split__nat,axiom,
% 5.52/5.89 ! [P: nat > $o,I: int] :
% 5.52/5.89 ( ( P @ ( nat2 @ I ) )
% 5.52/5.89 = ( ! [N3: nat] :
% 5.52/5.89 ( ( I
% 5.52/5.89 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.52/5.89 => ( P @ N3 ) )
% 5.52/5.89 & ( ( ord_less_int @ I @ zero_zero_int )
% 5.52/5.89 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % split_nat
% 5.52/5.89 thf(fact_9118_le__nat__iff,axiom,
% 5.52/5.89 ! [K: int,N: nat] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.89 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.52/5.89 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % le_nat_iff
% 5.52/5.89 thf(fact_9119_nat__add__distrib,axiom,
% 5.52/5.89 ! [Z: int,Z7: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.52/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.52/5.89 => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 5.52/5.89 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_add_distrib
% 5.52/5.89 thf(fact_9120_div__sgn__abs__cancel,axiom,
% 5.52/5.89 ! [V: int,K: int,L: int] :
% 5.52/5.89 ( ( V != zero_zero_int )
% 5.52/5.89 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L ) ) )
% 5.52/5.89 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % div_sgn_abs_cancel
% 5.52/5.89 thf(fact_9121_nat__mult__distrib,axiom,
% 5.52/5.89 ! [Z: int,Z7: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.52/5.89 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.52/5.89 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_mult_distrib
% 5.52/5.89 thf(fact_9122_nat__abs__triangle__ineq,axiom,
% 5.52/5.89 ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_abs_triangle_ineq
% 5.52/5.89 thf(fact_9123_nat__div__distrib,axiom,
% 5.52/5.89 ! [X2: int,Y2: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.89 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y2 ) )
% 5.52/5.89 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_div_distrib
% 5.52/5.89 thf(fact_9124_nat__div__distrib_H,axiom,
% 5.52/5.89 ! [Y2: int,X2: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.89 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y2 ) )
% 5.52/5.89 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_div_distrib'
% 5.52/5.89 thf(fact_9125_div__dvd__sgn__abs,axiom,
% 5.52/5.89 ! [L: int,K: int] :
% 5.52/5.89 ( ( dvd_dvd_int @ L @ K )
% 5.52/5.89 => ( ( divide_divide_int @ K @ L )
% 5.52/5.89 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % div_dvd_sgn_abs
% 5.52/5.89 thf(fact_9126_nat__power__eq,axiom,
% 5.52/5.89 ! [Z: int,N: nat] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.52/5.89 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 5.52/5.89 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_power_eq
% 5.52/5.89 thf(fact_9127_nat__floor__neg,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.52/5.89 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.89 = zero_zero_nat ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_floor_neg
% 5.52/5.89 thf(fact_9128_nat__mod__distrib,axiom,
% 5.52/5.89 ! [X2: int,Y2: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.89 => ( ( nat2 @ ( modulo_modulo_int @ X2 @ Y2 ) )
% 5.52/5.89 = ( modulo_modulo_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_mod_distrib
% 5.52/5.89 thf(fact_9129_div__abs__eq__div__nat,axiom,
% 5.52/5.89 ! [K: int,L: int] :
% 5.52/5.89 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.52/5.89 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % div_abs_eq_div_nat
% 5.52/5.89 thf(fact_9130_floor__eq3,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X2 )
% 5.52/5.89 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.52/5.89 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.89 = N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % floor_eq3
% 5.52/5.89 thf(fact_9131_le__nat__floor,axiom,
% 5.52/5.89 ! [X2: nat,A: real] :
% 5.52/5.89 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ A )
% 5.52/5.89 => ( ord_less_eq_nat @ X2 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % le_nat_floor
% 5.52/5.89 thf(fact_9132_mod__abs__eq__div__nat,axiom,
% 5.52/5.89 ! [K: int,L: int] :
% 5.52/5.89 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.52/5.89 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % mod_abs_eq_div_nat
% 5.52/5.89 thf(fact_9133_nat__take__bit__eq,axiom,
% 5.52/5.89 ! [K: int,N: nat] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.89 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.52/5.89 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_take_bit_eq
% 5.52/5.89 thf(fact_9134_take__bit__nat__eq,axiom,
% 5.52/5.89 ! [K: int,N: nat] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.89 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 5.52/5.89 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % take_bit_nat_eq
% 5.52/5.89 thf(fact_9135_bit__nat__iff,axiom,
% 5.52/5.89 ! [K: int,N: nat] :
% 5.52/5.89 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 5.52/5.89 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.89 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bit_nat_iff
% 5.52/5.89 thf(fact_9136_divide__int__def,axiom,
% 5.52/5.89 ( divide_divide_int
% 5.52/5.89 = ( ^ [K2: int,L2: int] :
% 5.52/5.89 ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 5.52/5.89 @ ( if_int
% 5.52/5.89 @ ( ( sgn_sgn_int @ K2 )
% 5.52/5.89 = ( sgn_sgn_int @ L2 ) )
% 5.52/5.89 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 5.52/5.89 @ ( uminus_uminus_int
% 5.52/5.89 @ ( semiri1314217659103216013at_int
% 5.52/5.89 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 5.52/5.89 @ ( zero_n2687167440665602831ol_nat
% 5.52/5.89 @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % divide_int_def
% 5.52/5.89 thf(fact_9137_modulo__int__def,axiom,
% 5.52/5.89 ( modulo_modulo_int
% 5.52/5.89 = ( ^ [K2: int,L2: int] :
% 5.52/5.89 ( if_int @ ( L2 = zero_zero_int ) @ K2
% 5.52/5.89 @ ( if_int
% 5.52/5.89 @ ( ( sgn_sgn_int @ K2 )
% 5.52/5.89 = ( sgn_sgn_int @ L2 ) )
% 5.52/5.89 @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 5.52/5.89 @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.52/5.89 @ ( minus_minus_int
% 5.52/5.89 @ ( times_times_int @ ( abs_abs_int @ L2 )
% 5.52/5.89 @ ( zero_n2684676970156552555ol_int
% 5.52/5.89 @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) )
% 5.52/5.89 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % modulo_int_def
% 5.52/5.89 thf(fact_9138_nat__2,axiom,
% 5.52/5.89 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.89 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_2
% 5.52/5.89 thf(fact_9139_nat__less__iff,axiom,
% 5.52/5.89 ! [W: int,M: nat] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.52/5.89 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.52/5.89 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_less_iff
% 5.52/5.89 thf(fact_9140_nat__mult__distrib__neg,axiom,
% 5.52/5.89 ! [Z: int,Z7: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.52/5.89 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.52/5.89 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_mult_distrib_neg
% 5.52/5.89 thf(fact_9141_nat__abs__int__diff,axiom,
% 5.52/5.89 ! [A: nat,B: nat] :
% 5.52/5.89 ( ( ( ord_less_eq_nat @ A @ B )
% 5.52/5.89 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.52/5.89 = ( minus_minus_nat @ B @ A ) ) )
% 5.52/5.89 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.52/5.89 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.52/5.89 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_abs_int_diff
% 5.52/5.89 thf(fact_9142_floor__eq4,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X2 )
% 5.52/5.89 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.52/5.89 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.52/5.89 = N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % floor_eq4
% 5.52/5.89 thf(fact_9143_diff__nat__eq__if,axiom,
% 5.52/5.89 ! [Z7: int,Z: int] :
% 5.52/5.89 ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 5.52/5.89 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.52/5.89 = ( nat2 @ Z ) ) )
% 5.52/5.89 & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 5.52/5.89 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.52/5.89 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % diff_nat_eq_if
% 5.52/5.89 thf(fact_9144_eucl__rel__int__remainderI,axiom,
% 5.52/5.89 ! [R: int,L: int,K: int,Q2: int] :
% 5.52/5.89 ( ( ( sgn_sgn_int @ R )
% 5.52/5.89 = ( sgn_sgn_int @ L ) )
% 5.52/5.89 => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L ) )
% 5.52/5.89 => ( ( K
% 5.52/5.89 = ( plus_plus_int @ ( times_times_int @ Q2 @ L ) @ R ) )
% 5.52/5.89 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % eucl_rel_int_remainderI
% 5.52/5.89 thf(fact_9145_eucl__rel__int_Ocases,axiom,
% 5.52/5.89 ! [A1: int,A22: int,A32: product_prod_int_int] :
% 5.52/5.89 ( ( eucl_rel_int @ A1 @ A22 @ A32 )
% 5.52/5.89 => ( ( ( A22 = zero_zero_int )
% 5.52/5.89 => ( A32
% 5.52/5.89 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 5.52/5.89 => ( ! [Q3: int] :
% 5.52/5.89 ( ( A32
% 5.52/5.89 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.52/5.89 => ( ( A22 != zero_zero_int )
% 5.52/5.89 => ( A1
% 5.52/5.89 != ( times_times_int @ Q3 @ A22 ) ) ) )
% 5.52/5.89 => ~ ! [R3: int,Q3: int] :
% 5.52/5.89 ( ( A32
% 5.52/5.89 = ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.52/5.89 => ( ( ( sgn_sgn_int @ R3 )
% 5.52/5.89 = ( sgn_sgn_int @ A22 ) )
% 5.52/5.89 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A22 ) )
% 5.52/5.89 => ( A1
% 5.52/5.89 != ( plus_plus_int @ ( times_times_int @ Q3 @ A22 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % eucl_rel_int.cases
% 5.52/5.89 thf(fact_9146_eucl__rel__int_Osimps,axiom,
% 5.52/5.89 ( eucl_rel_int
% 5.52/5.89 = ( ^ [A12: int,A23: int,A33: product_prod_int_int] :
% 5.52/5.89 ( ? [K2: int] :
% 5.52/5.89 ( ( A12 = K2 )
% 5.52/5.89 & ( A23 = zero_zero_int )
% 5.52/5.89 & ( A33
% 5.52/5.89 = ( product_Pair_int_int @ zero_zero_int @ K2 ) ) )
% 5.52/5.89 | ? [L2: int,K2: int,Q4: int] :
% 5.52/5.89 ( ( A12 = K2 )
% 5.52/5.89 & ( A23 = L2 )
% 5.52/5.89 & ( A33
% 5.52/5.89 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.52/5.89 & ( L2 != zero_zero_int )
% 5.52/5.89 & ( K2
% 5.52/5.89 = ( times_times_int @ Q4 @ L2 ) ) )
% 5.52/5.89 | ? [R5: int,L2: int,K2: int,Q4: int] :
% 5.52/5.89 ( ( A12 = K2 )
% 5.52/5.89 & ( A23 = L2 )
% 5.52/5.89 & ( A33
% 5.52/5.89 = ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.52/5.89 & ( ( sgn_sgn_int @ R5 )
% 5.52/5.89 = ( sgn_sgn_int @ L2 ) )
% 5.52/5.89 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 5.52/5.89 & ( K2
% 5.52/5.89 = ( plus_plus_int @ ( times_times_int @ Q4 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % eucl_rel_int.simps
% 5.52/5.89 thf(fact_9147_div__noneq__sgn__abs,axiom,
% 5.52/5.89 ! [L: int,K: int] :
% 5.52/5.89 ( ( L != zero_zero_int )
% 5.52/5.89 => ( ( ( sgn_sgn_int @ K )
% 5.52/5.89 != ( sgn_sgn_int @ L ) )
% 5.52/5.89 => ( ( divide_divide_int @ K @ L )
% 5.52/5.89 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 5.52/5.89 @ ( zero_n2684676970156552555ol_int
% 5.52/5.89 @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % div_noneq_sgn_abs
% 5.52/5.89 thf(fact_9148_even__nat__iff,axiom,
% 5.52/5.89 ! [K: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.89 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.52/5.89 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % even_nat_iff
% 5.52/5.89 thf(fact_9149_pi__half,axiom,
% 5.52/5.89 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.52/5.89 = ( the_real
% 5.52/5.89 @ ^ [X: real] :
% 5.52/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.52/5.89 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.52/5.89 & ( ( cos_real @ X )
% 5.52/5.89 = zero_zero_real ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % pi_half
% 5.52/5.89 thf(fact_9150_pi__def,axiom,
% 5.52/5.89 ( pi
% 5.52/5.89 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.52/5.89 @ ( the_real
% 5.52/5.89 @ ^ [X: real] :
% 5.52/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.52/5.89 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.52/5.89 & ( ( cos_real @ X )
% 5.52/5.89 = zero_zero_real ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % pi_def
% 5.52/5.89 thf(fact_9151_powr__real__of__int,axiom,
% 5.52/5.89 ! [X2: real,N: int] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.52/5.89 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.52/5.89 = ( power_power_real @ X2 @ ( nat2 @ N ) ) ) )
% 5.52/5.89 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 5.52/5.89 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.52/5.89 = ( inverse_inverse_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % powr_real_of_int
% 5.52/5.89 thf(fact_9152_divide__int__unfold,axiom,
% 5.52/5.89 ! [L: int,K: int,N: nat,M: nat] :
% 5.52/5.89 ( ( ( ( ( sgn_sgn_int @ L )
% 5.52/5.89 = zero_zero_int )
% 5.52/5.89 | ( ( sgn_sgn_int @ K )
% 5.52/5.89 = zero_zero_int )
% 5.52/5.89 | ( N = zero_zero_nat ) )
% 5.52/5.89 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.52/5.89 = zero_zero_int ) )
% 5.52/5.89 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.52/5.89 = zero_zero_int )
% 5.52/5.89 | ( ( sgn_sgn_int @ K )
% 5.52/5.89 = zero_zero_int )
% 5.52/5.89 | ( N = zero_zero_nat ) )
% 5.52/5.89 => ( ( ( ( sgn_sgn_int @ K )
% 5.52/5.89 = ( sgn_sgn_int @ L ) )
% 5.52/5.89 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.52/5.89 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 5.52/5.89 & ( ( ( sgn_sgn_int @ K )
% 5.52/5.89 != ( sgn_sgn_int @ L ) )
% 5.52/5.89 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.52/5.89 = ( uminus_uminus_int
% 5.52/5.89 @ ( semiri1314217659103216013at_int
% 5.52/5.89 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 5.52/5.89 @ ( zero_n2687167440665602831ol_nat
% 5.52/5.89 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % divide_int_unfold
% 5.52/5.89 thf(fact_9153_or__int__unfold,axiom,
% 5.52/5.89 ( bit_se1409905431419307370or_int
% 5.52/5.89 = ( ^ [K2: int,L2: int] :
% 5.52/5.89 ( if_int
% 5.52/5.89 @ ( ( K2
% 5.52/5.89 = ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.89 | ( L2
% 5.52/5.89 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.52/5.89 @ ( uminus_uminus_int @ one_one_int )
% 5.52/5.89 @ ( if_int @ ( K2 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_int_unfold
% 5.52/5.89 thf(fact_9154_arctan__inverse,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( X2 != zero_zero_real )
% 5.52/5.89 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X2 ) )
% 5.52/5.89 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % arctan_inverse
% 5.52/5.89 thf(fact_9155_setceilmax,axiom,
% 5.52/5.89 ! [S: vEBT_VEBT,M: nat,Listy: list_VEBT_VEBT,N: nat] :
% 5.52/5.89 ( ( vEBT_invar_vebt @ S @ M )
% 5.52/5.89 => ( ! [X4: vEBT_VEBT] :
% 5.52/5.89 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Listy ) )
% 5.52/5.89 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.52/5.89 => ( ( M
% 5.52/5.89 = ( suc @ N ) )
% 5.52/5.89 => ( ! [X4: vEBT_VEBT] :
% 5.52/5.89 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Listy ) )
% 5.52/5.89 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ X4 ) )
% 5.52/5.89 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.52/5.89 => ( ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ S ) )
% 5.52/5.89 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) )
% 5.52/5.89 => ( ( semiri1314217659103216013at_int @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ S @ ( set_VEBT_VEBT2 @ Listy ) ) ) ) )
% 5.52/5.89 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % setceilmax
% 5.52/5.89 thf(fact_9156_height__compose__list,axiom,
% 5.52/5.89 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.52/5.89 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.52/5.89 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ T ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % height_compose_list
% 5.52/5.89 thf(fact_9157_max__ins__scaled,axiom,
% 5.52/5.89 ! [N: nat,X14: vEBT_VEBT,M: nat,X13: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ X14 ) ) @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ ( lattic8265883725875713057ax_nat @ ( insert_nat @ ( vEBT_VEBT_height @ X14 ) @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % max_ins_scaled
% 5.52/5.89 thf(fact_9158_height__i__max,axiom,
% 5.52/5.89 ! [I: nat,X13: list_VEBT_VEBT,Foo: nat] :
% 5.52/5.89 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 5.52/5.89 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) @ ( ord_max_nat @ Foo @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % height_i_max
% 5.52/5.89 thf(fact_9159_max__idx__list,axiom,
% 5.52/5.89 ! [I: nat,X13: list_VEBT_VEBT,N: nat,X14: vEBT_VEBT] :
% 5.52/5.89 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 5.52/5.89 => ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) ) @ ( suc @ ( suc @ ( times_times_nat @ N @ ( ord_max_nat @ ( vEBT_VEBT_height @ X14 ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % max_idx_list
% 5.52/5.89 thf(fact_9160_or__nonnegative__int__iff,axiom,
% 5.52/5.89 ! [K: int,L: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.52/5.89 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.89 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_nonnegative_int_iff
% 5.52/5.89 thf(fact_9161_or__negative__int__iff,axiom,
% 5.52/5.89 ! [K: int,L: int] :
% 5.52/5.89 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 5.52/5.89 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.52/5.89 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_negative_int_iff
% 5.52/5.89 thf(fact_9162_or__minus__numerals_I2_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.52/5.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_minus_numerals(2)
% 5.52/5.89 thf(fact_9163_or__minus__numerals_I6_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.52/5.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_minus_numerals(6)
% 5.52/5.89 thf(fact_9164_bit__or__int__iff,axiom,
% 5.52/5.89 ! [K: int,L: int,N: nat] :
% 5.52/5.89 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ N )
% 5.52/5.89 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.52/5.89 | ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bit_or_int_iff
% 5.52/5.89 thf(fact_9165_or__greater__eq,axiom,
% 5.52/5.89 ! [L: int,K: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.52/5.89 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_greater_eq
% 5.52/5.89 thf(fact_9166_OR__lower,axiom,
% 5.52/5.89 ! [X2: int,Y2: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.89 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % OR_lower
% 5.52/5.89 thf(fact_9167_plus__and__or,axiom,
% 5.52/5.89 ! [X2: int,Y2: int] :
% 5.52/5.89 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X2 @ Y2 ) @ ( bit_se1409905431419307370or_int @ X2 @ Y2 ) )
% 5.52/5.89 = ( plus_plus_int @ X2 @ Y2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % plus_and_or
% 5.52/5.89 thf(fact_9168_VEBT__internal_Oheight_Osimps_I2_J,axiom,
% 5.52/5.89 ! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.52/5.89 ( ( vEBT_VEBT_height @ ( vEBT_Node @ Uu @ Deg @ TreeList @ Summary ) )
% 5.52/5.89 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % VEBT_internal.height.simps(2)
% 5.52/5.89 thf(fact_9169_sgn__real__def,axiom,
% 5.52/5.89 ( sgn_sgn_real
% 5.52/5.89 = ( ^ [A4: real] : ( if_real @ ( A4 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A4 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sgn_real_def
% 5.52/5.89 thf(fact_9170_VEBT__internal_Oheight_Oelims,axiom,
% 5.52/5.89 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.52/5.89 ( ( ( vEBT_VEBT_height @ X2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( ? [A3: $o,B2: $o] :
% 5.52/5.89 ( X2
% 5.52/5.89 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.89 => ( Y2 != zero_zero_nat ) )
% 5.52/5.89 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % VEBT_internal.height.elims
% 5.52/5.89 thf(fact_9171_divide__nat__def,axiom,
% 5.52/5.89 ( divide_divide_nat
% 5.52/5.89 = ( ^ [M3: nat,N3: nat] :
% 5.52/5.89 ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat
% 5.52/5.89 @ ( lattic8265883725875713057ax_nat
% 5.52/5.89 @ ( collect_nat
% 5.52/5.89 @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N3 ) @ M3 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % divide_nat_def
% 5.52/5.89 thf(fact_9172_sgn__power__injE,axiom,
% 5.52/5.89 ! [A: real,N: nat,X2: real,B: real] :
% 5.52/5.89 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.52/5.89 = X2 )
% 5.52/5.89 => ( ( X2
% 5.52/5.89 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 5.52/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( A = B ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sgn_power_injE
% 5.52/5.89 thf(fact_9173_OR__upper,axiom,
% 5.52/5.89 ! [X2: int,N: nat,Y2: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.89 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.89 => ( ( ord_less_int @ Y2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.89 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X2 @ Y2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % OR_upper
% 5.52/5.89 thf(fact_9174_or__int__rec,axiom,
% 5.52/5.89 ( bit_se1409905431419307370or_int
% 5.52/5.89 = ( ^ [K2: int,L2: int] :
% 5.52/5.89 ( plus_plus_int
% 5.52/5.89 @ ( zero_n2684676970156552555ol_int
% 5.52/5.89 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.52/5.89 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.52/5.89 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_int_rec
% 5.52/5.89 thf(fact_9175_or__minus__numerals_I1_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.52/5.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_minus_numerals(1)
% 5.52/5.89 thf(fact_9176_or__minus__numerals_I5_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.52/5.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_minus_numerals(5)
% 5.52/5.89 thf(fact_9177_or__nat__numerals_I4_J,axiom,
% 5.52/5.89 ! [X2: num] :
% 5.52/5.89 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.52/5.89 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_nat_numerals(4)
% 5.52/5.89 thf(fact_9178_or__nat__numerals_I2_J,axiom,
% 5.52/5.89 ! [Y2: num] :
% 5.52/5.89 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.52/5.89 = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_nat_numerals(2)
% 5.52/5.89 thf(fact_9179_or__nat__numerals_I3_J,axiom,
% 5.52/5.89 ! [X2: num] :
% 5.52/5.89 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.52/5.89 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_nat_numerals(3)
% 5.52/5.89 thf(fact_9180_or__nat__numerals_I1_J,axiom,
% 5.52/5.89 ! [Y2: num] :
% 5.52/5.89 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.52/5.89 = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_nat_numerals(1)
% 5.52/5.89 thf(fact_9181_or__minus__numerals_I4_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.52/5.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_minus_numerals(4)
% 5.52/5.89 thf(fact_9182_or__minus__numerals_I8_J,axiom,
% 5.52/5.89 ! [N: num,M: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.52/5.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_minus_numerals(8)
% 5.52/5.89 thf(fact_9183_or__minus__numerals_I3_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.52/5.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_minus_numerals(3)
% 5.52/5.89 thf(fact_9184_or__minus__numerals_I7_J,axiom,
% 5.52/5.89 ! [N: num,M: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.52/5.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_minus_numerals(7)
% 5.52/5.89 thf(fact_9185_or__not__num__neg_Osimps_I1_J,axiom,
% 5.52/5.89 ( ( bit_or_not_num_neg @ one @ one )
% 5.52/5.89 = one ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_num_neg.simps(1)
% 5.52/5.89 thf(fact_9186_or__not__num__neg_Osimps_I4_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 5.52/5.89 = ( bit0 @ one ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_num_neg.simps(4)
% 5.52/5.89 thf(fact_9187_or__not__num__neg_Osimps_I6_J,axiom,
% 5.52/5.89 ! [N: num,M: num] :
% 5.52/5.89 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 5.52/5.89 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_num_neg.simps(6)
% 5.52/5.89 thf(fact_9188_or__not__num__neg_Osimps_I7_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 5.52/5.89 = one ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_num_neg.simps(7)
% 5.52/5.89 thf(fact_9189_or__not__num__neg_Osimps_I3_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.52/5.89 = ( bit1 @ M ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_num_neg.simps(3)
% 5.52/5.89 thf(fact_9190_or__not__num__neg_Osimps_I5_J,axiom,
% 5.52/5.89 ! [N: num,M: num] :
% 5.52/5.89 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 5.52/5.89 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_num_neg.simps(5)
% 5.52/5.89 thf(fact_9191_or__not__num__neg_Osimps_I9_J,axiom,
% 5.52/5.89 ! [N: num,M: num] :
% 5.52/5.89 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 5.52/5.89 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_num_neg.simps(9)
% 5.52/5.89 thf(fact_9192_or__nat__def,axiom,
% 5.52/5.89 ( bit_se1412395901928357646or_nat
% 5.52/5.89 = ( ^ [M3: nat,N3: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_nat_def
% 5.52/5.89 thf(fact_9193_or__not__num__neg_Osimps_I2_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.52/5.89 = ( bit1 @ M ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_num_neg.simps(2)
% 5.52/5.89 thf(fact_9194_or__not__num__neg_Osimps_I8_J,axiom,
% 5.52/5.89 ! [N: num,M: num] :
% 5.52/5.89 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 5.52/5.89 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_num_neg.simps(8)
% 5.52/5.89 thf(fact_9195_image__Suc__lessThan,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.89 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % image_Suc_lessThan
% 5.52/5.89 thf(fact_9196_image__Suc__atMost,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.52/5.89 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % image_Suc_atMost
% 5.52/5.89 thf(fact_9197_or__not__num__neg_Oelims,axiom,
% 5.52/5.89 ! [X2: num,Xa2: num,Y2: num] :
% 5.52/5.89 ( ( ( bit_or_not_num_neg @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( Y2 != one ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ! [M4: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( bit1 @ M4 ) ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ! [M4: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( bit1 @ M4 ) ) ) )
% 5.52/5.89 => ( ( ? [N2: num] :
% 5.52/5.89 ( X2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( bit0 @ one ) ) ) )
% 5.52/5.89 => ( ! [N2: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ! [M4: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) )
% 5.52/5.89 => ( ! [N2: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ! [M4: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( bit0 @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) )
% 5.52/5.89 => ( ( ? [N2: num] :
% 5.52/5.89 ( X2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( Y2 != one ) ) )
% 5.52/5.89 => ( ! [N2: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ! [M4: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) )
% 5.52/5.89 => ~ ! [N2: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ! [M4: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_num_neg.elims
% 5.52/5.89 thf(fact_9198_Suc__0__or__eq,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.52/5.89 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Suc_0_or_eq
% 5.52/5.89 thf(fact_9199_or__Suc__0__eq,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.52/5.89 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_Suc_0_eq
% 5.52/5.89 thf(fact_9200_or__nat__rec,axiom,
% 5.52/5.89 ( bit_se1412395901928357646or_nat
% 5.52/5.89 = ( ^ [M3: nat,N3: nat] :
% 5.52/5.89 ( plus_plus_nat
% 5.52/5.89 @ ( zero_n2687167440665602831ol_nat
% 5.52/5.89 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 5.52/5.89 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.52/5.89 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_nat_rec
% 5.52/5.89 thf(fact_9201_or__nat__unfold,axiom,
% 5.52/5.89 ( bit_se1412395901928357646or_nat
% 5.52/5.89 = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_nat_unfold
% 5.52/5.89 thf(fact_9202_cis__2pi,axiom,
% 5.52/5.89 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.52/5.89 = one_one_complex ) ).
% 5.52/5.89
% 5.52/5.89 % cis_2pi
% 5.52/5.89 thf(fact_9203_i__even__power,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.89 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % i_even_power
% 5.52/5.89 thf(fact_9204_Suc__0__xor__eq,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.52/5.89 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.89 @ ( zero_n2687167440665602831ol_nat
% 5.52/5.89 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Suc_0_xor_eq
% 5.52/5.89 thf(fact_9205_xor__Suc__0__eq,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.52/5.89 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.89 @ ( zero_n2687167440665602831ol_nat
% 5.52/5.89 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_Suc_0_eq
% 5.52/5.89 thf(fact_9206_exp__two__pi__i_H,axiom,
% 5.52/5.89 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.52/5.89 = one_one_complex ) ).
% 5.52/5.89
% 5.52/5.89 % exp_two_pi_i'
% 5.52/5.89 thf(fact_9207_exp__two__pi__i,axiom,
% 5.52/5.89 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.52/5.89 = one_one_complex ) ).
% 5.52/5.89
% 5.52/5.89 % exp_two_pi_i
% 5.52/5.89 thf(fact_9208_xor__nat__numerals_I1_J,axiom,
% 5.52/5.89 ! [Y2: num] :
% 5.52/5.89 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.52/5.89 = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_nat_numerals(1)
% 5.52/5.89 thf(fact_9209_xor__nat__numerals_I2_J,axiom,
% 5.52/5.89 ! [Y2: num] :
% 5.52/5.89 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.52/5.89 = ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_nat_numerals(2)
% 5.52/5.89 thf(fact_9210_xor__nat__numerals_I3_J,axiom,
% 5.52/5.89 ! [X2: num] :
% 5.52/5.89 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.52/5.89 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_nat_numerals(3)
% 5.52/5.89 thf(fact_9211_xor__nat__numerals_I4_J,axiom,
% 5.52/5.89 ! [X2: num] :
% 5.52/5.89 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.52/5.89 = ( numeral_numeral_nat @ ( bit0 @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_nat_numerals(4)
% 5.52/5.89 thf(fact_9212_cis__pi__half,axiom,
% 5.52/5.89 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.89 = imaginary_unit ) ).
% 5.52/5.89
% 5.52/5.89 % cis_pi_half
% 5.52/5.89 thf(fact_9213_power2__i,axiom,
% 5.52/5.89 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.89 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.52/5.89
% 5.52/5.89 % power2_i
% 5.52/5.89 thf(fact_9214_cis__minus__pi__half,axiom,
% 5.52/5.89 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.52/5.89 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.52/5.89
% 5.52/5.89 % cis_minus_pi_half
% 5.52/5.89 thf(fact_9215_DeMoivre,axiom,
% 5.52/5.89 ! [A: real,N: nat] :
% 5.52/5.89 ( ( power_power_complex @ ( cis @ A ) @ N )
% 5.52/5.89 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % DeMoivre
% 5.52/5.89 thf(fact_9216_xor__nat__unfold,axiom,
% 5.52/5.89 ( bit_se6528837805403552850or_nat
% 5.52/5.89 = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_nat_unfold
% 5.52/5.89 thf(fact_9217_xor__nat__rec,axiom,
% 5.52/5.89 ( bit_se6528837805403552850or_nat
% 5.52/5.89 = ( ^ [M3: nat,N3: nat] :
% 5.52/5.89 ( plus_plus_nat
% 5.52/5.89 @ ( zero_n2687167440665602831ol_nat
% 5.52/5.89 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.52/5.89 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.52/5.89 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_nat_rec
% 5.52/5.89 thf(fact_9218_Arg__minus__ii,axiom,
% 5.52/5.89 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.52/5.89 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Arg_minus_ii
% 5.52/5.89 thf(fact_9219_Arg__ii,axiom,
% 5.52/5.89 ( ( arg @ imaginary_unit )
% 5.52/5.89 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Arg_ii
% 5.52/5.89 thf(fact_9220_bij__betw__roots__unity,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( bij_betw_nat_complex
% 5.52/5.89 @ ^ [K2: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.52/5.89 @ ( set_ord_lessThan_nat @ N )
% 5.52/5.89 @ ( collect_complex
% 5.52/5.89 @ ^ [Z2: complex] :
% 5.52/5.89 ( ( power_power_complex @ Z2 @ N )
% 5.52/5.89 = one_one_complex ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bij_betw_roots_unity
% 5.52/5.89 thf(fact_9221_csqrt__ii,axiom,
% 5.52/5.89 ( ( csqrt @ imaginary_unit )
% 5.52/5.89 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % csqrt_ii
% 5.52/5.89 thf(fact_9222_xor__nonnegative__int__iff,axiom,
% 5.52/5.89 ! [K: int,L: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.52/5.89 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.52/5.89 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_nonnegative_int_iff
% 5.52/5.89 thf(fact_9223_xor__negative__int__iff,axiom,
% 5.52/5.89 ! [K: int,L: int] :
% 5.52/5.89 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 5.52/5.89 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.52/5.89 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_negative_int_iff
% 5.52/5.89 thf(fact_9224_power2__csqrt,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.89 = Z ) ).
% 5.52/5.89
% 5.52/5.89 % power2_csqrt
% 5.52/5.89 thf(fact_9225_bit__xor__int__iff,axiom,
% 5.52/5.89 ! [K: int,L: int,N: nat] :
% 5.52/5.89 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ N )
% 5.52/5.89 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.52/5.89 != ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bit_xor_int_iff
% 5.52/5.89 thf(fact_9226_XOR__lower,axiom,
% 5.52/5.89 ! [X2: int,Y2: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.52/5.89 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % XOR_lower
% 5.52/5.89 thf(fact_9227_xor__nat__def,axiom,
% 5.52/5.89 ( bit_se6528837805403552850or_nat
% 5.52/5.89 = ( ^ [M3: nat,N3: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_nat_def
% 5.52/5.89 thf(fact_9228_Arg__bounded,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.52/5.89 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.52/5.89
% 5.52/5.89 % Arg_bounded
% 5.52/5.89 thf(fact_9229_XOR__upper,axiom,
% 5.52/5.89 ! [X2: int,N: nat,Y2: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.52/5.89 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.89 => ( ( ord_less_int @ Y2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.52/5.89 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X2 @ Y2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % XOR_upper
% 5.52/5.89 thf(fact_9230_xor__int__rec,axiom,
% 5.52/5.89 ( bit_se6526347334894502574or_int
% 5.52/5.89 = ( ^ [K2: int,L2: int] :
% 5.52/5.89 ( plus_plus_int
% 5.52/5.89 @ ( zero_n2684676970156552555ol_int
% 5.52/5.89 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) )
% 5.52/5.89 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.52/5.89 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_int_rec
% 5.52/5.89 thf(fact_9231_cis__Arg__unique,axiom,
% 5.52/5.89 ! [Z: complex,X2: real] :
% 5.52/5.89 ( ( ( sgn_sgn_complex @ Z )
% 5.52/5.89 = ( cis @ X2 ) )
% 5.52/5.89 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.52/5.89 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.52/5.89 => ( ( arg @ Z )
% 5.52/5.89 = X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % cis_Arg_unique
% 5.52/5.89 thf(fact_9232_Arg__correct,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( Z != zero_zero_complex )
% 5.52/5.89 => ( ( ( sgn_sgn_complex @ Z )
% 5.52/5.89 = ( cis @ ( arg @ Z ) ) )
% 5.52/5.89 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.52/5.89 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Arg_correct
% 5.52/5.89 thf(fact_9233_xor__int__unfold,axiom,
% 5.52/5.89 ( bit_se6526347334894502574or_int
% 5.52/5.89 = ( ^ [K2: int,L2: int] :
% 5.52/5.89 ( if_int
% 5.52/5.89 @ ( K2
% 5.52/5.89 = ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.89 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 5.52/5.89 @ ( if_int
% 5.52/5.89 @ ( L2
% 5.52/5.89 = ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.89 @ ( bit_ri7919022796975470100ot_int @ K2 )
% 5.52/5.89 @ ( if_int @ ( K2 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_int_unfold
% 5.52/5.89 thf(fact_9234_Arg__def,axiom,
% 5.52/5.89 ( arg
% 5.52/5.89 = ( ^ [Z2: complex] :
% 5.52/5.89 ( if_real @ ( Z2 = zero_zero_complex ) @ zero_zero_real
% 5.52/5.89 @ ( fChoice_real
% 5.52/5.89 @ ^ [A4: real] :
% 5.52/5.89 ( ( ( sgn_sgn_complex @ Z2 )
% 5.52/5.89 = ( cis @ A4 ) )
% 5.52/5.89 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A4 )
% 5.52/5.89 & ( ord_less_eq_real @ A4 @ pi ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Arg_def
% 5.52/5.89 thf(fact_9235_cis__multiple__2pi,axiom,
% 5.52/5.89 ! [N: real] :
% 5.52/5.89 ( ( member_real @ N @ ring_1_Ints_real )
% 5.52/5.89 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.52/5.89 = one_one_complex ) ) ).
% 5.52/5.89
% 5.52/5.89 % cis_multiple_2pi
% 5.52/5.89 thf(fact_9236_horner__sum__of__bool__2__less,axiom,
% 5.52/5.89 ! [Bs: list_o] : ( ord_less_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( size_size_list_o @ Bs ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % horner_sum_of_bool_2_less
% 5.52/5.89 thf(fact_9237_bij__betw__Suc,axiom,
% 5.52/5.89 ! [M7: set_nat,N4: set_nat] :
% 5.52/5.89 ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 5.52/5.89 = ( ( image_nat_nat @ suc @ M7 )
% 5.52/5.89 = N4 ) ) ).
% 5.52/5.89
% 5.52/5.89 % bij_betw_Suc
% 5.52/5.89 thf(fact_9238_not__negative__int__iff,axiom,
% 5.52/5.89 ! [K: int] :
% 5.52/5.89 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.52/5.89 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.52/5.89
% 5.52/5.89 % not_negative_int_iff
% 5.52/5.89 thf(fact_9239_not__nonnegative__int__iff,axiom,
% 5.52/5.89 ! [K: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.52/5.89 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.52/5.89
% 5.52/5.89 % not_nonnegative_int_iff
% 5.52/5.89 thf(fact_9240_and__minus__minus__numerals,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.89 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_minus_minus_numerals
% 5.52/5.89 thf(fact_9241_or__minus__minus__numerals,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.89 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_minus_minus_numerals
% 5.52/5.89 thf(fact_9242_bit__not__int__iff,axiom,
% 5.52/5.89 ! [K: int,N: nat] :
% 5.52/5.89 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 5.52/5.89 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bit_not_int_iff
% 5.52/5.89 thf(fact_9243_or__int__def,axiom,
% 5.52/5.89 ( bit_se1409905431419307370or_int
% 5.52/5.89 = ( ^ [K2: int,L2: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ ( bit_ri7919022796975470100ot_int @ L2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_int_def
% 5.52/5.89 thf(fact_9244_not__int__def,axiom,
% 5.52/5.89 ( bit_ri7919022796975470100ot_int
% 5.52/5.89 = ( ^ [K2: int] : ( minus_minus_int @ ( uminus_uminus_int @ K2 ) @ one_one_int ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % not_int_def
% 5.52/5.89 thf(fact_9245_and__not__numerals_I1_J,axiom,
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.52/5.89 = zero_zero_int ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_numerals(1)
% 5.52/5.89 thf(fact_9246_or__not__numerals_I1_J,axiom,
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.52/5.89 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_numerals(1)
% 5.52/5.89 thf(fact_9247_xor__int__def,axiom,
% 5.52/5.89 ( bit_se6526347334894502574or_int
% 5.52/5.89 = ( ^ [K2: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ L2 ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ L2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_int_def
% 5.52/5.89 thf(fact_9248_not__int__div__2,axiom,
% 5.52/5.89 ! [K: int] :
% 5.52/5.89 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.89 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % not_int_div_2
% 5.52/5.89 thf(fact_9249_even__not__iff__int,axiom,
% 5.52/5.89 ! [K: int] :
% 5.52/5.89 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.52/5.89 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % even_not_iff_int
% 5.52/5.89 thf(fact_9250_and__not__numerals_I2_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.52/5.89 = one_one_int ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_numerals(2)
% 5.52/5.89 thf(fact_9251_and__not__numerals_I4_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.52/5.89 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_numerals(4)
% 5.52/5.89 thf(fact_9252_or__not__numerals_I4_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.52/5.89 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_numerals(4)
% 5.52/5.89 thf(fact_9253_or__not__numerals_I2_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.52/5.89 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_numerals(2)
% 5.52/5.89 thf(fact_9254_bit__minus__int__iff,axiom,
% 5.52/5.89 ! [K: int,N: nat] :
% 5.52/5.89 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 5.52/5.89 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % bit_minus_int_iff
% 5.52/5.89 thf(fact_9255_numeral__or__not__num__eq,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 5.52/5.89 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % numeral_or_not_num_eq
% 5.52/5.89 thf(fact_9256_int__numeral__not__or__num__neg,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % int_numeral_not_or_num_neg
% 5.52/5.89 thf(fact_9257_int__numeral__or__not__num__neg,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % int_numeral_or_not_num_neg
% 5.52/5.89 thf(fact_9258_and__not__numerals_I5_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.52/5.89 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_numerals(5)
% 5.52/5.89 thf(fact_9259_and__not__numerals_I7_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.52/5.89 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_numerals(7)
% 5.52/5.89 thf(fact_9260_or__not__numerals_I3_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.52/5.89 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_numerals(3)
% 5.52/5.89 thf(fact_9261_and__not__numerals_I3_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.52/5.89 = zero_zero_int ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_numerals(3)
% 5.52/5.89 thf(fact_9262_or__not__numerals_I7_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.52/5.89 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_numerals(7)
% 5.52/5.89 thf(fact_9263_and__not__numerals_I6_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.52/5.89 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_numerals(6)
% 5.52/5.89 thf(fact_9264_and__not__numerals_I9_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.52/5.89 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_numerals(9)
% 5.52/5.89 thf(fact_9265_or__not__numerals_I6_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.52/5.89 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_numerals(6)
% 5.52/5.89 thf(fact_9266_or__not__numerals_I5_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.52/5.89 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_numerals(5)
% 5.52/5.89 thf(fact_9267_sin__integer__2pi,axiom,
% 5.52/5.89 ! [N: real] :
% 5.52/5.89 ( ( member_real @ N @ ring_1_Ints_real )
% 5.52/5.89 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.52/5.89 = zero_zero_real ) ) ).
% 5.52/5.89
% 5.52/5.89 % sin_integer_2pi
% 5.52/5.89 thf(fact_9268_cos__integer__2pi,axiom,
% 5.52/5.89 ! [N: real] :
% 5.52/5.89 ( ( member_real @ N @ ring_1_Ints_real )
% 5.52/5.89 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.52/5.89 = one_one_real ) ) ).
% 5.52/5.89
% 5.52/5.89 % cos_integer_2pi
% 5.52/5.89 thf(fact_9269_and__not__numerals_I8_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.52/5.89 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_numerals(8)
% 5.52/5.89 thf(fact_9270_or__not__numerals_I9_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.52/5.89 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_numerals(9)
% 5.52/5.89 thf(fact_9271_or__not__numerals_I8_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.52/5.89 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_numerals(8)
% 5.52/5.89 thf(fact_9272_not__int__rec,axiom,
% 5.52/5.89 ( bit_ri7919022796975470100ot_int
% 5.52/5.89 = ( ^ [K2: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % not_int_rec
% 5.52/5.89 thf(fact_9273_bij__betw__nth__root__unity,axiom,
% 5.52/5.89 ! [C: complex,N: nat] :
% 5.52/5.89 ( ( C != zero_zero_complex )
% 5.52/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.52/5.89 @ ( collect_complex
% 5.52/5.89 @ ^ [Z2: complex] :
% 5.52/5.89 ( ( power_power_complex @ Z2 @ N )
% 5.52/5.89 = one_one_complex ) )
% 5.52/5.89 @ ( collect_complex
% 5.52/5.89 @ ^ [Z2: complex] :
% 5.52/5.89 ( ( power_power_complex @ Z2 @ N )
% 5.52/5.89 = C ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bij_betw_nth_root_unity
% 5.52/5.89 thf(fact_9274_push__bit__nonnegative__int__iff,axiom,
% 5.52/5.89 ! [N: nat,K: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.52/5.89 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.52/5.89
% 5.52/5.89 % push_bit_nonnegative_int_iff
% 5.52/5.89 thf(fact_9275_push__bit__negative__int__iff,axiom,
% 5.52/5.89 ! [N: nat,K: int] :
% 5.52/5.89 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 5.52/5.89 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.52/5.89
% 5.52/5.89 % push_bit_negative_int_iff
% 5.52/5.89 thf(fact_9276_real__root__zero,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( root @ N @ zero_zero_real )
% 5.52/5.89 = zero_zero_real ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_zero
% 5.52/5.89 thf(fact_9277_concat__bit__of__zero__1,axiom,
% 5.52/5.89 ! [N: nat,L: int] :
% 5.52/5.89 ( ( bit_concat_bit @ N @ zero_zero_int @ L )
% 5.52/5.89 = ( bit_se545348938243370406it_int @ N @ L ) ) ).
% 5.52/5.89
% 5.52/5.89 % concat_bit_of_zero_1
% 5.52/5.89 thf(fact_9278_real__root__Suc__0,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( root @ ( suc @ zero_zero_nat ) @ X2 )
% 5.52/5.89 = X2 ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_Suc_0
% 5.52/5.89 thf(fact_9279_real__root__eq__iff,axiom,
% 5.52/5.89 ! [N: nat,X2: real,Y2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ( root @ N @ X2 )
% 5.52/5.89 = ( root @ N @ Y2 ) )
% 5.52/5.89 = ( X2 = Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_eq_iff
% 5.52/5.89 thf(fact_9280_root__0,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( root @ zero_zero_nat @ X2 )
% 5.52/5.89 = zero_zero_real ) ).
% 5.52/5.89
% 5.52/5.89 % root_0
% 5.52/5.89 thf(fact_9281_real__root__eq__0__iff,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ( root @ N @ X2 )
% 5.52/5.89 = zero_zero_real )
% 5.52/5.89 = ( X2 = zero_zero_real ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_eq_0_iff
% 5.52/5.89 thf(fact_9282_real__root__less__iff,axiom,
% 5.52/5.89 ! [N: nat,X2: real,Y2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N @ Y2 ) )
% 5.52/5.89 = ( ord_less_real @ X2 @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_less_iff
% 5.52/5.89 thf(fact_9283_real__root__le__iff,axiom,
% 5.52/5.89 ! [N: nat,X2: real,Y2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N @ Y2 ) )
% 5.52/5.89 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_le_iff
% 5.52/5.89 thf(fact_9284_real__root__one,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( root @ N @ one_one_real )
% 5.52/5.89 = one_one_real ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_one
% 5.52/5.89 thf(fact_9285_real__root__eq__1__iff,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ( root @ N @ X2 )
% 5.52/5.89 = one_one_real )
% 5.52/5.89 = ( X2 = one_one_real ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_eq_1_iff
% 5.52/5.89 thf(fact_9286_real__root__gt__0__iff,axiom,
% 5.52/5.89 ! [N: nat,Y2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y2 ) )
% 5.52/5.89 = ( ord_less_real @ zero_zero_real @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_gt_0_iff
% 5.52/5.89 thf(fact_9287_real__root__lt__0__iff,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ ( root @ N @ X2 ) @ zero_zero_real )
% 5.52/5.89 = ( ord_less_real @ X2 @ zero_zero_real ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_lt_0_iff
% 5.52/5.89 thf(fact_9288_real__root__le__0__iff,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ zero_zero_real )
% 5.52/5.89 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_le_0_iff
% 5.52/5.89 thf(fact_9289_real__root__ge__0__iff,axiom,
% 5.52/5.89 ! [N: nat,Y2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y2 ) )
% 5.52/5.89 = ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_ge_0_iff
% 5.52/5.89 thf(fact_9290_real__root__gt__1__iff,axiom,
% 5.52/5.89 ! [N: nat,Y2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y2 ) )
% 5.52/5.89 = ( ord_less_real @ one_one_real @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_gt_1_iff
% 5.52/5.89 thf(fact_9291_real__root__lt__1__iff,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ ( root @ N @ X2 ) @ one_one_real )
% 5.52/5.89 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_lt_1_iff
% 5.52/5.89 thf(fact_9292_real__root__ge__1__iff,axiom,
% 5.52/5.89 ! [N: nat,Y2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y2 ) )
% 5.52/5.89 = ( ord_less_eq_real @ one_one_real @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_ge_1_iff
% 5.52/5.89 thf(fact_9293_real__root__le__1__iff,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ one_one_real )
% 5.52/5.89 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_le_1_iff
% 5.52/5.89 thf(fact_9294_push__bit__of__Suc__0,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.52/5.89 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % push_bit_of_Suc_0
% 5.52/5.89 thf(fact_9295_real__root__pow__pos2,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.52/5.89 = X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_pow_pos2
% 5.52/5.89 thf(fact_9296_real__root__minus,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( root @ N @ ( uminus_uminus_real @ X2 ) )
% 5.52/5.89 = ( uminus_uminus_real @ ( root @ N @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_minus
% 5.52/5.89 thf(fact_9297_real__root__commute,axiom,
% 5.52/5.89 ! [M: nat,N: nat,X2: real] :
% 5.52/5.89 ( ( root @ M @ ( root @ N @ X2 ) )
% 5.52/5.89 = ( root @ N @ ( root @ M @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_commute
% 5.52/5.89 thf(fact_9298_push__bit__nat__eq,axiom,
% 5.52/5.89 ! [N: nat,K: int] :
% 5.52/5.89 ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 5.52/5.89 = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % push_bit_nat_eq
% 5.52/5.89 thf(fact_9299_real__root__inverse,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( root @ N @ ( inverse_inverse_real @ X2 ) )
% 5.52/5.89 = ( inverse_inverse_real @ ( root @ N @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_inverse
% 5.52/5.89 thf(fact_9300_real__root__mult__exp,axiom,
% 5.52/5.89 ! [M: nat,N: nat,X2: real] :
% 5.52/5.89 ( ( root @ ( times_times_nat @ M @ N ) @ X2 )
% 5.52/5.89 = ( root @ M @ ( root @ N @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_mult_exp
% 5.52/5.89 thf(fact_9301_real__root__divide,axiom,
% 5.52/5.89 ! [N: nat,X2: real,Y2: real] :
% 5.52/5.89 ( ( root @ N @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.52/5.89 = ( divide_divide_real @ ( root @ N @ X2 ) @ ( root @ N @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_divide
% 5.52/5.89 thf(fact_9302_real__root__mult,axiom,
% 5.52/5.89 ! [N: nat,X2: real,Y2: real] :
% 5.52/5.89 ( ( root @ N @ ( times_times_real @ X2 @ Y2 ) )
% 5.52/5.89 = ( times_times_real @ ( root @ N @ X2 ) @ ( root @ N @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_mult
% 5.52/5.89 thf(fact_9303_real__root__pos__pos__le,axiom,
% 5.52/5.89 ! [X2: real,N: nat] :
% 5.52/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_pos_pos_le
% 5.52/5.89 thf(fact_9304_set__bit__nat__def,axiom,
% 5.52/5.89 ( bit_se7882103937844011126it_nat
% 5.52/5.89 = ( ^ [M3: nat,N3: nat] : ( bit_se1412395901928357646or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % set_bit_nat_def
% 5.52/5.89 thf(fact_9305_flip__bit__nat__def,axiom,
% 5.52/5.89 ( bit_se2161824704523386999it_nat
% 5.52/5.89 = ( ^ [M3: nat,N3: nat] : ( bit_se6528837805403552850or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % flip_bit_nat_def
% 5.52/5.89 thf(fact_9306_real__root__less__mono,axiom,
% 5.52/5.89 ! [N: nat,X2: real,Y2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ X2 @ Y2 )
% 5.52/5.89 => ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N @ Y2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_less_mono
% 5.52/5.89 thf(fact_9307_real__root__le__mono,axiom,
% 5.52/5.89 ! [N: nat,X2: real,Y2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.52/5.89 => ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N @ Y2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_le_mono
% 5.52/5.89 thf(fact_9308_real__root__power,axiom,
% 5.52/5.89 ! [N: nat,X2: real,K: nat] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( root @ N @ ( power_power_real @ X2 @ K ) )
% 5.52/5.89 = ( power_power_real @ ( root @ N @ X2 ) @ K ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_power
% 5.52/5.89 thf(fact_9309_real__root__abs,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( root @ N @ ( abs_abs_real @ X2 ) )
% 5.52/5.89 = ( abs_abs_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_abs
% 5.52/5.89 thf(fact_9310_sgn__root,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( sgn_sgn_real @ ( root @ N @ X2 ) )
% 5.52/5.89 = ( sgn_sgn_real @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sgn_root
% 5.52/5.89 thf(fact_9311_bit__push__bit__iff__int,axiom,
% 5.52/5.89 ! [M: nat,K: int,N: nat] :
% 5.52/5.89 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 5.52/5.89 = ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.89 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bit_push_bit_iff_int
% 5.52/5.89 thf(fact_9312_bit__push__bit__iff__nat,axiom,
% 5.52/5.89 ! [M: nat,Q2: nat,N: nat] :
% 5.52/5.89 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 5.52/5.89 = ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.89 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bit_push_bit_iff_nat
% 5.52/5.89 thf(fact_9313_concat__bit__eq,axiom,
% 5.52/5.89 ( bit_concat_bit
% 5.52/5.89 = ( ^ [N3: nat,K2: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N3 @ K2 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % concat_bit_eq
% 5.52/5.89 thf(fact_9314_concat__bit__def,axiom,
% 5.52/5.89 ( bit_concat_bit
% 5.52/5.89 = ( ^ [N3: nat,K2: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N3 @ K2 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % concat_bit_def
% 5.52/5.89 thf(fact_9315_set__bit__int__def,axiom,
% 5.52/5.89 ( bit_se7879613467334960850it_int
% 5.52/5.89 = ( ^ [N3: nat,K2: int] : ( bit_se1409905431419307370or_int @ K2 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % set_bit_int_def
% 5.52/5.89 thf(fact_9316_flip__bit__int__def,axiom,
% 5.52/5.89 ( bit_se2159334234014336723it_int
% 5.52/5.89 = ( ^ [N3: nat,K2: int] : ( bit_se6526347334894502574or_int @ K2 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % flip_bit_int_def
% 5.52/5.89 thf(fact_9317_real__root__gt__zero,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_gt_zero
% 5.52/5.89 thf(fact_9318_real__root__strict__decreasing,axiom,
% 5.52/5.89 ! [N: nat,N4: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_nat @ N @ N4 )
% 5.52/5.89 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.52/5.89 => ( ord_less_real @ ( root @ N4 @ X2 ) @ ( root @ N @ X2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_strict_decreasing
% 5.52/5.89 thf(fact_9319_sqrt__def,axiom,
% 5.52/5.89 ( sqrt
% 5.52/5.89 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sqrt_def
% 5.52/5.89 thf(fact_9320_root__abs__power,axiom,
% 5.52/5.89 ! [N: nat,Y2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y2 @ N ) ) )
% 5.52/5.89 = ( abs_abs_real @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % root_abs_power
% 5.52/5.89 thf(fact_9321_unset__bit__int__def,axiom,
% 5.52/5.89 ( bit_se4203085406695923979it_int
% 5.52/5.89 = ( ^ [N3: nat,K2: int] : ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % unset_bit_int_def
% 5.52/5.89 thf(fact_9322_real__root__pos__pos,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_pos_pos
% 5.52/5.89 thf(fact_9323_real__root__strict__increasing,axiom,
% 5.52/5.89 ! [N: nat,N4: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_nat @ N @ N4 )
% 5.52/5.89 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.52/5.89 => ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N4 @ X2 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_strict_increasing
% 5.52/5.89 thf(fact_9324_real__root__decreasing,axiom,
% 5.52/5.89 ! [N: nat,N4: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.52/5.89 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.52/5.89 => ( ord_less_eq_real @ ( root @ N4 @ X2 ) @ ( root @ N @ X2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_decreasing
% 5.52/5.89 thf(fact_9325_real__root__pow__pos,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.52/5.89 = X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_pow_pos
% 5.52/5.89 thf(fact_9326_real__root__power__cancel,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( root @ N @ ( power_power_real @ X2 @ N ) )
% 5.52/5.89 = X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_power_cancel
% 5.52/5.89 thf(fact_9327_real__root__pos__unique,axiom,
% 5.52/5.89 ! [N: nat,Y2: real,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.52/5.89 => ( ( ( power_power_real @ Y2 @ N )
% 5.52/5.89 = X2 )
% 5.52/5.89 => ( ( root @ N @ X2 )
% 5.52/5.89 = Y2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_pos_unique
% 5.52/5.89 thf(fact_9328_odd__real__root__pow,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.89 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.52/5.89 = X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % odd_real_root_pow
% 5.52/5.89 thf(fact_9329_odd__real__root__unique,axiom,
% 5.52/5.89 ! [N: nat,Y2: real,X2: real] :
% 5.52/5.89 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.89 => ( ( ( power_power_real @ Y2 @ N )
% 5.52/5.89 = X2 )
% 5.52/5.89 => ( ( root @ N @ X2 )
% 5.52/5.89 = Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % odd_real_root_unique
% 5.52/5.89 thf(fact_9330_odd__real__root__power__cancel,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.89 => ( ( root @ N @ ( power_power_real @ X2 @ N ) )
% 5.52/5.89 = X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % odd_real_root_power_cancel
% 5.52/5.89 thf(fact_9331_push__bit__int__def,axiom,
% 5.52/5.89 ( bit_se545348938243370406it_int
% 5.52/5.89 = ( ^ [N3: nat,K2: int] : ( times_times_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % push_bit_int_def
% 5.52/5.89 thf(fact_9332_push__bit__nat__def,axiom,
% 5.52/5.89 ( bit_se547839408752420682it_nat
% 5.52/5.89 = ( ^ [N3: nat,M3: nat] : ( times_times_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % push_bit_nat_def
% 5.52/5.89 thf(fact_9333_real__root__increasing,axiom,
% 5.52/5.89 ! [N: nat,N4: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.52/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.52/5.89 => ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N4 @ X2 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % real_root_increasing
% 5.52/5.89 thf(fact_9334_sgn__power__root,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X2 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X2 ) ) @ N ) )
% 5.52/5.89 = X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % sgn_power_root
% 5.52/5.89 thf(fact_9335_root__sgn__power,axiom,
% 5.52/5.89 ! [N: nat,Y2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N ) ) )
% 5.52/5.89 = Y2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % root_sgn_power
% 5.52/5.89 thf(fact_9336_push__bit__minus__one,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.89 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % push_bit_minus_one
% 5.52/5.89 thf(fact_9337_log__root,axiom,
% 5.52/5.89 ! [N: nat,A: real,B: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.52/5.89 => ( ( log @ B @ ( root @ N @ A ) )
% 5.52/5.89 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % log_root
% 5.52/5.89 thf(fact_9338_log__base__root,axiom,
% 5.52/5.89 ! [N: nat,B: real,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.89 => ( ( log @ ( root @ N @ B ) @ X2 )
% 5.52/5.89 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % log_base_root
% 5.52/5.89 thf(fact_9339_ln__root,axiom,
% 5.52/5.89 ! [N: nat,B: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.52/5.89 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 5.52/5.89 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % ln_root
% 5.52/5.89 thf(fact_9340_split__root,axiom,
% 5.52/5.89 ! [P: real > $o,N: nat,X2: real] :
% 5.52/5.89 ( ( P @ ( root @ N @ X2 ) )
% 5.52/5.89 = ( ( ( N = zero_zero_nat )
% 5.52/5.89 => ( P @ zero_zero_real ) )
% 5.52/5.89 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ! [Y: real] :
% 5.52/5.89 ( ( ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.52/5.89 = X2 )
% 5.52/5.89 => ( P @ Y ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % split_root
% 5.52/5.89 thf(fact_9341_root__powr__inverse,axiom,
% 5.52/5.89 ! [N: nat,X2: real] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.89 => ( ( root @ N @ X2 )
% 5.52/5.89 = ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % root_powr_inverse
% 5.52/5.89 thf(fact_9342_VEBT__internal_Oheight_Opelims,axiom,
% 5.52/5.89 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.52/5.89 ( ( ( vEBT_VEBT_height @ X2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ X2 )
% 5.52/5.89 => ( ! [A3: $o,B2: $o] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.89 => ( ( Y2 = zero_zero_nat )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.52/5.89 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % VEBT_internal.height.pelims
% 5.52/5.89 thf(fact_9343_Cauchy__iff2,axiom,
% 5.52/5.89 ( topolo4055970368930404560y_real
% 5.52/5.89 = ( ^ [X7: nat > real] :
% 5.52/5.89 ! [J3: nat] :
% 5.52/5.89 ? [M8: nat] :
% 5.52/5.89 ! [M3: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ M8 @ M3 )
% 5.52/5.89 => ! [N3: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ M8 @ N3 )
% 5.52/5.89 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X7 @ M3 ) @ ( X7 @ N3 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Cauchy_iff2
% 5.52/5.89 thf(fact_9344_Sum__Ico__nat,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( groups3542108847815614940at_nat
% 5.52/5.89 @ ^ [X: nat] : X
% 5.52/5.89 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.52/5.89 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Sum_Ico_nat
% 5.52/5.89 thf(fact_9345_ex__nat__less__eq,axiom,
% 5.52/5.89 ! [N: nat,P: nat > $o] :
% 5.52/5.89 ( ( ? [M3: nat] :
% 5.52/5.89 ( ( ord_less_nat @ M3 @ N )
% 5.52/5.89 & ( P @ M3 ) ) )
% 5.52/5.89 = ( ? [X: nat] :
% 5.52/5.89 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.52/5.89 & ( P @ X ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % ex_nat_less_eq
% 5.52/5.89 thf(fact_9346_all__nat__less__eq,axiom,
% 5.52/5.89 ! [N: nat,P: nat > $o] :
% 5.52/5.89 ( ( ! [M3: nat] :
% 5.52/5.89 ( ( ord_less_nat @ M3 @ N )
% 5.52/5.89 => ( P @ M3 ) ) )
% 5.52/5.89 = ( ! [X: nat] :
% 5.52/5.89 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.52/5.89 => ( P @ X ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % all_nat_less_eq
% 5.52/5.89 thf(fact_9347_atLeastLessThanSuc,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.89 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.52/5.89 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 5.52/5.89 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.52/5.89 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.52/5.89 = bot_bot_set_nat ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % atLeastLessThanSuc
% 5.52/5.89 thf(fact_9348_atLeastLessThan__nat__numeral,axiom,
% 5.52/5.89 ! [M: nat,K: num] :
% 5.52/5.89 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.52/5.89 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.52/5.89 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.52/5.89 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.52/5.89 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.52/5.89 = bot_bot_set_nat ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % atLeastLessThan_nat_numeral
% 5.52/5.89 thf(fact_9349_image__minus__const__atLeastLessThan__nat,axiom,
% 5.52/5.89 ! [C: nat,Y2: nat,X2: nat] :
% 5.52/5.89 ( ( ( ord_less_nat @ C @ Y2 )
% 5.52/5.89 => ( ( image_nat_nat
% 5.52/5.89 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.52/5.89 @ ( set_or4665077453230672383an_nat @ X2 @ Y2 ) )
% 5.52/5.89 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X2 @ C ) @ ( minus_minus_nat @ Y2 @ C ) ) ) )
% 5.52/5.89 & ( ~ ( ord_less_nat @ C @ Y2 )
% 5.52/5.89 => ( ( ( ord_less_nat @ X2 @ Y2 )
% 5.52/5.89 => ( ( image_nat_nat
% 5.52/5.89 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.52/5.89 @ ( set_or4665077453230672383an_nat @ X2 @ Y2 ) )
% 5.52/5.89 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.52/5.89 & ( ~ ( ord_less_nat @ X2 @ Y2 )
% 5.52/5.89 => ( ( image_nat_nat
% 5.52/5.89 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.52/5.89 @ ( set_or4665077453230672383an_nat @ X2 @ Y2 ) )
% 5.52/5.89 = bot_bot_set_nat ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % image_minus_const_atLeastLessThan_nat
% 5.52/5.89 thf(fact_9350_sum__power2,axiom,
% 5.52/5.89 ! [K: nat] :
% 5.52/5.89 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.52/5.89 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.52/5.89
% 5.52/5.89 % sum_power2
% 5.52/5.89 thf(fact_9351_vebt__mint_Opelims,axiom,
% 5.52/5.89 ! [X2: vEBT_VEBT,Y2: option_nat] :
% 5.52/5.89 ( ( ( vEBT_vebt_mint @ X2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X2 )
% 5.52/5.89 => ( ! [A3: $o,B2: $o] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.89 => ( ( ( A3
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( some_nat @ zero_zero_nat ) ) )
% 5.52/5.89 & ( ~ A3
% 5.52/5.89 => ( ( B2
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( some_nat @ one_one_nat ) ) )
% 5.52/5.89 & ( ~ B2
% 5.52/5.89 => ( Y2 = none_nat ) ) ) ) )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.52/5.89 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.89 => ( ( Y2 = none_nat )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.52/5.89 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_nat @ Mi2 ) )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % vebt_mint.pelims
% 5.52/5.89 thf(fact_9352_vebt__maxt_Opelims,axiom,
% 5.52/5.89 ! [X2: vEBT_VEBT,Y2: option_nat] :
% 5.52/5.89 ( ( ( vEBT_vebt_maxt @ X2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X2 )
% 5.52/5.89 => ( ! [A3: $o,B2: $o] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.89 => ( ( ( B2
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( some_nat @ one_one_nat ) ) )
% 5.52/5.89 & ( ~ B2
% 5.52/5.89 => ( ( A3
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( some_nat @ zero_zero_nat ) ) )
% 5.52/5.89 & ( ~ A3
% 5.52/5.89 => ( Y2 = none_nat ) ) ) ) )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.52/5.89 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.89 => ( ( Y2 = none_nat )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.52/5.89 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_nat @ Ma2 ) )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % vebt_maxt.pelims
% 5.52/5.89 thf(fact_9353_Chebyshev__sum__upper__nat,axiom,
% 5.52/5.89 ! [N: nat,A: nat > nat,B: nat > nat] :
% 5.52/5.89 ( ! [I2: nat,J2: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.52/5.89 => ( ( ord_less_nat @ J2 @ N )
% 5.52/5.89 => ( ord_less_eq_nat @ ( A @ I2 ) @ ( A @ J2 ) ) ) )
% 5.52/5.89 => ( ! [I2: nat,J2: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.52/5.89 => ( ( ord_less_nat @ J2 @ N )
% 5.52/5.89 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I2 ) ) ) )
% 5.52/5.89 => ( ord_less_eq_nat
% 5.52/5.89 @ ( times_times_nat @ N
% 5.52/5.89 @ ( groups3542108847815614940at_nat
% 5.52/5.89 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( B @ I4 ) )
% 5.52/5.89 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.52/5.89 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Chebyshev_sum_upper_nat
% 5.52/5.89 thf(fact_9354_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims,axiom,
% 5.52/5.89 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.52/5.89 ( ( ( vEBT_T_m_i_n_t @ X2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ X2 )
% 5.52/5.89 => ( ! [A3: $o,B2: $o] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A3 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.52/5.89 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.89 => ( ( Y2 = one_one_nat )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.52/5.89 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.89 => ( ( Y2 = one_one_nat )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.pelims
% 5.52/5.89 thf(fact_9355_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Opelims,axiom,
% 5.52/5.89 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.52/5.89 ( ( ( vEBT_T_m_a_x_t @ X2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ X2 )
% 5.52/5.89 => ( ! [A3: $o,B2: $o] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B2 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.52/5.89 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.52/5.89 => ( ( Y2 = one_one_nat )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.52/5.89 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.52/5.89 => ( ( Y2 = one_one_nat )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.pelims
% 5.52/5.89 thf(fact_9356_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Opelims,axiom,
% 5.52/5.89 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.52/5.89 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ X2 )
% 5.52/5.89 => ( ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ $false @ $false ) )
% 5.52/5.89 => ( ( Y2 = one_one_nat )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.52/5.89 => ( ! [Uv2: $o] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.52/5.89 => ( ( Y2 = one_one_nat )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.52/5.89 => ( ! [Uu2: $o] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.52/5.89 => ( ( Y2 = one_one_nat )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.52/5.89 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.52/5.89 => ( ( Y2 = one_one_nat )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.52/5.89 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.52/5.89 => ( ( Y2 = one_one_nat )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.pelims
% 5.52/5.89 thf(fact_9357_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.52/5.89 ! [X2: vEBT_VEBT,Y2: $o] :
% 5.52/5.89 ( ( ( vEBT_VEBT_minNull @ X2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.52/5.89 => ( ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ $false @ $false ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.52/5.89 => ( ! [Uv2: $o] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.52/5.89 => ( ~ Y2
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.52/5.89 => ( ! [Uu2: $o] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.52/5.89 => ( ~ Y2
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.52/5.89 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.52/5.89 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.52/5.89 => ( ~ Y2
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % VEBT_internal.minNull.pelims(1)
% 5.52/5.89 thf(fact_9358_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.52/5.89 ! [X2: vEBT_VEBT] :
% 5.52/5.89 ( ( vEBT_VEBT_minNull @ X2 )
% 5.52/5.89 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.52/5.89 => ( ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ $false @ $false ) )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.52/5.89 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % VEBT_internal.minNull.pelims(2)
% 5.52/5.89 thf(fact_9359_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.52/5.89 ! [X2: vEBT_VEBT] :
% 5.52/5.89 ( ~ ( vEBT_VEBT_minNull @ X2 )
% 5.52/5.89 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.52/5.89 => ( ! [Uv2: $o] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 5.52/5.89 => ( ! [Uu2: $o] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 5.52/5.89 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.52/5.89 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % VEBT_internal.minNull.pelims(3)
% 5.52/5.89 thf(fact_9360_valid__eq2,axiom,
% 5.52/5.89 ! [T: vEBT_VEBT,D2: nat] :
% 5.52/5.89 ( ( vEBT_VEBT_valid @ T @ D2 )
% 5.52/5.89 => ( vEBT_invar_vebt @ T @ D2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % valid_eq2
% 5.52/5.89 thf(fact_9361_valid__eq1,axiom,
% 5.52/5.89 ! [T: vEBT_VEBT,D2: nat] :
% 5.52/5.89 ( ( vEBT_invar_vebt @ T @ D2 )
% 5.52/5.89 => ( vEBT_VEBT_valid @ T @ D2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % valid_eq1
% 5.52/5.89 thf(fact_9362_valid__eq,axiom,
% 5.52/5.89 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.52/5.89
% 5.52/5.89 % valid_eq
% 5.52/5.89 thf(fact_9363_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.52/5.89 ! [Uu: $o,Uv: $o,D2: nat] :
% 5.52/5.89 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D2 )
% 5.52/5.89 = ( D2 = one_one_nat ) ) ).
% 5.52/5.89
% 5.52/5.89 % VEBT_internal.valid'.simps(1)
% 5.52/5.89 thf(fact_9364_Code__Target__Int_Opositive__def,axiom,
% 5.52/5.89 code_Target_positive = numeral_numeral_int ).
% 5.52/5.89
% 5.52/5.89 % Code_Target_Int.positive_def
% 5.52/5.89 thf(fact_9365_csqrt_Osimps_I1_J,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( re @ ( csqrt @ Z ) )
% 5.52/5.89 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % csqrt.simps(1)
% 5.52/5.89 thf(fact_9366_cos__n__Re__cis__pow__n,axiom,
% 5.52/5.89 ! [N: nat,A: real] :
% 5.52/5.89 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.52/5.89 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % cos_n_Re_cis_pow_n
% 5.52/5.89 thf(fact_9367_csqrt_Ocode,axiom,
% 5.52/5.89 ( csqrt
% 5.52/5.89 = ( ^ [Z2: complex] :
% 5.52/5.89 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( re @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.89 @ ( times_times_real
% 5.52/5.89 @ ( if_real
% 5.52/5.89 @ ( ( im @ Z2 )
% 5.52/5.89 = zero_zero_real )
% 5.52/5.89 @ one_one_real
% 5.52/5.89 @ ( sgn_sgn_real @ ( im @ Z2 ) ) )
% 5.52/5.89 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( re @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % csqrt.code
% 5.52/5.89 thf(fact_9368_csqrt_Osimps_I2_J,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( im @ ( csqrt @ Z ) )
% 5.52/5.89 = ( times_times_real
% 5.52/5.89 @ ( if_real
% 5.52/5.89 @ ( ( im @ Z )
% 5.52/5.89 = zero_zero_real )
% 5.52/5.89 @ one_one_real
% 5.52/5.89 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.52/5.89 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % csqrt.simps(2)
% 5.52/5.89 thf(fact_9369_Complex__divide,axiom,
% 5.52/5.89 ( divide1717551699836669952omplex
% 5.52/5.89 = ( ^ [X: complex,Y: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Complex_divide
% 5.52/5.89 thf(fact_9370_Im__power__real,axiom,
% 5.52/5.89 ! [X2: complex,N: nat] :
% 5.52/5.89 ( ( ( im @ X2 )
% 5.52/5.89 = zero_zero_real )
% 5.52/5.89 => ( ( im @ ( power_power_complex @ X2 @ N ) )
% 5.52/5.89 = zero_zero_real ) ) ).
% 5.52/5.89
% 5.52/5.89 % Im_power_real
% 5.52/5.89 thf(fact_9371_Re__power__real,axiom,
% 5.52/5.89 ! [X2: complex,N: nat] :
% 5.52/5.89 ( ( ( im @ X2 )
% 5.52/5.89 = zero_zero_real )
% 5.52/5.89 => ( ( re @ ( power_power_complex @ X2 @ N ) )
% 5.52/5.89 = ( power_power_real @ ( re @ X2 ) @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Re_power_real
% 5.52/5.89 thf(fact_9372_csqrt__minus,axiom,
% 5.52/5.89 ! [X2: complex] :
% 5.52/5.89 ( ( ( ord_less_real @ ( im @ X2 ) @ zero_zero_real )
% 5.52/5.89 | ( ( ( im @ X2 )
% 5.52/5.89 = zero_zero_real )
% 5.52/5.89 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X2 ) ) ) )
% 5.52/5.89 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.52/5.89 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % csqrt_minus
% 5.52/5.89 thf(fact_9373_csqrt__principal,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.52/5.89 | ( ( ( re @ ( csqrt @ Z ) )
% 5.52/5.89 = zero_zero_real )
% 5.52/5.89 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % csqrt_principal
% 5.52/5.89 thf(fact_9374_sin__n__Im__cis__pow__n,axiom,
% 5.52/5.89 ! [N: nat,A: real] :
% 5.52/5.89 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.52/5.89 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sin_n_Im_cis_pow_n
% 5.52/5.89 thf(fact_9375_cmod__power2,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.89 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % cmod_power2
% 5.52/5.89 thf(fact_9376_Im__power2,axiom,
% 5.52/5.89 ! [X2: complex] :
% 5.52/5.89 ( ( im @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.89 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X2 ) ) @ ( im @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Im_power2
% 5.52/5.89 thf(fact_9377_Re__power2,axiom,
% 5.52/5.89 ! [X2: complex] :
% 5.52/5.89 ( ( re @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.89 = ( minus_minus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Re_power2
% 5.52/5.89 thf(fact_9378_complex__eq__0,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( Z = zero_zero_complex )
% 5.52/5.89 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.89 = zero_zero_real ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_eq_0
% 5.52/5.89 thf(fact_9379_norm__complex__def,axiom,
% 5.52/5.89 ( real_V1022390504157884413omplex
% 5.52/5.89 = ( ^ [Z2: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % norm_complex_def
% 5.52/5.89 thf(fact_9380_inverse__complex_Osimps_I1_J,axiom,
% 5.52/5.89 ! [X2: complex] :
% 5.52/5.89 ( ( re @ ( invers8013647133539491842omplex @ X2 ) )
% 5.52/5.89 = ( divide_divide_real @ ( re @ X2 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % inverse_complex.simps(1)
% 5.52/5.89 thf(fact_9381_complex__neq__0,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( Z != zero_zero_complex )
% 5.52/5.89 = ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_neq_0
% 5.52/5.89 thf(fact_9382_Re__divide,axiom,
% 5.52/5.89 ! [X2: complex,Y2: complex] :
% 5.52/5.89 ( ( re @ ( divide1717551699836669952omplex @ X2 @ Y2 ) )
% 5.52/5.89 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Re_divide
% 5.52/5.89 thf(fact_9383_csqrt__unique,axiom,
% 5.52/5.89 ! [W: complex,Z: complex] :
% 5.52/5.89 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.89 = Z )
% 5.52/5.89 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.52/5.89 | ( ( ( re @ W )
% 5.52/5.89 = zero_zero_real )
% 5.52/5.89 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.52/5.89 => ( ( csqrt @ Z )
% 5.52/5.89 = W ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % csqrt_unique
% 5.52/5.89 thf(fact_9384_csqrt__square,axiom,
% 5.52/5.89 ! [B: complex] :
% 5.52/5.89 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.52/5.89 | ( ( ( re @ B )
% 5.52/5.89 = zero_zero_real )
% 5.52/5.89 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.52/5.89 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.89 = B ) ) ).
% 5.52/5.89
% 5.52/5.89 % csqrt_square
% 5.52/5.89 thf(fact_9385_inverse__complex_Osimps_I2_J,axiom,
% 5.52/5.89 ! [X2: complex] :
% 5.52/5.89 ( ( im @ ( invers8013647133539491842omplex @ X2 ) )
% 5.52/5.89 = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X2 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % inverse_complex.simps(2)
% 5.52/5.89 thf(fact_9386_Im__divide,axiom,
% 5.52/5.89 ! [X2: complex,Y2: complex] :
% 5.52/5.89 ( ( im @ ( divide1717551699836669952omplex @ X2 @ Y2 ) )
% 5.52/5.89 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Im_divide
% 5.52/5.89 thf(fact_9387_complex__abs__le__norm,axiom,
% 5.52/5.89 ! [Z: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_abs_le_norm
% 5.52/5.89 thf(fact_9388_complex__unit__circle,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( Z != zero_zero_complex )
% 5.52/5.89 => ( ( plus_plus_real @ ( power_power_real @ ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.89 = one_one_real ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_unit_circle
% 5.52/5.89 thf(fact_9389_inverse__complex_Ocode,axiom,
% 5.52/5.89 ( invers8013647133539491842omplex
% 5.52/5.89 = ( ^ [X: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % inverse_complex.code
% 5.52/5.89 thf(fact_9390_Im__Reals__divide,axiom,
% 5.52/5.89 ! [R: complex,Z: complex] :
% 5.52/5.89 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.52/5.89 => ( ( im @ ( divide1717551699836669952omplex @ R @ Z ) )
% 5.52/5.89 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Im_Reals_divide
% 5.52/5.89 thf(fact_9391_Re__Reals__divide,axiom,
% 5.52/5.89 ! [R: complex,Z: complex] :
% 5.52/5.89 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.52/5.89 => ( ( re @ ( divide1717551699836669952omplex @ R @ Z ) )
% 5.52/5.89 = ( divide_divide_real @ ( times_times_real @ ( re @ R ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Re_Reals_divide
% 5.52/5.89 thf(fact_9392_complex__mult__cnj,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.52/5.89 = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_mult_cnj
% 5.52/5.89 thf(fact_9393_divmod__step__integer__def,axiom,
% 5.52/5.89 ( unique4921790084139445826nteger
% 5.52/5.89 = ( ^ [L2: num] :
% 5.52/5.89 ( produc6916734918728496179nteger
% 5.52/5.89 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % divmod_step_integer_def
% 5.52/5.89 thf(fact_9394_complex__cnj__power,axiom,
% 5.52/5.89 ! [X2: complex,N: nat] :
% 5.52/5.89 ( ( cnj @ ( power_power_complex @ X2 @ N ) )
% 5.52/5.89 = ( power_power_complex @ ( cnj @ X2 ) @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_cnj_power
% 5.52/5.89 thf(fact_9395_sgn__integer__code,axiom,
% 5.52/5.89 ( sgn_sgn_Code_integer
% 5.52/5.89 = ( ^ [K2: code_integer] : ( if_Code_integer @ ( K2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sgn_integer_code
% 5.52/5.89 thf(fact_9396_one__natural_Orsp,axiom,
% 5.52/5.89 one_one_nat = one_one_nat ).
% 5.52/5.89
% 5.52/5.89 % one_natural.rsp
% 5.52/5.89 thf(fact_9397_Re__complex__div__gt__0,axiom,
% 5.52/5.89 ! [A: complex,B: complex] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.52/5.89 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Re_complex_div_gt_0
% 5.52/5.89 thf(fact_9398_Re__complex__div__lt__0,axiom,
% 5.52/5.89 ! [A: complex,B: complex] :
% 5.52/5.89 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.52/5.89 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.52/5.89
% 5.52/5.89 % Re_complex_div_lt_0
% 5.52/5.89 thf(fact_9399_Im__complex__div__gt__0,axiom,
% 5.52/5.89 ! [A: complex,B: complex] :
% 5.52/5.89 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.52/5.89 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Im_complex_div_gt_0
% 5.52/5.89 thf(fact_9400_Im__complex__div__lt__0,axiom,
% 5.52/5.89 ! [A: complex,B: complex] :
% 5.52/5.89 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.52/5.89 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.52/5.89
% 5.52/5.89 % Im_complex_div_lt_0
% 5.52/5.89 thf(fact_9401_complex__mod__mult__cnj,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.52/5.89 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_mod_mult_cnj
% 5.52/5.89 thf(fact_9402_complex__div__gt__0,axiom,
% 5.52/5.89 ! [A: complex,B: complex] :
% 5.52/5.89 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.52/5.89 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.52/5.89 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.52/5.89 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_div_gt_0
% 5.52/5.89 thf(fact_9403_complex__norm__square,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.89 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_norm_square
% 5.52/5.89 thf(fact_9404_complex__add__cnj,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.52/5.89 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_add_cnj
% 5.52/5.89 thf(fact_9405_complex__diff__cnj,axiom,
% 5.52/5.89 ! [Z: complex] :
% 5.52/5.89 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.52/5.89 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_diff_cnj
% 5.52/5.89 thf(fact_9406_complex__div__cnj,axiom,
% 5.52/5.89 ( divide1717551699836669952omplex
% 5.52/5.89 = ( ^ [A4: complex,B3: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A4 @ ( cnj @ B3 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % complex_div_cnj
% 5.52/5.89 thf(fact_9407_cnj__add__mult__eq__Re,axiom,
% 5.52/5.89 ! [Z: complex,W: complex] :
% 5.52/5.89 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.52/5.89 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % cnj_add_mult_eq_Re
% 5.52/5.89 thf(fact_9408_integer__of__int__code,axiom,
% 5.52/5.89 ( code_integer_of_int
% 5.52/5.89 = ( ^ [K2: int] :
% 5.52/5.89 ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K2 ) ) )
% 5.52/5.89 @ ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.52/5.89 @ ( if_Code_integer
% 5.52/5.89 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.52/5.89 = zero_zero_int )
% 5.52/5.89 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.52/5.89 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % integer_of_int_code
% 5.52/5.89 thf(fact_9409_integer__of__num_I3_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 5.52/5.89 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 5.52/5.89
% 5.52/5.89 % integer_of_num(3)
% 5.52/5.89 thf(fact_9410_card__Collect__less__nat,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( finite_card_nat
% 5.52/5.89 @ ( collect_nat
% 5.52/5.89 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) )
% 5.52/5.89 = N ) ).
% 5.52/5.89
% 5.52/5.89 % card_Collect_less_nat
% 5.52/5.89 thf(fact_9411_card__Collect__le__nat,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( finite_card_nat
% 5.52/5.89 @ ( collect_nat
% 5.52/5.89 @ ^ [I4: nat] : ( ord_less_eq_nat @ I4 @ N ) ) )
% 5.52/5.89 = ( suc @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % card_Collect_le_nat
% 5.52/5.89 thf(fact_9412_abs__integer__code,axiom,
% 5.52/5.89 ( abs_abs_Code_integer
% 5.52/5.89 = ( ^ [K2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K2 ) @ K2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % abs_integer_code
% 5.52/5.89 thf(fact_9413_less__integer__code_I1_J,axiom,
% 5.52/5.89 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 5.52/5.89
% 5.52/5.89 % less_integer_code(1)
% 5.52/5.89 thf(fact_9414_less__integer_Oabs__eq,axiom,
% 5.52/5.89 ! [Xa2: int,X2: int] :
% 5.52/5.89 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.52/5.89 = ( ord_less_int @ Xa2 @ X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % less_integer.abs_eq
% 5.52/5.89 thf(fact_9415_divide__integer_Oabs__eq,axiom,
% 5.52/5.89 ! [Xa2: int,X2: int] :
% 5.52/5.89 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.52/5.89 = ( code_integer_of_int @ ( divide_divide_int @ Xa2 @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % divide_integer.abs_eq
% 5.52/5.89 thf(fact_9416_card__less__Suc2,axiom,
% 5.52/5.89 ! [M7: set_nat,I: nat] :
% 5.52/5.89 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.52/5.89 => ( ( finite_card_nat
% 5.52/5.89 @ ( collect_nat
% 5.52/5.89 @ ^ [K2: nat] :
% 5.52/5.89 ( ( member_nat @ ( suc @ K2 ) @ M7 )
% 5.52/5.89 & ( ord_less_nat @ K2 @ I ) ) ) )
% 5.52/5.89 = ( finite_card_nat
% 5.52/5.89 @ ( collect_nat
% 5.52/5.89 @ ^ [K2: nat] :
% 5.52/5.89 ( ( member_nat @ K2 @ M7 )
% 5.52/5.89 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % card_less_Suc2
% 5.52/5.89 thf(fact_9417_card__less__Suc,axiom,
% 5.52/5.89 ! [M7: set_nat,I: nat] :
% 5.52/5.89 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.52/5.89 => ( ( suc
% 5.52/5.89 @ ( finite_card_nat
% 5.52/5.89 @ ( collect_nat
% 5.52/5.89 @ ^ [K2: nat] :
% 5.52/5.89 ( ( member_nat @ ( suc @ K2 ) @ M7 )
% 5.52/5.89 & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 5.52/5.89 = ( finite_card_nat
% 5.52/5.89 @ ( collect_nat
% 5.52/5.89 @ ^ [K2: nat] :
% 5.52/5.89 ( ( member_nat @ K2 @ M7 )
% 5.52/5.89 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % card_less_Suc
% 5.52/5.89 thf(fact_9418_card__less,axiom,
% 5.52/5.89 ! [M7: set_nat,I: nat] :
% 5.52/5.89 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.52/5.89 => ( ( finite_card_nat
% 5.52/5.89 @ ( collect_nat
% 5.52/5.89 @ ^ [K2: nat] :
% 5.52/5.89 ( ( member_nat @ K2 @ M7 )
% 5.52/5.89 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 5.52/5.89 != zero_zero_nat ) ) ).
% 5.52/5.89
% 5.52/5.89 % card_less
% 5.52/5.89 thf(fact_9419_subset__card__intvl__is__intvl,axiom,
% 5.52/5.89 ! [A2: set_nat,K: nat] :
% 5.52/5.89 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 5.52/5.89 => ( A2
% 5.52/5.89 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % subset_card_intvl_is_intvl
% 5.52/5.89 thf(fact_9420_card__le__Suc__Max,axiom,
% 5.52/5.89 ! [S3: set_nat] :
% 5.52/5.89 ( ( finite_finite_nat @ S3 )
% 5.52/5.89 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % card_le_Suc_Max
% 5.52/5.89 thf(fact_9421_subset__eq__atLeast0__lessThan__card,axiom,
% 5.52/5.89 ! [N4: set_nat,N: nat] :
% 5.52/5.89 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.52/5.89 => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % subset_eq_atLeast0_lessThan_card
% 5.52/5.89 thf(fact_9422_card__sum__le__nat__sum,axiom,
% 5.52/5.89 ! [S3: set_nat] :
% 5.52/5.89 ( ord_less_eq_nat
% 5.52/5.89 @ ( groups3542108847815614940at_nat
% 5.52/5.89 @ ^ [X: nat] : X
% 5.52/5.89 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 5.52/5.89 @ ( groups3542108847815614940at_nat
% 5.52/5.89 @ ^ [X: nat] : X
% 5.52/5.89 @ S3 ) ) ).
% 5.52/5.89
% 5.52/5.89 % card_sum_le_nat_sum
% 5.52/5.89 thf(fact_9423_card__nth__roots,axiom,
% 5.52/5.89 ! [C: complex,N: nat] :
% 5.52/5.89 ( ( C != zero_zero_complex )
% 5.52/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( finite_card_complex
% 5.52/5.89 @ ( collect_complex
% 5.52/5.89 @ ^ [Z2: complex] :
% 5.52/5.89 ( ( power_power_complex @ Z2 @ N )
% 5.52/5.89 = C ) ) )
% 5.52/5.89 = N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % card_nth_roots
% 5.52/5.89 thf(fact_9424_card__roots__unity__eq,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( finite_card_complex
% 5.52/5.89 @ ( collect_complex
% 5.52/5.89 @ ^ [Z2: complex] :
% 5.52/5.89 ( ( power_power_complex @ Z2 @ N )
% 5.52/5.89 = one_one_complex ) ) )
% 5.52/5.89 = N ) ) ).
% 5.52/5.89
% 5.52/5.89 % card_roots_unity_eq
% 5.52/5.89 thf(fact_9425_integer__of__num__triv_I1_J,axiom,
% 5.52/5.89 ( ( code_integer_of_num @ one )
% 5.52/5.89 = one_one_Code_integer ) ).
% 5.52/5.89
% 5.52/5.89 % integer_of_num_triv(1)
% 5.52/5.89 thf(fact_9426_integer__of__num_I2_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 5.52/5.89 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % integer_of_num(2)
% 5.52/5.89 thf(fact_9427_integer__of__num__triv_I2_J,axiom,
% 5.52/5.89 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.52/5.89 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % integer_of_num_triv(2)
% 5.52/5.89 thf(fact_9428_int__of__integer__code,axiom,
% 5.52/5.89 ( code_int_of_integer
% 5.52/5.89 = ( ^ [K2: code_integer] :
% 5.52/5.89 ( if_int @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K2 ) ) )
% 5.52/5.89 @ ( if_int @ ( K2 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.52/5.89 @ ( produc1553301316500091796er_int
% 5.52/5.89 @ ^ [L2: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 5.52/5.89 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % int_of_integer_code
% 5.52/5.89 thf(fact_9429_int__of__integer__numeral,axiom,
% 5.52/5.89 ! [K: num] :
% 5.52/5.89 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.52/5.89 = ( numeral_numeral_int @ K ) ) ).
% 5.52/5.89
% 5.52/5.89 % int_of_integer_numeral
% 5.52/5.89 thf(fact_9430_divide__integer_Orep__eq,axiom,
% 5.52/5.89 ! [X2: code_integer,Xa2: code_integer] :
% 5.52/5.89 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X2 @ Xa2 ) )
% 5.52/5.89 = ( divide_divide_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % divide_integer.rep_eq
% 5.52/5.89 thf(fact_9431_integer__less__iff,axiom,
% 5.52/5.89 ( ord_le6747313008572928689nteger
% 5.52/5.89 = ( ^ [K2: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % integer_less_iff
% 5.52/5.89 thf(fact_9432_less__integer_Orep__eq,axiom,
% 5.52/5.89 ( ord_le6747313008572928689nteger
% 5.52/5.89 = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % less_integer.rep_eq
% 5.52/5.89 thf(fact_9433_num__of__integer__code,axiom,
% 5.52/5.89 ( code_num_of_integer
% 5.52/5.89 = ( ^ [K2: code_integer] :
% 5.52/5.89 ( if_num @ ( ord_le3102999989581377725nteger @ K2 @ one_one_Code_integer ) @ one
% 5.52/5.89 @ ( produc7336495610019696514er_num
% 5.52/5.89 @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 5.52/5.89 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % num_of_integer_code
% 5.52/5.89 thf(fact_9434_nat__of__integer__code,axiom,
% 5.52/5.89 ( code_nat_of_integer
% 5.52/5.89 = ( ^ [K2: code_integer] :
% 5.52/5.89 ( if_nat @ ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.52/5.89 @ ( produc1555791787009142072er_nat
% 5.52/5.89 @ ^ [L2: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 5.52/5.89 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_of_integer_code
% 5.52/5.89 thf(fact_9435_bit__cut__integer__def,axiom,
% 5.52/5.89 ( code_bit_cut_integer
% 5.52/5.89 = ( ^ [K2: code_integer] :
% 5.52/5.89 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.52/5.89 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bit_cut_integer_def
% 5.52/5.89 thf(fact_9436_nat__of__integer__code__post_I3_J,axiom,
% 5.52/5.89 ! [K: num] :
% 5.52/5.89 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.52/5.89 = ( numeral_numeral_nat @ K ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_of_integer_code_post(3)
% 5.52/5.89 thf(fact_9437_nat__of__integer__code__post_I2_J,axiom,
% 5.52/5.89 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.52/5.89 = one_one_nat ) ).
% 5.52/5.89
% 5.52/5.89 % nat_of_integer_code_post(2)
% 5.52/5.89 thf(fact_9438_bit__cut__integer__code,axiom,
% 5.52/5.89 ( code_bit_cut_integer
% 5.52/5.89 = ( ^ [K2: code_integer] :
% 5.52/5.89 ( if_Pro5737122678794959658eger_o @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.52/5.89 @ ( produc9125791028180074456eger_o
% 5.52/5.89 @ ^ [R5: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 5.52/5.89 @ ( code_divmod_abs @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bit_cut_integer_code
% 5.52/5.89 thf(fact_9439_nat_Odisc__eq__case_I2_J,axiom,
% 5.52/5.89 ! [Nat: nat] :
% 5.52/5.89 ( ( Nat != zero_zero_nat )
% 5.52/5.89 = ( case_nat_o @ $false
% 5.52/5.89 @ ^ [Uu3: nat] : $true
% 5.52/5.89 @ Nat ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat.disc_eq_case(2)
% 5.52/5.89 thf(fact_9440_nat_Odisc__eq__case_I1_J,axiom,
% 5.52/5.89 ! [Nat: nat] :
% 5.52/5.89 ( ( Nat = zero_zero_nat )
% 5.52/5.89 = ( case_nat_o @ $true
% 5.52/5.89 @ ^ [Uu3: nat] : $false
% 5.52/5.89 @ Nat ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat.disc_eq_case(1)
% 5.52/5.89 thf(fact_9441_less__eq__nat_Osimps_I2_J,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.52/5.89 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % less_eq_nat.simps(2)
% 5.52/5.89 thf(fact_9442_max__Suc1,axiom,
% 5.52/5.89 ! [N: nat,M: nat] :
% 5.52/5.89 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 5.52/5.89 = ( case_nat_nat @ ( suc @ N )
% 5.52/5.89 @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ N @ M5 ) )
% 5.52/5.89 @ M ) ) ).
% 5.52/5.89
% 5.52/5.89 % max_Suc1
% 5.52/5.89 thf(fact_9443_max__Suc2,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 5.52/5.89 = ( case_nat_nat @ ( suc @ N )
% 5.52/5.89 @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ M5 @ N ) )
% 5.52/5.89 @ M ) ) ).
% 5.52/5.89
% 5.52/5.89 % max_Suc2
% 5.52/5.89 thf(fact_9444_diff__Suc,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.52/5.89 = ( case_nat_nat @ zero_zero_nat
% 5.52/5.89 @ ^ [K2: nat] : K2
% 5.52/5.89 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % diff_Suc
% 5.52/5.89 thf(fact_9445_divmod__integer__code,axiom,
% 5.52/5.89 ( code_divmod_integer
% 5.52/5.89 = ( ^ [K2: code_integer,L2: code_integer] :
% 5.52/5.89 ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.52/5.89 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.52/5.89 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ ( code_divmod_abs @ K2 @ L2 )
% 5.52/5.89 @ ( produc6916734918728496179nteger
% 5.52/5.89 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S6 ) ) )
% 5.52/5.89 @ ( code_divmod_abs @ K2 @ L2 ) ) )
% 5.52/5.89 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 5.52/5.89 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.52/5.89 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K2 @ L2 )
% 5.52/5.89 @ ( produc6916734918728496179nteger
% 5.52/5.89 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S6 ) ) )
% 5.52/5.89 @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % divmod_integer_code
% 5.52/5.89 thf(fact_9446_pred__def,axiom,
% 5.52/5.89 ( pred
% 5.52/5.89 = ( case_nat_nat @ zero_zero_nat
% 5.52/5.89 @ ^ [X24: nat] : X24 ) ) ).
% 5.52/5.89
% 5.52/5.89 % pred_def
% 5.52/5.89 thf(fact_9447_floor__real__def,axiom,
% 5.52/5.89 ( archim6058952711729229775r_real
% 5.52/5.89 = ( ^ [X: real] :
% 5.52/5.89 ( the_int
% 5.52/5.89 @ ^ [Z2: int] :
% 5.52/5.89 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X )
% 5.52/5.89 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % floor_real_def
% 5.52/5.89 thf(fact_9448_floor__rat__def,axiom,
% 5.52/5.89 ( archim3151403230148437115or_rat
% 5.52/5.89 = ( ^ [X: rat] :
% 5.52/5.89 ( the_int
% 5.52/5.89 @ ^ [Z2: int] :
% 5.52/5.89 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X )
% 5.52/5.89 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % floor_rat_def
% 5.52/5.89 thf(fact_9449_drop__bit__numeral__minus__bit1,axiom,
% 5.52/5.89 ! [L: num,K: num] :
% 5.52/5.89 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.52/5.89 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % drop_bit_numeral_minus_bit1
% 5.52/5.89 thf(fact_9450_drop__bit__nonnegative__int__iff,axiom,
% 5.52/5.89 ! [N: nat,K: int] :
% 5.52/5.89 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 5.52/5.89 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.52/5.89
% 5.52/5.89 % drop_bit_nonnegative_int_iff
% 5.52/5.89 thf(fact_9451_drop__bit__negative__int__iff,axiom,
% 5.52/5.89 ! [N: nat,K: int] :
% 5.52/5.89 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 5.52/5.89 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.52/5.89
% 5.52/5.89 % drop_bit_negative_int_iff
% 5.52/5.89 thf(fact_9452_drop__bit__minus__one,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.52/5.89 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.52/5.89
% 5.52/5.89 % drop_bit_minus_one
% 5.52/5.89 thf(fact_9453_drop__bit__Suc__minus__bit0,axiom,
% 5.52/5.89 ! [N: nat,K: num] :
% 5.52/5.89 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.52/5.89 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % drop_bit_Suc_minus_bit0
% 5.52/5.89 thf(fact_9454_drop__bit__numeral__minus__bit0,axiom,
% 5.52/5.89 ! [L: num,K: num] :
% 5.52/5.89 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.52/5.89 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % drop_bit_numeral_minus_bit0
% 5.52/5.89 thf(fact_9455_drop__bit__Suc__minus__bit1,axiom,
% 5.52/5.89 ! [N: nat,K: num] :
% 5.52/5.89 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.52/5.89 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % drop_bit_Suc_minus_bit1
% 5.52/5.89 thf(fact_9456_sgn__rat__def,axiom,
% 5.52/5.89 ( sgn_sgn_rat
% 5.52/5.89 = ( ^ [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 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sgn_rat_def
% 5.52/5.89 thf(fact_9457_less__eq__rat__def,axiom,
% 5.52/5.89 ( ord_less_eq_rat
% 5.52/5.89 = ( ^ [X: rat,Y: rat] :
% 5.52/5.89 ( ( ord_less_rat @ X @ Y )
% 5.52/5.89 | ( X = Y ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % less_eq_rat_def
% 5.52/5.89 thf(fact_9458_obtain__pos__sum,axiom,
% 5.52/5.89 ! [R: rat] :
% 5.52/5.89 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.52/5.89 => ~ ! [S2: rat] :
% 5.52/5.89 ( ( ord_less_rat @ zero_zero_rat @ S2 )
% 5.52/5.89 => ! [T4: rat] :
% 5.52/5.89 ( ( ord_less_rat @ zero_zero_rat @ T4 )
% 5.52/5.89 => ( R
% 5.52/5.89 != ( plus_plus_rat @ S2 @ T4 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % obtain_pos_sum
% 5.52/5.89 thf(fact_9459_abs__rat__def,axiom,
% 5.52/5.89 ( abs_abs_rat
% 5.52/5.89 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % abs_rat_def
% 5.52/5.89 thf(fact_9460_drop__bit__push__bit__int,axiom,
% 5.52/5.89 ! [M: nat,N: nat,K: int] :
% 5.52/5.89 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.52/5.89 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % drop_bit_push_bit_int
% 5.52/5.89 thf(fact_9461_drop__bit__int__def,axiom,
% 5.52/5.89 ( bit_se8568078237143864401it_int
% 5.52/5.89 = ( ^ [N3: nat,K2: int] : ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % drop_bit_int_def
% 5.52/5.89 thf(fact_9462_normalize__negative,axiom,
% 5.52/5.89 ! [Q2: int,P6: int] :
% 5.52/5.89 ( ( ord_less_int @ Q2 @ zero_zero_int )
% 5.52/5.89 => ( ( normalize @ ( product_Pair_int_int @ P6 @ Q2 ) )
% 5.52/5.89 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P6 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % normalize_negative
% 5.52/5.89 thf(fact_9463_prod__decode__aux_Osimps,axiom,
% 5.52/5.89 ( nat_prod_decode_aux
% 5.52/5.89 = ( ^ [K2: nat,M3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M3 @ K2 ) @ ( product_Pair_nat_nat @ M3 @ ( minus_minus_nat @ K2 @ M3 ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M3 @ ( suc @ K2 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % prod_decode_aux.simps
% 5.52/5.89 thf(fact_9464_prod__decode__aux_Oelims,axiom,
% 5.52/5.89 ! [X2: nat,Xa2: nat,Y2: product_prod_nat_nat] :
% 5.52/5.89 ( ( ( nat_prod_decode_aux @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X2 @ Xa2 ) ) ) )
% 5.52/5.89 & ( ~ ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X2 ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % prod_decode_aux.elims
% 5.52/5.89 thf(fact_9465_drop__bit__of__Suc__0,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.52/5.89 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % drop_bit_of_Suc_0
% 5.52/5.89 thf(fact_9466_drop__bit__nat__eq,axiom,
% 5.52/5.89 ! [N: nat,K: int] :
% 5.52/5.89 ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 5.52/5.89 = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % drop_bit_nat_eq
% 5.52/5.89 thf(fact_9467_normalize__denom__pos,axiom,
% 5.52/5.89 ! [R: product_prod_int_int,P6: int,Q2: int] :
% 5.52/5.89 ( ( ( normalize @ R )
% 5.52/5.89 = ( product_Pair_int_int @ P6 @ Q2 ) )
% 5.52/5.89 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % normalize_denom_pos
% 5.52/5.89 thf(fact_9468_drop__bit__nat__def,axiom,
% 5.52/5.89 ( bit_se8570568707652914677it_nat
% 5.52/5.89 = ( ^ [N3: nat,M3: nat] : ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % drop_bit_nat_def
% 5.52/5.89 thf(fact_9469_Suc__0__mod__numeral,axiom,
% 5.52/5.89 ! [K: num] :
% 5.52/5.89 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.52/5.89 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Suc_0_mod_numeral
% 5.52/5.89 thf(fact_9470_Suc__0__div__numeral,axiom,
% 5.52/5.89 ! [K: num] :
% 5.52/5.89 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.52/5.89 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Suc_0_div_numeral
% 5.52/5.89 thf(fact_9471_finite__enumerate,axiom,
% 5.52/5.89 ! [S3: set_nat] :
% 5.52/5.89 ( ( finite_finite_nat @ S3 )
% 5.52/5.89 => ? [R3: nat > nat] :
% 5.52/5.89 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S3 ) ) )
% 5.52/5.89 & ! [N7: nat] :
% 5.52/5.89 ( ( ord_less_nat @ N7 @ ( finite_card_nat @ S3 ) )
% 5.52/5.89 => ( member_nat @ ( R3 @ N7 ) @ S3 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % finite_enumerate
% 5.52/5.89 thf(fact_9472_fst__divmod__nat,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.52/5.89 = ( divide_divide_nat @ M @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % fst_divmod_nat
% 5.52/5.89 thf(fact_9473_snd__divmod__nat,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.52/5.89 = ( modulo_modulo_nat @ M @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % snd_divmod_nat
% 5.52/5.89 thf(fact_9474_minus__one__mod__numeral,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.89 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % minus_one_mod_numeral
% 5.52/5.89 thf(fact_9475_one__mod__minus__numeral,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.89 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % one_mod_minus_numeral
% 5.52/5.89 thf(fact_9476_numeral__mod__minus__numeral,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.89 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % numeral_mod_minus_numeral
% 5.52/5.89 thf(fact_9477_minus__numeral__mod__numeral,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.89 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % minus_numeral_mod_numeral
% 5.52/5.89 thf(fact_9478_Divides_Oadjust__mod__def,axiom,
% 5.52/5.89 ( adjust_mod
% 5.52/5.89 = ( ^ [L2: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R5 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Divides.adjust_mod_def
% 5.52/5.89 thf(fact_9479_bezw_Osimps,axiom,
% 5.52/5.89 ( bezw
% 5.52/5.89 = ( ^ [X: nat,Y: nat] : ( if_Pro3027730157355071871nt_int @ ( Y = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bezw.simps
% 5.52/5.89 thf(fact_9480_bezw_Oelims,axiom,
% 5.52/5.89 ! [X2: nat,Xa2: nat,Y2: product_prod_int_int] :
% 5.52/5.89 ( ( ( bezw @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.52/5.89 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bezw.elims
% 5.52/5.89 thf(fact_9481_bezw__non__0,axiom,
% 5.52/5.89 ! [Y2: nat,X2: nat] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ Y2 )
% 5.52/5.89 => ( ( bezw @ X2 @ Y2 )
% 5.52/5.89 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bezw_non_0
% 5.52/5.89 thf(fact_9482_bezw_Opelims,axiom,
% 5.52/5.89 ! [X2: nat,Xa2: nat,Y2: product_prod_int_int] :
% 5.52/5.89 ( ( ( bezw @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.52/5.89 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.52/5.89 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa2 ) ) ) ) ) ) ) )
% 5.52/5.89 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bezw.pelims
% 5.52/5.89 thf(fact_9483_normalize__def,axiom,
% 5.52/5.89 ( normalize
% 5.52/5.89 = ( ^ [P4: product_prod_int_int] :
% 5.52/5.89 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P4 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P4 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P4 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) )
% 5.52/5.89 @ ( if_Pro3027730157355071871nt_int
% 5.52/5.89 @ ( ( product_snd_int_int @ P4 )
% 5.52/5.89 = zero_zero_int )
% 5.52/5.89 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.52/5.89 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P4 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P4 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % normalize_def
% 5.52/5.89 thf(fact_9484_gcd__pos__int,axiom,
% 5.52/5.89 ! [M: int,N: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 5.52/5.89 = ( ( M != zero_zero_int )
% 5.52/5.89 | ( N != zero_zero_int ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_pos_int
% 5.52/5.89 thf(fact_9485_gcd__neg__numeral__1__int,axiom,
% 5.52/5.89 ! [N: num,X2: int] :
% 5.52/5.89 ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X2 )
% 5.52/5.89 = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_neg_numeral_1_int
% 5.52/5.89 thf(fact_9486_gcd__neg__numeral__2__int,axiom,
% 5.52/5.89 ! [X2: int,N: num] :
% 5.52/5.89 ( ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.89 = ( gcd_gcd_int @ X2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_neg_numeral_2_int
% 5.52/5.89 thf(fact_9487_gcd__le1__int,axiom,
% 5.52/5.89 ! [A: int,B: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ A )
% 5.52/5.89 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_le1_int
% 5.52/5.89 thf(fact_9488_gcd__le2__int,axiom,
% 5.52/5.89 ! [B: int,A: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.89 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_le2_int
% 5.52/5.89 thf(fact_9489_gcd__non__0__int,axiom,
% 5.52/5.89 ! [Y2: int,X2: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ Y2 )
% 5.52/5.89 => ( ( gcd_gcd_int @ X2 @ Y2 )
% 5.52/5.89 = ( gcd_gcd_int @ Y2 @ ( modulo_modulo_int @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_non_0_int
% 5.52/5.89 thf(fact_9490_prod__decode__aux_Opelims,axiom,
% 5.52/5.89 ! [X2: nat,Xa2: nat,Y2: product_prod_nat_nat] :
% 5.52/5.89 ( ( ( nat_prod_decode_aux @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.52/5.89 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X2 @ Xa2 ) ) ) )
% 5.52/5.89 & ( ~ ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X2 ) ) ) ) ) )
% 5.52/5.89 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % prod_decode_aux.pelims
% 5.52/5.89 thf(fact_9491_gcd__1__nat,axiom,
% 5.52/5.89 ! [M: nat] :
% 5.52/5.89 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 5.52/5.89 = one_one_nat ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_1_nat
% 5.52/5.89 thf(fact_9492_gcd__pos__nat,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 5.52/5.89 = ( ( M != zero_zero_nat )
% 5.52/5.89 | ( N != zero_zero_nat ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_pos_nat
% 5.52/5.89 thf(fact_9493_gcd__mult__distrib__nat,axiom,
% 5.52/5.89 ! [K: nat,M: nat,N: nat] :
% 5.52/5.89 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 5.52/5.89 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_mult_distrib_nat
% 5.52/5.89 thf(fact_9494_gcd__le1__nat,axiom,
% 5.52/5.89 ! [A: nat,B: nat] :
% 5.52/5.89 ( ( A != zero_zero_nat )
% 5.52/5.89 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_le1_nat
% 5.52/5.89 thf(fact_9495_gcd__le2__nat,axiom,
% 5.52/5.89 ! [B: nat,A: nat] :
% 5.52/5.89 ( ( B != zero_zero_nat )
% 5.52/5.89 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_le2_nat
% 5.52/5.89 thf(fact_9496_gcd__diff2__nat,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.89 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 5.52/5.89 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_diff2_nat
% 5.52/5.89 thf(fact_9497_gcd__diff1__nat,axiom,
% 5.52/5.89 ! [N: nat,M: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ N @ M )
% 5.52/5.89 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 5.52/5.89 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_diff1_nat
% 5.52/5.89 thf(fact_9498_bezout__nat,axiom,
% 5.52/5.89 ! [A: nat,B: nat] :
% 5.52/5.89 ( ( A != zero_zero_nat )
% 5.52/5.89 => ? [X4: nat,Y3: nat] :
% 5.52/5.89 ( ( times_times_nat @ A @ X4 )
% 5.52/5.89 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bezout_nat
% 5.52/5.89 thf(fact_9499_bezout__gcd__nat_H,axiom,
% 5.52/5.89 ! [B: nat,A: nat] :
% 5.52/5.89 ? [X4: nat,Y3: nat] :
% 5.52/5.89 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X4 ) )
% 5.52/5.89 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.52/5.89 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.52/5.89 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X4 ) )
% 5.52/5.89 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.52/5.89 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % bezout_gcd_nat'
% 5.52/5.89 thf(fact_9500_gcd__is__Max__divisors__nat,axiom,
% 5.52/5.89 ! [N: nat,M: nat] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( gcd_gcd_nat @ M @ N )
% 5.52/5.89 = ( lattic8265883725875713057ax_nat
% 5.52/5.89 @ ( collect_nat
% 5.52/5.89 @ ^ [D: nat] :
% 5.52/5.89 ( ( dvd_dvd_nat @ D @ M )
% 5.52/5.89 & ( dvd_dvd_nat @ D @ N ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_is_Max_divisors_nat
% 5.52/5.89 thf(fact_9501_nat__descend__induct,axiom,
% 5.52/5.89 ! [N: nat,P: nat > $o,M: nat] :
% 5.52/5.89 ( ! [K3: nat] :
% 5.52/5.89 ( ( ord_less_nat @ N @ K3 )
% 5.52/5.89 => ( P @ K3 ) )
% 5.52/5.89 => ( ! [K3: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ K3 @ N )
% 5.52/5.89 => ( ! [I3: nat] :
% 5.52/5.89 ( ( ord_less_nat @ K3 @ I3 )
% 5.52/5.89 => ( P @ I3 ) )
% 5.52/5.89 => ( P @ K3 ) ) )
% 5.52/5.89 => ( P @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_descend_induct
% 5.52/5.89 thf(fact_9502_gcd__nat_Opelims,axiom,
% 5.52/5.89 ! [X2: nat,Xa2: nat,Y2: nat] :
% 5.52/5.89 ( ( ( gcd_gcd_nat @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.52/5.89 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.52/5.89 => ( Y2 = X2 ) )
% 5.52/5.89 & ( ( Xa2 != zero_zero_nat )
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) ) )
% 5.52/5.89 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % gcd_nat.pelims
% 5.52/5.89 thf(fact_9503_quotient__of__number_I5_J,axiom,
% 5.52/5.89 ! [K: num] :
% 5.52/5.89 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.52/5.89 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.52/5.89
% 5.52/5.89 % quotient_of_number(5)
% 5.52/5.89 thf(fact_9504_xor__minus__numerals_I2_J,axiom,
% 5.52/5.89 ! [K: int,N: num] :
% 5.52/5.89 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.89 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_minus_numerals(2)
% 5.52/5.89 thf(fact_9505_quotient__of__number_I3_J,axiom,
% 5.52/5.89 ! [K: num] :
% 5.52/5.89 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.52/5.89 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.52/5.89
% 5.52/5.89 % quotient_of_number(3)
% 5.52/5.89 thf(fact_9506_xor__minus__numerals_I1_J,axiom,
% 5.52/5.89 ! [N: num,K: int] :
% 5.52/5.89 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 5.52/5.89 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_minus_numerals(1)
% 5.52/5.89 thf(fact_9507_quotient__of__denom__pos,axiom,
% 5.52/5.89 ! [R: rat,P6: int,Q2: int] :
% 5.52/5.89 ( ( ( quotient_of @ R )
% 5.52/5.89 = ( product_Pair_int_int @ P6 @ Q2 ) )
% 5.52/5.89 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % quotient_of_denom_pos
% 5.52/5.89 thf(fact_9508_quotient__of__denom__pos_H,axiom,
% 5.52/5.89 ! [R: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % quotient_of_denom_pos'
% 5.52/5.89 thf(fact_9509_sub__BitM__One__eq,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 5.52/5.89 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sub_BitM_One_eq
% 5.52/5.89 thf(fact_9510_rat__less__code,axiom,
% 5.52/5.89 ( ord_less_rat
% 5.52/5.89 = ( ^ [P4: rat,Q4: rat] :
% 5.52/5.89 ( produc4947309494688390418_int_o
% 5.52/5.89 @ ^ [A4: int,C3: int] :
% 5.52/5.89 ( produc4947309494688390418_int_o
% 5.52/5.89 @ ^ [B3: int,D: int] : ( ord_less_int @ ( times_times_int @ A4 @ D ) @ ( times_times_int @ C3 @ B3 ) )
% 5.52/5.89 @ ( quotient_of @ Q4 ) )
% 5.52/5.89 @ ( quotient_of @ P4 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % rat_less_code
% 5.52/5.89 thf(fact_9511_rat__floor__code,axiom,
% 5.52/5.89 ( archim3151403230148437115or_rat
% 5.52/5.89 = ( ^ [P4: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P4 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % rat_floor_code
% 5.52/5.89 thf(fact_9512_Frct__code__post_I5_J,axiom,
% 5.52/5.89 ! [K: num] :
% 5.52/5.89 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.52/5.89 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Frct_code_post(5)
% 5.52/5.89 thf(fact_9513_Frct__code__post_I4_J,axiom,
% 5.52/5.89 ! [K: num] :
% 5.52/5.89 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.52/5.89 = ( numeral_numeral_rat @ K ) ) ).
% 5.52/5.89
% 5.52/5.89 % Frct_code_post(4)
% 5.52/5.89 thf(fact_9514_Frct__code__post_I6_J,axiom,
% 5.52/5.89 ! [K: num,L: num] :
% 5.52/5.89 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 5.52/5.89 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Frct_code_post(6)
% 5.52/5.89 thf(fact_9515_Suc__funpow,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( compow_nat_nat @ N @ suc )
% 5.52/5.89 = ( plus_plus_nat @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % Suc_funpow
% 5.52/5.89 thf(fact_9516_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.52/5.89 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.52/5.89 @ ^ [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X )
% 5.52/5.89 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X ) ) ).
% 5.52/5.89
% 5.52/5.89 % max_nat.semilattice_neutr_order_axioms
% 5.52/5.89 thf(fact_9517_times__int_Oabs__eq,axiom,
% 5.52/5.89 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.52/5.89 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.52/5.89 = ( abs_Integ
% 5.52/5.89 @ ( produc27273713700761075at_nat
% 5.52/5.89 @ ^ [X: nat,Y: nat] :
% 5.52/5.89 ( produc2626176000494625587at_nat
% 5.52/5.89 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) )
% 5.52/5.89 @ Xa2
% 5.52/5.89 @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % times_int.abs_eq
% 5.52/5.89 thf(fact_9518_eq__Abs__Integ,axiom,
% 5.52/5.89 ! [Z: int] :
% 5.52/5.89 ~ ! [X4: nat,Y3: nat] :
% 5.52/5.89 ( Z
% 5.52/5.89 != ( abs_Integ @ ( product_Pair_nat_nat @ X4 @ Y3 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % eq_Abs_Integ
% 5.52/5.89 thf(fact_9519_zero__int__def,axiom,
% 5.52/5.89 ( zero_zero_int
% 5.52/5.89 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % zero_int_def
% 5.52/5.89 thf(fact_9520_int__def,axiom,
% 5.52/5.89 ( semiri1314217659103216013at_int
% 5.52/5.89 = ( ^ [N3: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N3 @ zero_zero_nat ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % int_def
% 5.52/5.89 thf(fact_9521_uminus__int_Oabs__eq,axiom,
% 5.52/5.89 ! [X2: product_prod_nat_nat] :
% 5.52/5.89 ( ( uminus_uminus_int @ ( abs_Integ @ X2 ) )
% 5.52/5.89 = ( abs_Integ
% 5.52/5.89 @ ( produc2626176000494625587at_nat
% 5.52/5.89 @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X )
% 5.52/5.89 @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % uminus_int.abs_eq
% 5.52/5.89 thf(fact_9522_one__int__def,axiom,
% 5.52/5.89 ( one_one_int
% 5.52/5.89 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % one_int_def
% 5.52/5.89 thf(fact_9523_less__int_Oabs__eq,axiom,
% 5.52/5.89 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.52/5.89 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.52/5.89 = ( produc8739625826339149834_nat_o
% 5.52/5.89 @ ^ [X: nat,Y: nat] :
% 5.52/5.89 ( produc6081775807080527818_nat_o
% 5.52/5.89 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 5.52/5.89 @ Xa2
% 5.52/5.89 @ X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % less_int.abs_eq
% 5.52/5.89 thf(fact_9524_less__eq__int_Oabs__eq,axiom,
% 5.52/5.89 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.52/5.89 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.52/5.89 = ( produc8739625826339149834_nat_o
% 5.52/5.89 @ ^ [X: nat,Y: nat] :
% 5.52/5.89 ( produc6081775807080527818_nat_o
% 5.52/5.89 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 5.52/5.89 @ Xa2
% 5.52/5.89 @ X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % less_eq_int.abs_eq
% 5.52/5.89 thf(fact_9525_plus__int_Oabs__eq,axiom,
% 5.52/5.89 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.52/5.89 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.52/5.89 = ( abs_Integ
% 5.52/5.89 @ ( produc27273713700761075at_nat
% 5.52/5.89 @ ^ [X: nat,Y: nat] :
% 5.52/5.89 ( produc2626176000494625587at_nat
% 5.52/5.89 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) )
% 5.52/5.89 @ Xa2
% 5.52/5.89 @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % plus_int.abs_eq
% 5.52/5.89 thf(fact_9526_minus__int_Oabs__eq,axiom,
% 5.52/5.89 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.52/5.89 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.52/5.89 = ( abs_Integ
% 5.52/5.89 @ ( produc27273713700761075at_nat
% 5.52/5.89 @ ^ [X: nat,Y: nat] :
% 5.52/5.89 ( produc2626176000494625587at_nat
% 5.52/5.89 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) )
% 5.52/5.89 @ Xa2
% 5.52/5.89 @ X2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % minus_int.abs_eq
% 5.52/5.89 thf(fact_9527_num__of__nat_Osimps_I2_J,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( num_of_nat @ ( suc @ N ) )
% 5.52/5.89 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.52/5.89 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( num_of_nat @ ( suc @ N ) )
% 5.52/5.89 = one ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % num_of_nat.simps(2)
% 5.52/5.89 thf(fact_9528_pow_Osimps_I3_J,axiom,
% 5.52/5.89 ! [X2: num,Y2: num] :
% 5.52/5.89 ( ( pow @ X2 @ ( bit1 @ Y2 ) )
% 5.52/5.89 = ( times_times_num @ ( sqr @ ( pow @ X2 @ Y2 ) ) @ X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % pow.simps(3)
% 5.52/5.89 thf(fact_9529_num__of__nat__numeral__eq,axiom,
% 5.52/5.89 ! [Q2: num] :
% 5.52/5.89 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.52/5.89 = Q2 ) ).
% 5.52/5.89
% 5.52/5.89 % num_of_nat_numeral_eq
% 5.52/5.89 thf(fact_9530_sqr_Osimps_I2_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( sqr @ ( bit0 @ N ) )
% 5.52/5.89 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sqr.simps(2)
% 5.52/5.89 thf(fact_9531_sqr_Osimps_I1_J,axiom,
% 5.52/5.89 ( ( sqr @ one )
% 5.52/5.89 = one ) ).
% 5.52/5.89
% 5.52/5.89 % sqr.simps(1)
% 5.52/5.89 thf(fact_9532_sqr__conv__mult,axiom,
% 5.52/5.89 ( sqr
% 5.52/5.89 = ( ^ [X: num] : ( times_times_num @ X @ X ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sqr_conv_mult
% 5.52/5.89 thf(fact_9533_num__of__nat_Osimps_I1_J,axiom,
% 5.52/5.89 ( ( num_of_nat @ zero_zero_nat )
% 5.52/5.89 = one ) ).
% 5.52/5.89
% 5.52/5.89 % num_of_nat.simps(1)
% 5.52/5.89 thf(fact_9534_numeral__num__of__nat,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.52/5.89 = N ) ) ).
% 5.52/5.89
% 5.52/5.89 % numeral_num_of_nat
% 5.52/5.89 thf(fact_9535_num__of__nat__One,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.52/5.89 => ( ( num_of_nat @ N )
% 5.52/5.89 = one ) ) ).
% 5.52/5.89
% 5.52/5.89 % num_of_nat_One
% 5.52/5.89 thf(fact_9536_pow_Osimps_I2_J,axiom,
% 5.52/5.89 ! [X2: num,Y2: num] :
% 5.52/5.89 ( ( pow @ X2 @ ( bit0 @ Y2 ) )
% 5.52/5.89 = ( sqr @ ( pow @ X2 @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % pow.simps(2)
% 5.52/5.89 thf(fact_9537_num__of__nat__double,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.52/5.89 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % num_of_nat_double
% 5.52/5.89 thf(fact_9538_num__of__nat__plus__distrib,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 5.52/5.89 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % num_of_nat_plus_distrib
% 5.52/5.89 thf(fact_9539_sqr_Osimps_I3_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( sqr @ ( bit1 @ N ) )
% 5.52/5.89 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % sqr.simps(3)
% 5.52/5.89 thf(fact_9540_less__eq__int_Orep__eq,axiom,
% 5.52/5.89 ( ord_less_eq_int
% 5.52/5.89 = ( ^ [X: int,Xa4: int] :
% 5.52/5.89 ( produc8739625826339149834_nat_o
% 5.52/5.89 @ ^ [Y: nat,Z2: nat] :
% 5.52/5.89 ( produc6081775807080527818_nat_o
% 5.52/5.89 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z2 ) ) )
% 5.52/5.89 @ ( rep_Integ @ X )
% 5.52/5.89 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % less_eq_int.rep_eq
% 5.52/5.89 thf(fact_9541_less__int_Orep__eq,axiom,
% 5.52/5.89 ( ord_less_int
% 5.52/5.89 = ( ^ [X: int,Xa4: int] :
% 5.52/5.89 ( produc8739625826339149834_nat_o
% 5.52/5.89 @ ^ [Y: nat,Z2: nat] :
% 5.52/5.89 ( produc6081775807080527818_nat_o
% 5.52/5.89 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z2 ) ) )
% 5.52/5.89 @ ( rep_Integ @ X )
% 5.52/5.89 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % less_int.rep_eq
% 5.52/5.89 thf(fact_9542_uminus__int__def,axiom,
% 5.52/5.89 ( uminus_uminus_int
% 5.52/5.89 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.52/5.89 @ ( produc2626176000494625587at_nat
% 5.52/5.89 @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % uminus_int_def
% 5.52/5.89 thf(fact_9543_rat__floor__lemma,axiom,
% 5.52/5.89 ! [A: int,B: int] :
% 5.52/5.89 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.52/5.89 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % rat_floor_lemma
% 5.52/5.89 thf(fact_9544_floor__Fract,axiom,
% 5.52/5.89 ! [A: int,B: int] :
% 5.52/5.89 ( ( archim3151403230148437115or_rat @ ( fract @ A @ B ) )
% 5.52/5.89 = ( divide_divide_int @ A @ B ) ) ).
% 5.52/5.89
% 5.52/5.89 % floor_Fract
% 5.52/5.89 thf(fact_9545_less__rat,axiom,
% 5.52/5.89 ! [B: int,D2: int,A: int,C: int] :
% 5.52/5.89 ( ( B != zero_zero_int )
% 5.52/5.89 => ( ( D2 != zero_zero_int )
% 5.52/5.89 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D2 ) )
% 5.52/5.89 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ D2 ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % less_rat
% 5.52/5.89 thf(fact_9546_Rat__induct__pos,axiom,
% 5.52/5.89 ! [P: rat > $o,Q2: rat] :
% 5.52/5.89 ( ! [A3: int,B2: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.52/5.89 => ( P @ ( fract @ A3 @ B2 ) ) )
% 5.52/5.89 => ( P @ Q2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % Rat_induct_pos
% 5.52/5.89 thf(fact_9547_Fract__coprime,axiom,
% 5.52/5.89 ! [A: int,B: int] :
% 5.52/5.89 ( ( fract @ ( divide_divide_int @ A @ ( gcd_gcd_int @ A @ B ) ) @ ( divide_divide_int @ B @ ( gcd_gcd_int @ A @ B ) ) )
% 5.52/5.89 = ( fract @ A @ B ) ) ).
% 5.52/5.89
% 5.52/5.89 % Fract_coprime
% 5.52/5.89 thf(fact_9548_rat__number__collapse_I3_J,axiom,
% 5.52/5.89 ! [W: num] :
% 5.52/5.89 ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 5.52/5.89 = ( numeral_numeral_rat @ W ) ) ).
% 5.52/5.89
% 5.52/5.89 % rat_number_collapse(3)
% 5.52/5.89 thf(fact_9549_rat__number__expand_I3_J,axiom,
% 5.52/5.89 ( numeral_numeral_rat
% 5.52/5.89 = ( ^ [K2: num] : ( fract @ ( numeral_numeral_int @ K2 ) @ one_one_int ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % rat_number_expand(3)
% 5.52/5.89 thf(fact_9550_zero__less__Fract__iff,axiom,
% 5.52/5.89 ! [B: int,A: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.89 => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.52/5.89 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % zero_less_Fract_iff
% 5.52/5.89 thf(fact_9551_Fract__less__zero__iff,axiom,
% 5.52/5.89 ! [B: int,A: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.89 => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.52/5.89 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Fract_less_zero_iff
% 5.52/5.89 thf(fact_9552_Fract__less__one__iff,axiom,
% 5.52/5.89 ! [B: int,A: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.89 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.52/5.89 = ( ord_less_int @ A @ B ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Fract_less_one_iff
% 5.52/5.89 thf(fact_9553_one__less__Fract__iff,axiom,
% 5.52/5.89 ! [B: int,A: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.89 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.52/5.89 = ( ord_less_int @ B @ A ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % one_less_Fract_iff
% 5.52/5.89 thf(fact_9554_Fract__le__zero__iff,axiom,
% 5.52/5.89 ! [B: int,A: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.89 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.52/5.89 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Fract_le_zero_iff
% 5.52/5.89 thf(fact_9555_zero__le__Fract__iff,axiom,
% 5.52/5.89 ! [B: int,A: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.52/5.89 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % zero_le_Fract_iff
% 5.52/5.89 thf(fact_9556_Fract__le__one__iff,axiom,
% 5.52/5.89 ! [B: int,A: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.89 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.52/5.89 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Fract_le_one_iff
% 5.52/5.89 thf(fact_9557_one__le__Fract__iff,axiom,
% 5.52/5.89 ! [B: int,A: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.52/5.89 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.52/5.89 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % one_le_Fract_iff
% 5.52/5.89 thf(fact_9558_rat__number__collapse_I4_J,axiom,
% 5.52/5.89 ! [W: num] :
% 5.52/5.89 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 5.52/5.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % rat_number_collapse(4)
% 5.52/5.89 thf(fact_9559_rat__number__expand_I5_J,axiom,
% 5.52/5.89 ! [K: num] :
% 5.52/5.89 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 5.52/5.89 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.52/5.89
% 5.52/5.89 % rat_number_expand(5)
% 5.52/5.89 thf(fact_9560_times__int__def,axiom,
% 5.52/5.89 ( times_times_int
% 5.52/5.89 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.52/5.89 @ ( produc27273713700761075at_nat
% 5.52/5.89 @ ^ [X: nat,Y: nat] :
% 5.52/5.89 ( produc2626176000494625587at_nat
% 5.52/5.89 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % times_int_def
% 5.52/5.89 thf(fact_9561_minus__int__def,axiom,
% 5.52/5.89 ( minus_minus_int
% 5.52/5.89 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.52/5.89 @ ( produc27273713700761075at_nat
% 5.52/5.89 @ ^ [X: nat,Y: nat] :
% 5.52/5.89 ( produc2626176000494625587at_nat
% 5.52/5.89 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % minus_int_def
% 5.52/5.89 thf(fact_9562_plus__int__def,axiom,
% 5.52/5.89 ( plus_plus_int
% 5.52/5.89 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.52/5.89 @ ( produc27273713700761075at_nat
% 5.52/5.89 @ ^ [X: nat,Y: nat] :
% 5.52/5.89 ( produc2626176000494625587at_nat
% 5.52/5.89 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % plus_int_def
% 5.52/5.89 thf(fact_9563_take__bit__numeral__minus__numeral__int,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.89 = ( case_option_int_num @ zero_zero_int
% 5.52/5.89 @ ^ [Q4: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q4 ) ) )
% 5.52/5.89 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % take_bit_numeral_minus_numeral_int
% 5.52/5.89 thf(fact_9564_positive__rat,axiom,
% 5.52/5.89 ! [A: int,B: int] :
% 5.52/5.89 ( ( positive @ ( fract @ A @ B ) )
% 5.52/5.89 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % positive_rat
% 5.52/5.89 thf(fact_9565_take__bit__num__simps_I1_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.52/5.89 = none_num ) ).
% 5.52/5.89
% 5.52/5.89 % take_bit_num_simps(1)
% 5.52/5.89 thf(fact_9566_take__bit__num__simps_I2_J,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 5.52/5.89 = ( some_num @ one ) ) ).
% 5.52/5.89
% 5.52/5.89 % take_bit_num_simps(2)
% 5.52/5.89 thf(fact_9567_take__bit__num__simps_I5_J,axiom,
% 5.52/5.89 ! [R: num] :
% 5.52/5.89 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ one )
% 5.52/5.89 = ( some_num @ one ) ) ).
% 5.52/5.89
% 5.52/5.89 % take_bit_num_simps(5)
% 5.52/5.89 thf(fact_9568_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( bit_take_bit_num @ N @ one )
% 5.52/5.89 = ( case_nat_option_num @ none_num
% 5.52/5.89 @ ^ [N3: nat] : ( some_num @ one )
% 5.52/5.89 @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.52/5.89 thf(fact_9569_less__rat__def,axiom,
% 5.52/5.89 ( ord_less_rat
% 5.52/5.89 = ( ^ [X: rat,Y: rat] : ( positive @ ( minus_minus_rat @ Y @ X ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % less_rat_def
% 5.52/5.89 thf(fact_9570_take__bit__num__def,axiom,
% 5.52/5.89 ( bit_take_bit_num
% 5.52/5.89 = ( ^ [N3: nat,M3: num] :
% 5.52/5.89 ( if_option_num
% 5.52/5.89 @ ( ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M3 ) )
% 5.52/5.89 = zero_zero_nat )
% 5.52/5.89 @ none_num
% 5.52/5.89 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M3 ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % take_bit_num_def
% 5.52/5.89 thf(fact_9571_and__minus__numerals_I3_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.52/5.89 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_minus_numerals(3)
% 5.52/5.89 thf(fact_9572_and__minus__numerals_I7_J,axiom,
% 5.52/5.89 ! [N: num,M: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.52/5.89 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_minus_numerals(7)
% 5.52/5.89 thf(fact_9573_and__minus__numerals_I4_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.52/5.89 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_minus_numerals(4)
% 5.52/5.89 thf(fact_9574_take__bit__num__simps_I4_J,axiom,
% 5.52/5.89 ! [N: nat,M: num] :
% 5.52/5.89 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 5.52/5.89 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % take_bit_num_simps(4)
% 5.52/5.89 thf(fact_9575_take__bit__num__simps_I3_J,axiom,
% 5.52/5.89 ! [N: nat,M: num] :
% 5.52/5.89 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 5.52/5.89 = ( case_o6005452278849405969um_num @ none_num
% 5.52/5.89 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.52/5.89 @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % take_bit_num_simps(3)
% 5.52/5.89 thf(fact_9576_take__bit__num__simps_I7_J,axiom,
% 5.52/5.89 ! [R: num,M: num] :
% 5.52/5.89 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit1 @ M ) )
% 5.52/5.89 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % take_bit_num_simps(7)
% 5.52/5.89 thf(fact_9577_take__bit__num__simps_I6_J,axiom,
% 5.52/5.89 ! [R: num,M: num] :
% 5.52/5.89 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit0 @ M ) )
% 5.52/5.89 = ( case_o6005452278849405969um_num @ none_num
% 5.52/5.89 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.52/5.89 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % take_bit_num_simps(6)
% 5.52/5.89 thf(fact_9578_and__minus__numerals_I8_J,axiom,
% 5.52/5.89 ! [N: num,M: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.52/5.89 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_minus_numerals(8)
% 5.52/5.89 thf(fact_9579_and__not__num_Osimps_I8_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.52/5.89 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.52/5.89 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.52/5.89 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num.simps(8)
% 5.52/5.89 thf(fact_9580_and__not__num_Osimps_I1_J,axiom,
% 5.52/5.89 ( ( bit_and_not_num @ one @ one )
% 5.52/5.89 = none_num ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num.simps(1)
% 5.52/5.89 thf(fact_9581_and__not__num_Osimps_I4_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.52/5.89 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num.simps(4)
% 5.52/5.89 thf(fact_9582_and__not__num_Osimps_I2_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 5.52/5.89 = ( some_num @ one ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num.simps(2)
% 5.52/5.89 thf(fact_9583_and__not__num_Osimps_I3_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 5.52/5.89 = none_num ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num.simps(3)
% 5.52/5.89 thf(fact_9584_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.52/5.89 ! [N: nat,M: num] :
% 5.52/5.89 ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 5.52/5.89 = ( case_nat_option_num @ none_num
% 5.52/5.89 @ ^ [N3: nat] :
% 5.52/5.89 ( case_o6005452278849405969um_num @ none_num
% 5.52/5.89 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.52/5.89 @ ( bit_take_bit_num @ N3 @ M ) )
% 5.52/5.89 @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.52/5.89 thf(fact_9585_and__not__num_Osimps_I7_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.52/5.89 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num.simps(7)
% 5.52/5.89 thf(fact_9586_and__not__num__eq__Some__iff,axiom,
% 5.52/5.89 ! [M: num,N: num,Q2: num] :
% 5.52/5.89 ( ( ( bit_and_not_num @ M @ N )
% 5.52/5.89 = ( some_num @ Q2 ) )
% 5.52/5.89 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.89 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num_eq_Some_iff
% 5.52/5.89 thf(fact_9587_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.52/5.89 ! [N: nat,M: num] :
% 5.52/5.89 ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 5.52/5.89 = ( case_nat_option_num @ none_num
% 5.52/5.89 @ ^ [N3: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N3 @ M ) ) )
% 5.52/5.89 @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.52/5.89 thf(fact_9588_and__not__num__eq__None__iff,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( ( bit_and_not_num @ M @ N )
% 5.52/5.89 = none_num )
% 5.52/5.89 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.89 = zero_zero_int ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num_eq_None_iff
% 5.52/5.89 thf(fact_9589_int__numeral__and__not__num,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.89 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % int_numeral_and_not_num
% 5.52/5.89 thf(fact_9590_int__numeral__not__and__num,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.89 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % int_numeral_not_and_num
% 5.52/5.89 thf(fact_9591_Bit__Operations_Otake__bit__num__code,axiom,
% 5.52/5.89 ( bit_take_bit_num
% 5.52/5.89 = ( ^ [N3: nat,M3: num] :
% 5.52/5.89 ( produc478579273971653890on_num
% 5.52/5.89 @ ^ [A4: nat,X: num] :
% 5.52/5.89 ( case_nat_option_num @ none_num
% 5.52/5.89 @ ^ [O: nat] :
% 5.52/5.89 ( case_num_option_num @ ( some_num @ one )
% 5.52/5.89 @ ^ [P4: num] :
% 5.52/5.89 ( case_o6005452278849405969um_num @ none_num
% 5.52/5.89 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.52/5.89 @ ( bit_take_bit_num @ O @ P4 ) )
% 5.52/5.89 @ ^ [P4: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P4 ) ) )
% 5.52/5.89 @ X )
% 5.52/5.89 @ A4 )
% 5.52/5.89 @ ( product_Pair_nat_num @ N3 @ M3 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Bit_Operations.take_bit_num_code
% 5.52/5.89 thf(fact_9592_Rat_Opositive_Orep__eq,axiom,
% 5.52/5.89 ( positive
% 5.52/5.89 = ( ^ [X: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X ) ) @ ( product_snd_int_int @ ( rep_Rat @ X ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Rat.positive.rep_eq
% 5.52/5.89 thf(fact_9593_and__not__num_Oelims,axiom,
% 5.52/5.89 ! [X2: num,Xa2: num,Y2: option_num] :
% 5.52/5.89 ( ( ( bit_and_not_num @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( Y2 != none_num ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ( ? [N2: num] :
% 5.52/5.89 ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( some_num @ one ) ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ( ? [N2: num] :
% 5.52/5.89 ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( Y2 != none_num ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.52/5.89 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.52/5.89 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 5.52/5.89 => ~ ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num.elims
% 5.52/5.89 thf(fact_9594_xor__num_Osimps_I6_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.52/5.89 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_num.simps(6)
% 5.52/5.89 thf(fact_9595_xor__num_Osimps_I8_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.52/5.89 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_num.simps(8)
% 5.52/5.89 thf(fact_9596_xor__num_Osimps_I9_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_num.simps(9)
% 5.52/5.89 thf(fact_9597_xor__num_Osimps_I5_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_num.simps(5)
% 5.52/5.89 thf(fact_9598_and__not__num_Osimps_I5_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num.simps(5)
% 5.52/5.89 thf(fact_9599_and__not__num_Osimps_I6_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num.simps(6)
% 5.52/5.89 thf(fact_9600_and__not__num_Osimps_I9_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num.simps(9)
% 5.52/5.89 thf(fact_9601_xor__num_Osimps_I1_J,axiom,
% 5.52/5.89 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.52/5.89 = none_num ) ).
% 5.52/5.89
% 5.52/5.89 % xor_num.simps(1)
% 5.52/5.89 thf(fact_9602_xor__num_Oelims,axiom,
% 5.52/5.89 ! [X2: num,Xa2: num,Y2: option_num] :
% 5.52/5.89 ( ( ( bit_un2480387367778600638or_num @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( Y2 != none_num ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( some_num @ ( bit1 @ N2 ) ) ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( some_num @ ( bit0 @ N2 ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( some_num @ ( bit1 @ M4 ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ~ ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_num.elims
% 5.52/5.89 thf(fact_9603_xor__num_Osimps_I7_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.52/5.89 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_num.simps(7)
% 5.52/5.89 thf(fact_9604_xor__num_Osimps_I4_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.52/5.89 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_num.simps(4)
% 5.52/5.89 thf(fact_9605_xor__num_Osimps_I3_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 5.52/5.89 = ( some_num @ ( bit0 @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_num.simps(3)
% 5.52/5.89 thf(fact_9606_xor__num_Osimps_I2_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 5.52/5.89 = ( some_num @ ( bit1 @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_num.simps(2)
% 5.52/5.89 thf(fact_9607_and__num_Oelims,axiom,
% 5.52/5.89 ! [X2: num,Xa2: num,Y2: option_num] :
% 5.52/5.89 ( ( ( bit_un7362597486090784418nd_num @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( some_num @ one ) ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ( ? [N2: num] :
% 5.52/5.89 ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( Y2 != none_num ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ( ? [N2: num] :
% 5.52/5.89 ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( some_num @ one ) ) ) )
% 5.52/5.89 => ( ( ? [M4: num] :
% 5.52/5.89 ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( Y2 != none_num ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 5.52/5.89 => ( ( ? [M4: num] :
% 5.52/5.89 ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( some_num @ one ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 5.52/5.89 => ~ ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.52/5.89 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.52/5.89 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_num.elims
% 5.52/5.89 thf(fact_9608_xor__num__dict,axiom,
% 5.52/5.89 bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 5.52/5.89
% 5.52/5.89 % xor_num_dict
% 5.52/5.89 thf(fact_9609_and__num_Osimps_I1_J,axiom,
% 5.52/5.89 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.52/5.89 = ( some_num @ one ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_num.simps(1)
% 5.52/5.89 thf(fact_9610_and__num_Osimps_I5_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_num.simps(5)
% 5.52/5.89 thf(fact_9611_and__num_Osimps_I3_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 5.52/5.89 = ( some_num @ one ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_num.simps(3)
% 5.52/5.89 thf(fact_9612_and__num_Osimps_I7_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.52/5.89 = ( some_num @ one ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_num.simps(7)
% 5.52/5.89 thf(fact_9613_and__num_Osimps_I2_J,axiom,
% 5.52/5.89 ! [N: num] :
% 5.52/5.89 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 5.52/5.89 = none_num ) ).
% 5.52/5.89
% 5.52/5.89 % and_num.simps(2)
% 5.52/5.89 thf(fact_9614_and__num_Osimps_I4_J,axiom,
% 5.52/5.89 ! [M: num] :
% 5.52/5.89 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 5.52/5.89 = none_num ) ).
% 5.52/5.89
% 5.52/5.89 % and_num.simps(4)
% 5.52/5.89 thf(fact_9615_and__num_Osimps_I8_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_num.simps(8)
% 5.52/5.89 thf(fact_9616_and__num_Osimps_I6_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_num.simps(6)
% 5.52/5.89 thf(fact_9617_and__num_Osimps_I9_J,axiom,
% 5.52/5.89 ! [M: num,N: num] :
% 5.52/5.89 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.52/5.89 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.52/5.89 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.52/5.89 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_num.simps(9)
% 5.52/5.89 thf(fact_9618_and__num__dict,axiom,
% 5.52/5.89 bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 5.52/5.89
% 5.52/5.89 % and_num_dict
% 5.52/5.89 thf(fact_9619_min__enat__simps_I2_J,axiom,
% 5.52/5.89 ! [Q2: extended_enat] :
% 5.52/5.89 ( ( ord_mi8085742599997312461d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.52/5.89 = zero_z5237406670263579293d_enat ) ).
% 5.52/5.89
% 5.52/5.89 % min_enat_simps(2)
% 5.52/5.89 thf(fact_9620_min__enat__simps_I3_J,axiom,
% 5.52/5.89 ! [Q2: extended_enat] :
% 5.52/5.89 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.52/5.89 = zero_z5237406670263579293d_enat ) ).
% 5.52/5.89
% 5.52/5.89 % min_enat_simps(3)
% 5.52/5.89 thf(fact_9621_min__Suc__Suc,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.52/5.89 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % min_Suc_Suc
% 5.52/5.89 thf(fact_9622_min__0R,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( ord_min_nat @ N @ zero_zero_nat )
% 5.52/5.89 = zero_zero_nat ) ).
% 5.52/5.89
% 5.52/5.89 % min_0R
% 5.52/5.89 thf(fact_9623_min__0L,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( ord_min_nat @ zero_zero_nat @ N )
% 5.52/5.89 = zero_zero_nat ) ).
% 5.52/5.89
% 5.52/5.89 % min_0L
% 5.52/5.89 thf(fact_9624_min__Suc__numeral,axiom,
% 5.52/5.89 ! [N: nat,K: num] :
% 5.52/5.89 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.52/5.89 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % min_Suc_numeral
% 5.52/5.89 thf(fact_9625_min__numeral__Suc,axiom,
% 5.52/5.89 ! [K: num,N: nat] :
% 5.52/5.89 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.52/5.89 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % min_numeral_Suc
% 5.52/5.89 thf(fact_9626_nat__mult__min__right,axiom,
% 5.52/5.89 ! [M: nat,N: nat,Q2: nat] :
% 5.52/5.89 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q2 ) )
% 5.52/5.89 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_mult_min_right
% 5.52/5.89 thf(fact_9627_nat__mult__min__left,axiom,
% 5.52/5.89 ! [M: nat,N: nat,Q2: nat] :
% 5.52/5.89 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q2 )
% 5.52/5.89 = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % nat_mult_min_left
% 5.52/5.89 thf(fact_9628_min__diff,axiom,
% 5.52/5.89 ! [M: nat,I: nat,N: nat] :
% 5.52/5.89 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 5.52/5.89 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 5.52/5.89
% 5.52/5.89 % min_diff
% 5.52/5.89 thf(fact_9629_concat__bit__assoc__sym,axiom,
% 5.52/5.89 ! [M: nat,N: nat,K: int,L: int,R: int] :
% 5.52/5.89 ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L ) @ R )
% 5.52/5.89 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L @ R ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % concat_bit_assoc_sym
% 5.52/5.89 thf(fact_9630_take__bit__concat__bit__eq,axiom,
% 5.52/5.89 ! [M: nat,N: nat,K: int,L: int] :
% 5.52/5.89 ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L ) )
% 5.52/5.89 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % take_bit_concat_bit_eq
% 5.52/5.89 thf(fact_9631_min__Suc1,axiom,
% 5.52/5.89 ! [N: nat,M: nat] :
% 5.52/5.89 ( ( ord_min_nat @ ( suc @ N ) @ M )
% 5.52/5.89 = ( case_nat_nat @ zero_zero_nat
% 5.52/5.89 @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ N @ M5 ) )
% 5.52/5.89 @ M ) ) ).
% 5.52/5.89
% 5.52/5.89 % min_Suc1
% 5.52/5.89 thf(fact_9632_min__Suc2,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( ord_min_nat @ M @ ( suc @ N ) )
% 5.52/5.89 = ( case_nat_nat @ zero_zero_nat
% 5.52/5.89 @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ M5 @ N ) )
% 5.52/5.89 @ M ) ) ).
% 5.52/5.89
% 5.52/5.89 % min_Suc2
% 5.52/5.89 thf(fact_9633_prod__encode__prod__decode__aux,axiom,
% 5.52/5.89 ! [K: nat,M: nat] :
% 5.52/5.89 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.52/5.89 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.52/5.89
% 5.52/5.89 % prod_encode_prod_decode_aux
% 5.52/5.89 thf(fact_9634_quotient__of__def,axiom,
% 5.52/5.89 ( quotient_of
% 5.52/5.89 = ( ^ [X: rat] :
% 5.52/5.89 ( the_Pr4378521158711661632nt_int
% 5.52/5.89 @ ^ [Pair: product_prod_int_int] :
% 5.52/5.89 ( ( X
% 5.52/5.89 = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 5.52/5.89 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 5.52/5.89 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % quotient_of_def
% 5.52/5.89 thf(fact_9635_coprime__abs__right__iff,axiom,
% 5.52/5.89 ! [K: int,L: int] :
% 5.52/5.89 ( ( algebr932160517623751201me_int @ K @ ( abs_abs_int @ L ) )
% 5.52/5.89 = ( algebr932160517623751201me_int @ K @ L ) ) ).
% 5.52/5.89
% 5.52/5.89 % coprime_abs_right_iff
% 5.52/5.89 thf(fact_9636_coprime__abs__left__iff,axiom,
% 5.52/5.89 ! [K: int,L: int] :
% 5.52/5.89 ( ( algebr932160517623751201me_int @ ( abs_abs_int @ K ) @ L )
% 5.52/5.89 = ( algebr932160517623751201me_int @ K @ L ) ) ).
% 5.52/5.89
% 5.52/5.89 % coprime_abs_left_iff
% 5.52/5.89 thf(fact_9637_normalize__stable,axiom,
% 5.52/5.89 ! [Q2: int,P6: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ Q2 )
% 5.52/5.89 => ( ( algebr932160517623751201me_int @ P6 @ Q2 )
% 5.52/5.89 => ( ( normalize @ ( product_Pair_int_int @ P6 @ Q2 ) )
% 5.52/5.89 = ( product_Pair_int_int @ P6 @ Q2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % normalize_stable
% 5.52/5.89 thf(fact_9638_Rat__induct,axiom,
% 5.52/5.89 ! [P: rat > $o,Q2: rat] :
% 5.52/5.89 ( ! [A3: int,B2: int] :
% 5.52/5.89 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.52/5.89 => ( ( algebr932160517623751201me_int @ A3 @ B2 )
% 5.52/5.89 => ( P @ ( fract @ A3 @ B2 ) ) ) )
% 5.52/5.89 => ( P @ Q2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % Rat_induct
% 5.52/5.89 thf(fact_9639_Rat__cases,axiom,
% 5.52/5.89 ! [Q2: rat] :
% 5.52/5.89 ~ ! [A3: int,B2: int] :
% 5.52/5.89 ( ( Q2
% 5.52/5.89 = ( fract @ A3 @ B2 ) )
% 5.52/5.89 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.52/5.89 => ~ ( algebr932160517623751201me_int @ A3 @ B2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Rat_cases
% 5.52/5.89 thf(fact_9640_coprime__common__divisor__int,axiom,
% 5.52/5.89 ! [A: int,B: int,X2: int] :
% 5.52/5.89 ( ( algebr932160517623751201me_int @ A @ B )
% 5.52/5.89 => ( ( dvd_dvd_int @ X2 @ A )
% 5.52/5.89 => ( ( dvd_dvd_int @ X2 @ B )
% 5.52/5.89 => ( ( abs_abs_int @ X2 )
% 5.52/5.89 = one_one_int ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % coprime_common_divisor_int
% 5.52/5.89 thf(fact_9641_le__prod__encode__1,axiom,
% 5.52/5.89 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % le_prod_encode_1
% 5.52/5.89 thf(fact_9642_le__prod__encode__2,axiom,
% 5.52/5.89 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % le_prod_encode_2
% 5.52/5.89 thf(fact_9643_Rat__cases__nonzero,axiom,
% 5.52/5.89 ! [Q2: rat] :
% 5.52/5.89 ( ! [A3: int,B2: int] :
% 5.52/5.89 ( ( Q2
% 5.52/5.89 = ( fract @ A3 @ B2 ) )
% 5.52/5.89 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.52/5.89 => ( ( A3 != zero_zero_int )
% 5.52/5.89 => ~ ( algebr932160517623751201me_int @ A3 @ B2 ) ) ) )
% 5.52/5.89 => ( Q2 = zero_zero_rat ) ) ).
% 5.52/5.89
% 5.52/5.89 % Rat_cases_nonzero
% 5.52/5.89 thf(fact_9644_prod__encode__def,axiom,
% 5.52/5.89 ( nat_prod_encode
% 5.52/5.89 = ( produc6842872674320459806at_nat
% 5.52/5.89 @ ^ [M3: nat,N3: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M3 @ N3 ) ) @ M3 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % prod_encode_def
% 5.52/5.89 thf(fact_9645_quotient__of__unique,axiom,
% 5.52/5.89 ! [R: rat] :
% 5.52/5.89 ? [X4: product_prod_int_int] :
% 5.52/5.89 ( ( R
% 5.52/5.89 = ( fract @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 5.52/5.89 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X4 ) )
% 5.52/5.89 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) )
% 5.52/5.89 & ! [Y4: product_prod_int_int] :
% 5.52/5.89 ( ( ( R
% 5.52/5.89 = ( fract @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 5.52/5.89 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y4 ) )
% 5.52/5.89 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 5.52/5.89 => ( Y4 = X4 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % quotient_of_unique
% 5.52/5.89 thf(fact_9646_Rats__abs__iff,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( member_real @ ( abs_abs_real @ X2 ) @ field_5140801741446780682s_real )
% 5.52/5.89 = ( member_real @ X2 @ field_5140801741446780682s_real ) ) ).
% 5.52/5.89
% 5.52/5.89 % Rats_abs_iff
% 5.52/5.89 thf(fact_9647_coprime__int__iff,axiom,
% 5.52/5.89 ! [M: nat,N: nat] :
% 5.52/5.89 ( ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.52/5.89 = ( algebr934650988132801477me_nat @ M @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % coprime_int_iff
% 5.52/5.89 thf(fact_9648_coprime__nat__abs__left__iff,axiom,
% 5.52/5.89 ! [K: int,N: nat] :
% 5.52/5.89 ( ( algebr934650988132801477me_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 5.52/5.89 = ( algebr932160517623751201me_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % coprime_nat_abs_left_iff
% 5.52/5.89 thf(fact_9649_coprime__nat__abs__right__iff,axiom,
% 5.52/5.89 ! [N: nat,K: int] :
% 5.52/5.89 ( ( algebr934650988132801477me_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.52/5.89 = ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 5.52/5.89
% 5.52/5.89 % coprime_nat_abs_right_iff
% 5.52/5.89 thf(fact_9650_coprime__common__divisor__nat,axiom,
% 5.52/5.89 ! [A: nat,B: nat,X2: nat] :
% 5.52/5.89 ( ( algebr934650988132801477me_nat @ A @ B )
% 5.52/5.89 => ( ( dvd_dvd_nat @ X2 @ A )
% 5.52/5.89 => ( ( dvd_dvd_nat @ X2 @ B )
% 5.52/5.89 => ( X2 = one_one_nat ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % coprime_common_divisor_nat
% 5.52/5.89 thf(fact_9651_coprime__crossproduct__nat,axiom,
% 5.52/5.89 ! [A: nat,D2: nat,B: nat,C: nat] :
% 5.52/5.89 ( ( algebr934650988132801477me_nat @ A @ D2 )
% 5.52/5.89 => ( ( algebr934650988132801477me_nat @ B @ C )
% 5.52/5.89 => ( ( ( times_times_nat @ A @ C )
% 5.52/5.89 = ( times_times_nat @ B @ D2 ) )
% 5.52/5.89 = ( ( A = B )
% 5.52/5.89 & ( C = D2 ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % coprime_crossproduct_nat
% 5.52/5.89 thf(fact_9652_coprime__Suc__0__left,axiom,
% 5.52/5.89 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 5.52/5.89
% 5.52/5.89 % coprime_Suc_0_left
% 5.52/5.89 thf(fact_9653_coprime__Suc__0__right,axiom,
% 5.52/5.89 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 5.52/5.89
% 5.52/5.89 % coprime_Suc_0_right
% 5.52/5.89 thf(fact_9654_Rats__dense__in__real,axiom,
% 5.52/5.89 ! [X2: real,Y2: real] :
% 5.52/5.89 ( ( ord_less_real @ X2 @ Y2 )
% 5.52/5.89 => ? [X4: real] :
% 5.52/5.89 ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 5.52/5.89 & ( ord_less_real @ X2 @ X4 )
% 5.52/5.89 & ( ord_less_real @ X4 @ Y2 ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Rats_dense_in_real
% 5.52/5.89 thf(fact_9655_Rats__no__bot__less,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ? [X4: real] :
% 5.52/5.89 ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 5.52/5.89 & ( ord_less_real @ X4 @ X2 ) ) ).
% 5.52/5.89
% 5.52/5.89 % Rats_no_bot_less
% 5.52/5.89 thf(fact_9656_Rats__no__top__le,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ? [X4: real] :
% 5.52/5.89 ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 5.52/5.89 & ( ord_less_eq_real @ X2 @ X4 ) ) ).
% 5.52/5.89
% 5.52/5.89 % Rats_no_top_le
% 5.52/5.89 thf(fact_9657_Rats__abs__nat__div__natE,axiom,
% 5.52/5.89 ! [X2: real] :
% 5.52/5.89 ( ( member_real @ X2 @ field_5140801741446780682s_real )
% 5.52/5.89 => ~ ! [M4: nat,N2: nat] :
% 5.52/5.89 ( ( N2 != zero_zero_nat )
% 5.52/5.89 => ( ( ( abs_abs_real @ X2 )
% 5.52/5.89 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.52/5.89 => ~ ( algebr934650988132801477me_nat @ M4 @ N2 ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % Rats_abs_nat_div_natE
% 5.52/5.89 thf(fact_9658_coprime__diff__one__right__nat,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % coprime_diff_one_right_nat
% 5.52/5.89 thf(fact_9659_coprime__diff__one__left__nat,axiom,
% 5.52/5.89 ! [N: nat] :
% 5.52/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.89 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 5.52/5.89
% 5.52/5.89 % coprime_diff_one_left_nat
% 5.52/5.89 thf(fact_9660_and__not__num_Opelims,axiom,
% 5.52/5.89 ! [X2: num,Xa2: num,Y2: option_num] :
% 5.52/5.89 ( ( ( bit_and_not_num @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X2 @ Xa2 ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( ( Y2 = none_num )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_num @ one ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( ( Y2 = none_num )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.52/5.89 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.52/5.89 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ~ ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_not_num.pelims
% 5.52/5.89 thf(fact_9661_card__length__sum__list__rec,axiom,
% 5.52/5.89 ! [M: nat,N4: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.52/5.89 => ( ( finite_card_list_nat
% 5.52/5.89 @ ( collect_list_nat
% 5.52/5.89 @ ^ [L2: list_nat] :
% 5.52/5.89 ( ( ( size_size_list_nat @ L2 )
% 5.52/5.89 = M )
% 5.52/5.89 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.52/5.89 = N4 ) ) ) )
% 5.52/5.89 = ( plus_plus_nat
% 5.52/5.89 @ ( finite_card_list_nat
% 5.52/5.89 @ ( collect_list_nat
% 5.52/5.89 @ ^ [L2: list_nat] :
% 5.52/5.89 ( ( ( size_size_list_nat @ L2 )
% 5.52/5.89 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.52/5.89 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.52/5.89 = N4 ) ) ) )
% 5.52/5.89 @ ( finite_card_list_nat
% 5.52/5.89 @ ( collect_list_nat
% 5.52/5.89 @ ^ [L2: list_nat] :
% 5.52/5.89 ( ( ( size_size_list_nat @ L2 )
% 5.52/5.89 = M )
% 5.52/5.89 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 5.52/5.89 = N4 ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % card_length_sum_list_rec
% 5.52/5.89 thf(fact_9662_card__length__sum__list,axiom,
% 5.52/5.89 ! [M: nat,N4: nat] :
% 5.52/5.89 ( ( finite_card_list_nat
% 5.52/5.89 @ ( collect_list_nat
% 5.52/5.89 @ ^ [L2: list_nat] :
% 5.52/5.89 ( ( ( size_size_list_nat @ L2 )
% 5.52/5.89 = M )
% 5.52/5.89 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.52/5.89 = N4 ) ) ) )
% 5.52/5.89 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 5.52/5.89
% 5.52/5.89 % card_length_sum_list
% 5.52/5.89 thf(fact_9663_and__num_Opelims,axiom,
% 5.52/5.89 ! [X2: num,Xa2: num,Y2: option_num] :
% 5.52/5.89 ( ( ( bit_un7362597486090784418nd_num @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X2 @ Xa2 ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_num @ one ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( ( Y2 = none_num )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_num @ one ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( ( Y2 = none_num )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_num @ one ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ~ ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.52/5.89 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.52/5.89 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % and_num.pelims
% 5.52/5.89 thf(fact_9664_xor__num_Opelims,axiom,
% 5.52/5.89 ! [X2: num,Xa2: num,Y2: option_num] :
% 5.52/5.89 ( ( ( bit_un2480387367778600638or_num @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X2 @ Xa2 ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( ( Y2 = none_num )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_num @ ( bit1 @ N2 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_num @ ( bit0 @ N2 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_num @ ( bit1 @ M4 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.52/5.89 => ( ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.52/5.89 => ~ ! [M4: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ! [N2: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % xor_num.pelims
% 5.52/5.89 thf(fact_9665_or__not__num__neg_Opelims,axiom,
% 5.52/5.89 ! [X2: num,Xa2: num,Y2: num] :
% 5.52/5.89 ( ( ( bit_or_not_num_neg @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X2 @ Xa2 ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( ( Y2 = one )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ! [M4: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 5.52/5.89 => ( ( ( X2 = one )
% 5.52/5.89 => ! [M4: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 5.52/5.89 => ( ! [N2: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( bit0 @ one ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N2 ) @ one ) ) ) ) )
% 5.52/5.89 => ( ! [N2: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ! [M4: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N2 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.52/5.89 => ( ! [N2: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit0 @ N2 ) )
% 5.52/5.89 => ! [M4: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( bit0 @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N2 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 5.52/5.89 => ( ! [N2: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ( ( Xa2 = one )
% 5.52/5.89 => ( ( Y2 = one )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N2 ) @ one ) ) ) ) )
% 5.52/5.89 => ( ! [N2: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ! [M4: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit0 @ M4 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N2 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.52/5.89 => ~ ! [N2: num] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( bit1 @ N2 ) )
% 5.52/5.89 => ! [M4: num] :
% 5.52/5.89 ( ( Xa2
% 5.52/5.89 = ( bit1 @ M4 ) )
% 5.52/5.89 => ( ( Y2
% 5.52/5.89 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 5.52/5.89 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N2 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % or_not_num_neg.pelims
% 5.52/5.89 thf(fact_9666_xor__num__rel__dict,axiom,
% 5.52/5.89 bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 5.52/5.89
% 5.52/5.89 % xor_num_rel_dict
% 5.52/5.89 thf(fact_9667_and__num__rel__dict,axiom,
% 5.52/5.89 bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 5.52/5.89
% 5.52/5.89 % and_num_rel_dict
% 5.52/5.89 thf(fact_9668_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.52/5.89 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.52/5.89 ( ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.52/5.89 = Y2 )
% 5.52/5.89 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.52/5.89 ( X2
% 5.52/5.89 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( Xa2 != one_one_nat ) ) )
% 5.52/5.89 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.89 ( ( X2
% 5.52/5.89 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.89 => ( Y2
% 5.52/5.89 = ( ~ ( ( Deg2 = Xa2 )
% 5.52/5.89 & ! [X: vEBT_VEBT] :
% 5.52/5.89 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.89 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.89 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.89 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.52/5.89 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.89 & ( case_o184042715313410164at_nat
% 5.52/5.89 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.52/5.89 & ! [X: vEBT_VEBT] :
% 5.52/5.89 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.89 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.89 @ ( produc6081775807080527818_nat_o
% 5.52/5.89 @ ^ [Mi3: nat,Ma3: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.52/5.89 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.89 & ! [I4: nat] :
% 5.52/5.89 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.89 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X7 ) )
% 5.52/5.89 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.52/5.89 & ( ( Mi3 = Ma3 )
% 5.52/5.89 => ! [X: vEBT_VEBT] :
% 5.52/5.89 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.89 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.89 & ( ( Mi3 != Ma3 )
% 5.52/5.89 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.52/5.89 & ! [X: nat] :
% 5.52/5.89 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.89 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.52/5.89 => ( ( ord_less_nat @ Mi3 @ X )
% 5.52/5.89 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.52/5.89 @ Mima ) ) ) ) ) ) ) ).
% 5.52/5.89
% 5.52/5.89 % VEBT_internal.valid'.elims(1)
% 5.52/5.89 thf(fact_9669_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.52/5.89 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.52/5.89 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 5.52/5.89 = ( ( Deg = Deg4 )
% 5.52/5.89 & ! [X: vEBT_VEBT] :
% 5.52/5.89 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.52/5.89 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.89 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.89 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.52/5.89 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.89 & ( case_o184042715313410164at_nat
% 5.52/5.89 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X7 )
% 5.52/5.89 & ! [X: vEBT_VEBT] :
% 5.52/5.89 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.52/5.89 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.89 @ ( produc6081775807080527818_nat_o
% 5.52/5.89 @ ^ [Mi3: nat,Ma3: nat] :
% 5.52/5.89 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.52/5.89 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.52/5.89 & ! [I4: nat] :
% 5.52/5.89 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.89 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X7 ) )
% 5.52/5.89 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.52/5.89 & ( ( Mi3 = Ma3 )
% 5.52/5.89 => ! [X: vEBT_VEBT] :
% 5.52/5.89 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.52/5.89 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.89 & ( ( Mi3 != Ma3 )
% 5.52/5.89 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.52/5.89 & ! [X: nat] :
% 5.52/5.89 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.52/5.89 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X )
% 5.52/5.89 => ( ( ord_less_nat @ Mi3 @ X )
% 5.52/5.89 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.52/5.90 @ Mima2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT_internal.valid'.simps(2)
% 5.52/5.90 thf(fact_9670_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.52/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.90 ( ~ ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.52/5.90 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.52/5.90 ( X2
% 5.52/5.90 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.52/5.90 => ( Xa2 = one_one_nat ) )
% 5.52/5.90 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.90 => ( ( Deg2 = Xa2 )
% 5.52/5.90 & ! [X4: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.52/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 & ( case_o184042715313410164at_nat
% 5.52/5.90 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.52/5.90 & ! [X: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [Mi3: nat,Ma3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.52/5.90 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.90 & ! [I4: nat] :
% 5.52/5.90 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X7 ) )
% 5.52/5.90 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.52/5.90 & ( ( Mi3 = Ma3 )
% 5.52/5.90 => ! [X: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.90 & ( ( Mi3 != Ma3 )
% 5.52/5.90 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.52/5.90 & ! [X: nat] :
% 5.52/5.90 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.90 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.52/5.90 => ( ( ord_less_nat @ Mi3 @ X )
% 5.52/5.90 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.52/5.90 @ Mima ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT_internal.valid'.elims(3)
% 5.52/5.90 thf(fact_9671_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.52/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.90 ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.52/5.90 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.52/5.90 ( X2
% 5.52/5.90 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.52/5.90 => ( Xa2 != one_one_nat ) )
% 5.52/5.90 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.90 => ~ ( ( Deg2 = Xa2 )
% 5.52/5.90 & ! [X6: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ( vEBT_VEBT_valid @ X6 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.52/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 & ( case_o184042715313410164at_nat
% 5.52/5.90 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.52/5.90 & ! [X: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [Mi3: nat,Ma3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.52/5.90 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.90 & ! [I4: nat] :
% 5.52/5.90 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X7 ) )
% 5.52/5.90 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.52/5.90 & ( ( Mi3 = Ma3 )
% 5.52/5.90 => ! [X: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.90 & ( ( Mi3 != Ma3 )
% 5.52/5.90 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.52/5.90 & ! [X: nat] :
% 5.52/5.90 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.90 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.52/5.90 => ( ( ord_less_nat @ Mi3 @ X )
% 5.52/5.90 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.52/5.90 @ Mima ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT_internal.valid'.elims(2)
% 5.52/5.90 thf(fact_9672_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.52/5.90 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.52/5.90 ( ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.52/5.90 = Y2 )
% 5.52/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.90 => ( ! [Uu2: $o,Uv2: $o] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.52/5.90 => ( ( Y2
% 5.52/5.90 = ( Xa2 = one_one_nat ) )
% 5.52/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.52/5.90 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.90 => ( ( Y2
% 5.52/5.90 = ( ( Deg2 = Xa2 )
% 5.52/5.90 & ! [X: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.52/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 & ( case_o184042715313410164at_nat
% 5.52/5.90 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.52/5.90 & ! [X: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [Mi3: nat,Ma3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.52/5.90 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.90 & ! [I4: nat] :
% 5.52/5.90 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X7 ) )
% 5.52/5.90 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.52/5.90 & ( ( Mi3 = Ma3 )
% 5.52/5.90 => ! [X: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.90 & ( ( Mi3 != Ma3 )
% 5.52/5.90 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.52/5.90 & ! [X: nat] :
% 5.52/5.90 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.90 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.52/5.90 => ( ( ord_less_nat @ Mi3 @ X )
% 5.52/5.90 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.52/5.90 @ Mima ) ) )
% 5.52/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT_internal.valid'.pelims(1)
% 5.52/5.90 thf(fact_9673_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.52/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.90 ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.52/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.90 => ( ! [Uu2: $o,Uv2: $o] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.52/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.52/5.90 => ( Xa2 != one_one_nat ) ) )
% 5.52/5.90 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.52/5.90 => ~ ( ( Deg2 = Xa2 )
% 5.52/5.90 & ! [X6: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ( vEBT_VEBT_valid @ X6 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.52/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 & ( case_o184042715313410164at_nat
% 5.52/5.90 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.52/5.90 & ! [X: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [Mi3: nat,Ma3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.52/5.90 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.90 & ! [I4: nat] :
% 5.52/5.90 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X7 ) )
% 5.52/5.90 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.52/5.90 & ( ( Mi3 = Ma3 )
% 5.52/5.90 => ! [X: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.90 & ( ( Mi3 != Ma3 )
% 5.52/5.90 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.52/5.90 & ! [X: nat] :
% 5.52/5.90 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.90 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.52/5.90 => ( ( ord_less_nat @ Mi3 @ X )
% 5.52/5.90 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.52/5.90 @ Mima ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT_internal.valid'.pelims(2)
% 5.52/5.90 thf(fact_9674_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.52/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.52/5.90 ( ~ ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.52/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.52/5.90 => ( ! [Uu2: $o,Uv2: $o] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.52/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.52/5.90 => ( Xa2 = one_one_nat ) ) )
% 5.52/5.90 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.52/5.90 => ( ( Deg2 = Xa2 )
% 5.52/5.90 & ! [X4: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.52/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 & ( case_o184042715313410164at_nat
% 5.52/5.90 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.52/5.90 & ! [X: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [Mi3: nat,Ma3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.52/5.90 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.90 & ! [I4: nat] :
% 5.52/5.90 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X7 ) )
% 5.52/5.90 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.52/5.90 & ( ( Mi3 = Ma3 )
% 5.52/5.90 => ! [X: vEBT_VEBT] :
% 5.52/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.52/5.90 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X @ X7 ) ) )
% 5.52/5.90 & ( ( Mi3 != Ma3 )
% 5.52/5.90 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.52/5.90 & ! [X: nat] :
% 5.52/5.90 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.52/5.90 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.52/5.90 => ( ( ord_less_nat @ Mi3 @ X )
% 5.52/5.90 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.52/5.90 @ Mima ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT_internal.valid'.pelims(3)
% 5.52/5.90 thf(fact_9675_GreatestI__nat,axiom,
% 5.52/5.90 ! [P: nat > $o,K: nat,B: nat] :
% 5.52/5.90 ( ( P @ K )
% 5.52/5.90 => ( ! [Y3: nat] :
% 5.52/5.90 ( ( P @ Y3 )
% 5.52/5.90 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.52/5.90 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % GreatestI_nat
% 5.52/5.90 thf(fact_9676_Greatest__le__nat,axiom,
% 5.52/5.90 ! [P: nat > $o,K: nat,B: nat] :
% 5.52/5.90 ( ( P @ K )
% 5.52/5.90 => ( ! [Y3: nat] :
% 5.52/5.90 ( ( P @ Y3 )
% 5.52/5.90 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.52/5.90 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Greatest_le_nat
% 5.52/5.90 thf(fact_9677_GreatestI__ex__nat,axiom,
% 5.52/5.90 ! [P: nat > $o,B: nat] :
% 5.52/5.90 ( ? [X_12: nat] : ( P @ X_12 )
% 5.52/5.90 => ( ! [Y3: nat] :
% 5.52/5.90 ( ( P @ Y3 )
% 5.52/5.90 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.52/5.90 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % GreatestI_ex_nat
% 5.52/5.90 thf(fact_9678_Rats__eq__int__div__int,axiom,
% 5.52/5.90 ( field_5140801741446780682s_real
% 5.52/5.90 = ( collect_real
% 5.52/5.90 @ ^ [Uu3: real] :
% 5.52/5.90 ? [I4: int,J3: int] :
% 5.52/5.90 ( ( Uu3
% 5.52/5.90 = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 5.52/5.90 & ( J3 != zero_zero_int ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rats_eq_int_div_int
% 5.52/5.90 thf(fact_9679_Rats__eq__int__div__nat,axiom,
% 5.52/5.90 ( field_5140801741446780682s_real
% 5.52/5.90 = ( collect_real
% 5.52/5.90 @ ^ [Uu3: real] :
% 5.52/5.90 ? [I4: int,N3: nat] :
% 5.52/5.90 ( ( Uu3
% 5.52/5.90 = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 5.52/5.90 & ( N3 != zero_zero_nat ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rats_eq_int_div_nat
% 5.52/5.90 thf(fact_9680_VEBT_Osize_I3_J,axiom,
% 5.52/5.90 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.52/5.90 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.52/5.90 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT.size(3)
% 5.52/5.90 thf(fact_9681_VEBT_Osize__gen_I1_J,axiom,
% 5.52/5.90 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.52/5.90 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.52/5.90 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT.size_gen(1)
% 5.52/5.90 thf(fact_9682_nth__upt,axiom,
% 5.52/5.90 ! [I: nat,K: nat,J: nat] :
% 5.52/5.90 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 5.52/5.90 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 5.52/5.90 = ( plus_plus_nat @ I @ K ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % nth_upt
% 5.52/5.90 thf(fact_9683_take__upt,axiom,
% 5.52/5.90 ! [I: nat,M: nat,N: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N )
% 5.52/5.90 => ( ( take_nat @ M @ ( upt @ I @ N ) )
% 5.52/5.90 = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % take_upt
% 5.52/5.90 thf(fact_9684_sum__list__upt,axiom,
% 5.52/5.90 ! [M: nat,N: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ M @ N )
% 5.52/5.90 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 5.52/5.90 = ( groups3542108847815614940at_nat
% 5.52/5.90 @ ^ [X: nat] : X
% 5.52/5.90 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % sum_list_upt
% 5.52/5.90 thf(fact_9685_map__add__upt,axiom,
% 5.52/5.90 ! [N: nat,M: nat] :
% 5.52/5.90 ( ( map_nat_nat
% 5.52/5.90 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N )
% 5.52/5.90 @ ( upt @ zero_zero_nat @ M ) )
% 5.52/5.90 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % map_add_upt
% 5.52/5.90 thf(fact_9686_sorted__wrt__upt,axiom,
% 5.52/5.90 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % sorted_wrt_upt
% 5.52/5.90 thf(fact_9687_sorted__upt,axiom,
% 5.52/5.90 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % sorted_upt
% 5.52/5.90 thf(fact_9688_sorted__wrt__less__idx,axiom,
% 5.52/5.90 ! [Ns: list_nat,I: nat] :
% 5.52/5.90 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.52/5.90 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 5.52/5.90 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % sorted_wrt_less_idx
% 5.52/5.90 thf(fact_9689_upt__conv__Nil,axiom,
% 5.52/5.90 ! [J: nat,I: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ J @ I )
% 5.52/5.90 => ( ( upt @ I @ J )
% 5.52/5.90 = nil_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % upt_conv_Nil
% 5.52/5.90 thf(fact_9690_upt__eq__Nil__conv,axiom,
% 5.52/5.90 ! [I: nat,J: nat] :
% 5.52/5.90 ( ( ( upt @ I @ J )
% 5.52/5.90 = nil_nat )
% 5.52/5.90 = ( ( J = zero_zero_nat )
% 5.52/5.90 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upt_eq_Nil_conv
% 5.52/5.90 thf(fact_9691_range__mod,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ( image_nat_nat
% 5.52/5.90 @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N )
% 5.52/5.90 @ top_top_set_nat )
% 5.52/5.90 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % range_mod
% 5.52/5.90 thf(fact_9692_cauchyD,axiom,
% 5.52/5.90 ! [X8: nat > rat,R: rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.52/5.90 => ? [K3: nat] :
% 5.52/5.90 ! [M2: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K3 @ M2 )
% 5.52/5.90 => ! [N7: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K3 @ N7 )
% 5.52/5.90 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M2 ) @ ( X8 @ N7 ) ) ) @ R ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % cauchyD
% 5.52/5.90 thf(fact_9693_cauchyI,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ! [R3: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.52/5.90 => ? [K4: nat] :
% 5.52/5.90 ! [M4: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K4 @ M4 )
% 5.52/5.90 => ! [N2: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K4 @ N2 )
% 5.52/5.90 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M4 ) @ ( X8 @ N2 ) ) ) @ R3 ) ) ) )
% 5.52/5.90 => ( cauchy @ X8 ) ) ).
% 5.52/5.90
% 5.52/5.90 % cauchyI
% 5.52/5.90 thf(fact_9694_cauchy__diff,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( cauchy @ Y6 )
% 5.52/5.90 => ( cauchy
% 5.52/5.90 @ ^ [N3: nat] : ( minus_minus_rat @ ( X8 @ N3 ) @ ( Y6 @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % cauchy_diff
% 5.52/5.90 thf(fact_9695_cauchy__minus,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( cauchy
% 5.52/5.90 @ ^ [N3: nat] : ( uminus_uminus_rat @ ( X8 @ N3 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % cauchy_minus
% 5.52/5.90 thf(fact_9696_cauchy__mult,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( cauchy @ Y6 )
% 5.52/5.90 => ( cauchy
% 5.52/5.90 @ ^ [N3: nat] : ( times_times_rat @ ( X8 @ N3 ) @ ( Y6 @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % cauchy_mult
% 5.52/5.90 thf(fact_9697_cauchy__const,axiom,
% 5.52/5.90 ! [X2: rat] :
% 5.52/5.90 ( cauchy
% 5.52/5.90 @ ^ [N3: nat] : X2 ) ).
% 5.52/5.90
% 5.52/5.90 % cauchy_const
% 5.52/5.90 thf(fact_9698_cauchy__add,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( cauchy @ Y6 )
% 5.52/5.90 => ( cauchy
% 5.52/5.90 @ ^ [N3: nat] : ( plus_plus_rat @ ( X8 @ N3 ) @ ( Y6 @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % cauchy_add
% 5.52/5.90 thf(fact_9699_cauchy__imp__bounded,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ? [B2: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.52/5.90 & ! [N7: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N7 ) ) @ B2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % cauchy_imp_bounded
% 5.52/5.90 thf(fact_9700_cauchy__def,axiom,
% 5.52/5.90 ( cauchy
% 5.52/5.90 = ( ^ [X7: nat > rat] :
% 5.52/5.90 ! [R5: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.52/5.90 => ? [K2: nat] :
% 5.52/5.90 ! [M3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K2 @ M3 )
% 5.52/5.90 => ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K2 @ N3 )
% 5.52/5.90 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X7 @ M3 ) @ ( X7 @ N3 ) ) ) @ R5 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % cauchy_def
% 5.52/5.90 thf(fact_9701_le__Real,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( cauchy @ Y6 )
% 5.52/5.90 => ( ( ord_less_eq_real @ ( real2 @ X8 ) @ ( real2 @ Y6 ) )
% 5.52/5.90 = ( ! [R5: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.52/5.90 => ? [K2: nat] :
% 5.52/5.90 ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K2 @ N3 )
% 5.52/5.90 => ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( plus_plus_rat @ ( Y6 @ N3 ) @ R5 ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % le_Real
% 5.52/5.90 thf(fact_9702_cauchy__not__vanishes,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ~ ( vanishes @ X8 )
% 5.52/5.90 => ? [B2: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.52/5.90 & ? [K3: nat] :
% 5.52/5.90 ! [N7: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K3 @ N7 )
% 5.52/5.90 => ( ord_less_rat @ B2 @ ( abs_abs_rat @ ( X8 @ N7 ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % cauchy_not_vanishes
% 5.52/5.90 thf(fact_9703_card__UNIV__unit,axiom,
% 5.52/5.90 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.52/5.90 = one_one_nat ) ).
% 5.52/5.90
% 5.52/5.90 % card_UNIV_unit
% 5.52/5.90 thf(fact_9704_vanishes__const,axiom,
% 5.52/5.90 ! [C: rat] :
% 5.52/5.90 ( ( vanishes
% 5.52/5.90 @ ^ [N3: nat] : C )
% 5.52/5.90 = ( C = zero_zero_rat ) ) ).
% 5.52/5.90
% 5.52/5.90 % vanishes_const
% 5.52/5.90 thf(fact_9705_card__UNIV__bool,axiom,
% 5.52/5.90 ( ( finite_card_o @ top_top_set_o )
% 5.52/5.90 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % card_UNIV_bool
% 5.52/5.90 thf(fact_9706_eq__Real,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( cauchy @ Y6 )
% 5.52/5.90 => ( ( ( real2 @ X8 )
% 5.52/5.90 = ( real2 @ Y6 ) )
% 5.52/5.90 = ( vanishes
% 5.52/5.90 @ ^ [N3: nat] : ( minus_minus_rat @ ( X8 @ N3 ) @ ( Y6 @ N3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % eq_Real
% 5.52/5.90 thf(fact_9707_inverse__Real,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( ( vanishes @ X8 )
% 5.52/5.90 => ( ( inverse_inverse_real @ ( real2 @ X8 ) )
% 5.52/5.90 = zero_zero_real ) )
% 5.52/5.90 & ( ~ ( vanishes @ X8 )
% 5.52/5.90 => ( ( inverse_inverse_real @ ( real2 @ X8 ) )
% 5.52/5.90 = ( real2
% 5.52/5.90 @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X8 @ N3 ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % inverse_Real
% 5.52/5.90 thf(fact_9708_cauchy__inverse,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ~ ( vanishes @ X8 )
% 5.52/5.90 => ( cauchy
% 5.52/5.90 @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X8 @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % cauchy_inverse
% 5.52/5.90 thf(fact_9709_Real__induct,axiom,
% 5.52/5.90 ! [P: real > $o,X2: real] :
% 5.52/5.90 ( ! [X9: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X9 )
% 5.52/5.90 => ( P @ ( real2 @ X9 ) ) )
% 5.52/5.90 => ( P @ X2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % Real_induct
% 5.52/5.90 thf(fact_9710_vanishes__minus,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ( vanishes @ X8 )
% 5.52/5.90 => ( vanishes
% 5.52/5.90 @ ^ [N3: nat] : ( uminus_uminus_rat @ ( X8 @ N3 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % vanishes_minus
% 5.52/5.90 thf(fact_9711_of__nat__Real,axiom,
% 5.52/5.90 ( semiri5074537144036343181t_real
% 5.52/5.90 = ( ^ [X: nat] :
% 5.52/5.90 ( real2
% 5.52/5.90 @ ^ [N3: nat] : ( semiri681578069525770553at_rat @ X ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % of_nat_Real
% 5.52/5.90 thf(fact_9712_vanishes__add,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ( vanishes @ X8 )
% 5.52/5.90 => ( ( vanishes @ Y6 )
% 5.52/5.90 => ( vanishes
% 5.52/5.90 @ ^ [N3: nat] : ( plus_plus_rat @ ( X8 @ N3 ) @ ( Y6 @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % vanishes_add
% 5.52/5.90 thf(fact_9713_vanishes__diff,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ( vanishes @ X8 )
% 5.52/5.90 => ( ( vanishes @ Y6 )
% 5.52/5.90 => ( vanishes
% 5.52/5.90 @ ^ [N3: nat] : ( minus_minus_rat @ ( X8 @ N3 ) @ ( Y6 @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % vanishes_diff
% 5.52/5.90 thf(fact_9714_zero__real__def,axiom,
% 5.52/5.90 ( zero_zero_real
% 5.52/5.90 = ( real2
% 5.52/5.90 @ ^ [N3: nat] : zero_zero_rat ) ) ).
% 5.52/5.90
% 5.52/5.90 % zero_real_def
% 5.52/5.90 thf(fact_9715_mult__Real,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( cauchy @ Y6 )
% 5.52/5.90 => ( ( times_times_real @ ( real2 @ X8 ) @ ( real2 @ Y6 ) )
% 5.52/5.90 = ( real2
% 5.52/5.90 @ ^ [N3: nat] : ( times_times_rat @ ( X8 @ N3 ) @ ( Y6 @ N3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % mult_Real
% 5.52/5.90 thf(fact_9716_one__real__def,axiom,
% 5.52/5.90 ( one_one_real
% 5.52/5.90 = ( real2
% 5.52/5.90 @ ^ [N3: nat] : one_one_rat ) ) ).
% 5.52/5.90
% 5.52/5.90 % one_real_def
% 5.52/5.90 thf(fact_9717_of__int__Real,axiom,
% 5.52/5.90 ( ring_1_of_int_real
% 5.52/5.90 = ( ^ [X: int] :
% 5.52/5.90 ( real2
% 5.52/5.90 @ ^ [N3: nat] : ( ring_1_of_int_rat @ X ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % of_int_Real
% 5.52/5.90 thf(fact_9718_vanishes__diff__inverse,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ~ ( vanishes @ X8 )
% 5.52/5.90 => ( ( cauchy @ Y6 )
% 5.52/5.90 => ( ~ ( vanishes @ Y6 )
% 5.52/5.90 => ( ( vanishes
% 5.52/5.90 @ ^ [N3: nat] : ( minus_minus_rat @ ( X8 @ N3 ) @ ( Y6 @ N3 ) ) )
% 5.52/5.90 => ( vanishes
% 5.52/5.90 @ ^ [N3: nat] : ( minus_minus_rat @ ( inverse_inverse_rat @ ( X8 @ N3 ) ) @ ( inverse_inverse_rat @ ( Y6 @ N3 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % vanishes_diff_inverse
% 5.52/5.90 thf(fact_9719_minus__Real,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( uminus_uminus_real @ ( real2 @ X8 ) )
% 5.52/5.90 = ( real2
% 5.52/5.90 @ ^ [N3: nat] : ( uminus_uminus_rat @ ( X8 @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % minus_Real
% 5.52/5.90 thf(fact_9720_add__Real,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( cauchy @ Y6 )
% 5.52/5.90 => ( ( plus_plus_real @ ( real2 @ X8 ) @ ( real2 @ Y6 ) )
% 5.52/5.90 = ( real2
% 5.52/5.90 @ ^ [N3: nat] : ( plus_plus_rat @ ( X8 @ N3 ) @ ( Y6 @ N3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % add_Real
% 5.52/5.90 thf(fact_9721_diff__Real,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( cauchy @ Y6 )
% 5.52/5.90 => ( ( minus_minus_real @ ( real2 @ X8 ) @ ( real2 @ Y6 ) )
% 5.52/5.90 = ( real2
% 5.52/5.90 @ ^ [N3: nat] : ( minus_minus_rat @ ( X8 @ N3 ) @ ( Y6 @ N3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % diff_Real
% 5.52/5.90 thf(fact_9722_vanishes__mult__bounded,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ? [A8: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ A8 )
% 5.52/5.90 & ! [N2: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N2 ) ) @ A8 ) )
% 5.52/5.90 => ( ( vanishes @ Y6 )
% 5.52/5.90 => ( vanishes
% 5.52/5.90 @ ^ [N3: nat] : ( times_times_rat @ ( X8 @ N3 ) @ ( Y6 @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % vanishes_mult_bounded
% 5.52/5.90 thf(fact_9723_vanishes__def,axiom,
% 5.52/5.90 ( vanishes
% 5.52/5.90 = ( ^ [X7: nat > rat] :
% 5.52/5.90 ! [R5: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.52/5.90 => ? [K2: nat] :
% 5.52/5.90 ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K2 @ N3 )
% 5.52/5.90 => ( ord_less_rat @ ( abs_abs_rat @ ( X7 @ N3 ) ) @ R5 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % vanishes_def
% 5.52/5.90 thf(fact_9724_vanishesI,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ! [R3: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.52/5.90 => ? [K4: nat] :
% 5.52/5.90 ! [N2: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K4 @ N2 )
% 5.52/5.90 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N2 ) ) @ R3 ) ) )
% 5.52/5.90 => ( vanishes @ X8 ) ) ).
% 5.52/5.90
% 5.52/5.90 % vanishesI
% 5.52/5.90 thf(fact_9725_vanishesD,axiom,
% 5.52/5.90 ! [X8: nat > rat,R: rat] :
% 5.52/5.90 ( ( vanishes @ X8 )
% 5.52/5.90 => ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.52/5.90 => ? [K3: nat] :
% 5.52/5.90 ! [N7: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K3 @ N7 )
% 5.52/5.90 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N7 ) ) @ R ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % vanishesD
% 5.52/5.90 thf(fact_9726_cauchy__not__vanishes__cases,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ~ ( vanishes @ X8 )
% 5.52/5.90 => ? [B2: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.52/5.90 & ? [K3: nat] :
% 5.52/5.90 ( ! [N7: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K3 @ N7 )
% 5.52/5.90 => ( ord_less_rat @ B2 @ ( uminus_uminus_rat @ ( X8 @ N7 ) ) ) )
% 5.52/5.90 | ! [N7: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K3 @ N7 )
% 5.52/5.90 => ( ord_less_rat @ B2 @ ( X8 @ N7 ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % cauchy_not_vanishes_cases
% 5.52/5.90 thf(fact_9727_root__def,axiom,
% 5.52/5.90 ( root
% 5.52/5.90 = ( ^ [N3: nat,X: real] :
% 5.52/5.90 ( if_real @ ( N3 = zero_zero_nat ) @ zero_zero_real
% 5.52/5.90 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.52/5.90 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N3 ) )
% 5.52/5.90 @ X ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % root_def
% 5.52/5.90 thf(fact_9728_not__positive__Real,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( ~ ( positive2 @ ( real2 @ X8 ) ) )
% 5.52/5.90 = ( ! [R5: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.52/5.90 => ? [K2: nat] :
% 5.52/5.90 ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K2 @ N3 )
% 5.52/5.90 => ( ord_less_eq_rat @ ( X8 @ N3 ) @ R5 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % not_positive_Real
% 5.52/5.90 thf(fact_9729_Real_Opositive__add,axiom,
% 5.52/5.90 ! [X2: real,Y2: real] :
% 5.52/5.90 ( ( positive2 @ X2 )
% 5.52/5.90 => ( ( positive2 @ Y2 )
% 5.52/5.90 => ( positive2 @ ( plus_plus_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Real.positive_add
% 5.52/5.90 thf(fact_9730_Real_Opositive__zero,axiom,
% 5.52/5.90 ~ ( positive2 @ zero_zero_real ) ).
% 5.52/5.90
% 5.52/5.90 % Real.positive_zero
% 5.52/5.90 thf(fact_9731_Real_Opositive__mult,axiom,
% 5.52/5.90 ! [X2: real,Y2: real] :
% 5.52/5.90 ( ( positive2 @ X2 )
% 5.52/5.90 => ( ( positive2 @ Y2 )
% 5.52/5.90 => ( positive2 @ ( times_times_real @ X2 @ Y2 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Real.positive_mult
% 5.52/5.90 thf(fact_9732_Real_Opositive__minus,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ~ ( positive2 @ X2 )
% 5.52/5.90 => ( ( X2 != zero_zero_real )
% 5.52/5.90 => ( positive2 @ ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Real.positive_minus
% 5.52/5.90 thf(fact_9733_less__real__def,axiom,
% 5.52/5.90 ( ord_less_real
% 5.52/5.90 = ( ^ [X: real,Y: real] : ( positive2 @ ( minus_minus_real @ Y @ X ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_real_def
% 5.52/5.90 thf(fact_9734_positive__Real,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( positive2 @ ( real2 @ X8 ) )
% 5.52/5.90 = ( ? [R5: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.52/5.90 & ? [K2: nat] :
% 5.52/5.90 ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K2 @ N3 )
% 5.52/5.90 => ( ord_less_rat @ R5 @ ( X8 @ N3 ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % positive_Real
% 5.52/5.90 thf(fact_9735_card__UNIV__char,axiom,
% 5.52/5.90 ( ( finite_card_char @ top_top_set_char )
% 5.52/5.90 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % card_UNIV_char
% 5.52/5.90 thf(fact_9736_DERIV__even__real__root,axiom,
% 5.52/5.90 ! [N: nat,X2: real] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.90 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_even_real_root
% 5.52/5.90 thf(fact_9737_DERIV__real__root__generic,axiom,
% 5.52/5.90 ! [N: nat,X2: real,D4: real] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ( X2 != zero_zero_real )
% 5.52/5.90 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.90 => ( D4
% 5.52/5.90 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.52/5.90 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.90 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.52/5.90 => ( D4
% 5.52/5.90 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.52/5.90 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.90 => ( D4
% 5.52/5.90 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_real_root_generic
% 5.52/5.90 thf(fact_9738_DERIV__neg__dec__left,axiom,
% 5.52/5.90 ! [F: real > real,L: real,X2: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.52/5.90 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.52/5.90 => ? [D3: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.52/5.90 & ! [H4: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.52/5.90 => ( ( ord_less_real @ H4 @ D3 )
% 5.52/5.90 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_neg_dec_left
% 5.52/5.90 thf(fact_9739_DERIV__pos__inc__left,axiom,
% 5.52/5.90 ! [F: real > real,L: real,X2: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.52/5.90 => ? [D3: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.52/5.90 & ! [H4: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.52/5.90 => ( ( ord_less_real @ H4 @ D3 )
% 5.52/5.90 => ( ord_less_real @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_pos_inc_left
% 5.52/5.90 thf(fact_9740_DERIV__pos__inc__right,axiom,
% 5.52/5.90 ! [F: real > real,L: real,X2: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.52/5.90 => ? [D3: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.52/5.90 & ! [H4: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.52/5.90 => ( ( ord_less_real @ H4 @ D3 )
% 5.52/5.90 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_pos_inc_right
% 5.52/5.90 thf(fact_9741_DERIV__neg__dec__right,axiom,
% 5.52/5.90 ! [F: real > real,L: real,X2: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.52/5.90 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.52/5.90 => ? [D3: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.52/5.90 & ! [H4: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.52/5.90 => ( ( ord_less_real @ H4 @ D3 )
% 5.52/5.90 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_neg_dec_right
% 5.52/5.90 thf(fact_9742_DERIV__pos__imp__increasing,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ A @ X4 )
% 5.52/5.90 => ( ( ord_less_eq_real @ X4 @ B )
% 5.52/5.90 => ? [Y4: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.52/5.90 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 5.52/5.90 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_pos_imp_increasing
% 5.52/5.90 thf(fact_9743_DERIV__neg__imp__decreasing,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ A @ X4 )
% 5.52/5.90 => ( ( ord_less_eq_real @ X4 @ B )
% 5.52/5.90 => ? [Y4: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.52/5.90 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 5.52/5.90 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_neg_imp_decreasing
% 5.52/5.90 thf(fact_9744_Inf__real__def,axiom,
% 5.52/5.90 ( comple4887499456419720421f_real
% 5.52/5.90 = ( ^ [X7: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X7 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Inf_real_def
% 5.52/5.90 thf(fact_9745_has__real__derivative__neg__dec__left,axiom,
% 5.52/5.90 ! [F: real > real,L: real,X2: real,S3: set_real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S3 ) )
% 5.52/5.90 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.52/5.90 => ? [D3: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.52/5.90 & ! [H4: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.52/5.90 => ( ( member_real @ ( minus_minus_real @ X2 @ H4 ) @ S3 )
% 5.52/5.90 => ( ( ord_less_real @ H4 @ D3 )
% 5.52/5.90 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % has_real_derivative_neg_dec_left
% 5.52/5.90 thf(fact_9746_has__real__derivative__pos__inc__left,axiom,
% 5.52/5.90 ! [F: real > real,L: real,X2: real,S3: set_real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S3 ) )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.52/5.90 => ? [D3: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.52/5.90 & ! [H4: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.52/5.90 => ( ( member_real @ ( minus_minus_real @ X2 @ H4 ) @ S3 )
% 5.52/5.90 => ( ( ord_less_real @ H4 @ D3 )
% 5.52/5.90 => ( ord_less_real @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % has_real_derivative_pos_inc_left
% 5.52/5.90 thf(fact_9747_has__real__derivative__pos__inc__right,axiom,
% 5.52/5.90 ! [F: real > real,L: real,X2: real,S3: set_real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S3 ) )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.52/5.90 => ? [D3: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.52/5.90 & ! [H4: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.52/5.90 => ( ( member_real @ ( plus_plus_real @ X2 @ H4 ) @ S3 )
% 5.52/5.90 => ( ( ord_less_real @ H4 @ D3 )
% 5.52/5.90 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % has_real_derivative_pos_inc_right
% 5.52/5.90 thf(fact_9748_has__real__derivative__neg__dec__right,axiom,
% 5.52/5.90 ! [F: real > real,L: real,X2: real,S3: set_real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S3 ) )
% 5.52/5.90 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.52/5.90 => ? [D3: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.52/5.90 & ! [H4: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.52/5.90 => ( ( member_real @ ( plus_plus_real @ X2 @ H4 ) @ S3 )
% 5.52/5.90 => ( ( ord_less_real @ H4 @ D3 )
% 5.52/5.90 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % has_real_derivative_neg_dec_right
% 5.52/5.90 thf(fact_9749_MVT2,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real,F4: real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ A @ X4 )
% 5.52/5.90 => ( ( ord_less_eq_real @ X4 @ B )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.52/5.90 => ? [Z3: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ Z3 )
% 5.52/5.90 & ( ord_less_real @ Z3 @ B )
% 5.52/5.90 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.52/5.90 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % MVT2
% 5.52/5.90 thf(fact_9750_DERIV__local__const,axiom,
% 5.52/5.90 ! [F: real > real,L: real,X2: real,D2: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.52/5.90 => ( ! [Y3: real] :
% 5.52/5.90 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ D2 )
% 5.52/5.90 => ( ( F @ X2 )
% 5.52/5.90 = ( F @ Y3 ) ) )
% 5.52/5.90 => ( L = zero_zero_real ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_local_const
% 5.52/5.90 thf(fact_9751_DERIV__ln,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_ln
% 5.52/5.90 thf(fact_9752_DERIV__const__average,axiom,
% 5.52/5.90 ! [A: real,B: real,V: real > real,K: real] :
% 5.52/5.90 ( ( A != B )
% 5.52/5.90 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.52/5.90 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.52/5.90 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_const_average
% 5.52/5.90 thf(fact_9753_DERIV__local__min,axiom,
% 5.52/5.90 ! [F: real > real,L: real,X2: real,D2: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.52/5.90 => ( ! [Y3: real] :
% 5.52/5.90 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ D2 )
% 5.52/5.90 => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 5.52/5.90 => ( L = zero_zero_real ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_local_min
% 5.52/5.90 thf(fact_9754_DERIV__local__max,axiom,
% 5.52/5.90 ! [F: real > real,L: real,X2: real,D2: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.52/5.90 => ( ! [Y3: real] :
% 5.52/5.90 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ D2 )
% 5.52/5.90 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 5.52/5.90 => ( L = zero_zero_real ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_local_max
% 5.52/5.90 thf(fact_9755_DERIV__ln__divide,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_ln_divide
% 5.52/5.90 thf(fact_9756_DERIV__pow,axiom,
% 5.52/5.90 ! [N: nat,X2: real,S: set_real] :
% 5.52/5.90 ( has_fi5821293074295781190e_real
% 5.52/5.90 @ ^ [X: real] : ( power_power_real @ X @ N )
% 5.52/5.90 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X2 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.52/5.90 @ ( topolo2177554685111907308n_real @ X2 @ S ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_pow
% 5.52/5.90 thf(fact_9757_DERIV__fun__pow,axiom,
% 5.52/5.90 ! [G: real > real,M: real,X2: real,N: nat] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real
% 5.52/5.90 @ ^ [X: real] : ( power_power_real @ ( G @ X ) @ N )
% 5.52/5.90 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X2 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 5.52/5.90 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_fun_pow
% 5.52/5.90 thf(fact_9758_has__real__derivative__powr,axiom,
% 5.52/5.90 ! [Z: real,R: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.52/5.90 => ( has_fi5821293074295781190e_real
% 5.52/5.90 @ ^ [Z2: real] : ( powr_real @ Z2 @ R )
% 5.52/5.90 @ ( times_times_real @ R @ ( powr_real @ Z @ ( minus_minus_real @ R @ one_one_real ) ) )
% 5.52/5.90 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % has_real_derivative_powr
% 5.52/5.90 thf(fact_9759_DERIV__log,axiom,
% 5.52/5.90 ! [X2: real,B: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X2 ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_log
% 5.52/5.90 thf(fact_9760_DERIV__fun__powr,axiom,
% 5.52/5.90 ! [G: real > real,M: real,X2: real,R: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ ( G @ X2 ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real
% 5.52/5.90 @ ^ [X: real] : ( powr_real @ ( G @ X ) @ R )
% 5.52/5.90 @ ( times_times_real @ ( times_times_real @ R @ ( powr_real @ ( G @ X2 ) @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.52/5.90 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_fun_powr
% 5.52/5.90 thf(fact_9761_DERIV__powr,axiom,
% 5.52/5.90 ! [G: real > real,M: real,X2: real,F: real > real,R: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ ( G @ X2 ) )
% 5.52/5.90 => ( ( has_fi5821293074295781190e_real @ F @ R @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real
% 5.52/5.90 @ ^ [X: real] : ( powr_real @ ( G @ X ) @ ( F @ X ) )
% 5.52/5.90 @ ( times_times_real @ ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) ) @ ( plus_plus_real @ ( times_times_real @ R @ ( ln_ln_real @ ( G @ X2 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X2 ) ) @ ( G @ X2 ) ) ) )
% 5.52/5.90 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_powr
% 5.52/5.90 thf(fact_9762_DERIV__real__sqrt,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_real_sqrt
% 5.52/5.90 thf(fact_9763_DERIV__arctan,axiom,
% 5.52/5.90 ! [X2: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_arctan
% 5.52/5.90 thf(fact_9764_arsinh__real__has__field__derivative,axiom,
% 5.52/5.90 ! [X2: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % arsinh_real_has_field_derivative
% 5.52/5.90 thf(fact_9765_DERIV__real__sqrt__generic,axiom,
% 5.52/5.90 ! [X2: real,D4: real] :
% 5.52/5.90 ( ( X2 != zero_zero_real )
% 5.52/5.90 => ( ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.90 => ( D4
% 5.52/5.90 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 => ( ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.52/5.90 => ( D4
% 5.52/5.90 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_real_sqrt_generic
% 5.52/5.90 thf(fact_9766_arcosh__real__has__field__derivative,axiom,
% 5.52/5.90 ! [X2: real,A2: set_real] :
% 5.52/5.90 ( ( ord_less_real @ one_one_real @ X2 )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % arcosh_real_has_field_derivative
% 5.52/5.90 thf(fact_9767_artanh__real__has__field__derivative,axiom,
% 5.52/5.90 ! [X2: real,A2: set_real] :
% 5.52/5.90 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % artanh_real_has_field_derivative
% 5.52/5.90 thf(fact_9768_DERIV__real__root,axiom,
% 5.52/5.90 ! [N: nat,X2: real] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_real_root
% 5.52/5.90 thf(fact_9769_DERIV__arccos,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.90 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_arccos
% 5.52/5.90 thf(fact_9770_DERIV__arcsin,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.90 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_arcsin
% 5.52/5.90 thf(fact_9771_Maclaurin__all__le,axiom,
% 5.52/5.90 ! [Diff: nat > real > real,F: real > real,X2: real,N: nat] :
% 5.52/5.90 ( ( ( Diff @ zero_zero_nat )
% 5.52/5.90 = F )
% 5.52/5.90 => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.52/5.90 => ? [T4: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.52/5.90 & ( ( F @ X2 )
% 5.52/5.90 = ( plus_plus_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.90 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Maclaurin_all_le
% 5.52/5.90 thf(fact_9772_Maclaurin__all__le__objl,axiom,
% 5.52/5.90 ! [Diff: nat > real > real,F: real > real,X2: real,N: nat] :
% 5.52/5.90 ( ( ( ( Diff @ zero_zero_nat )
% 5.52/5.90 = F )
% 5.52/5.90 & ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.52/5.90 => ? [T4: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.52/5.90 & ( ( F @ X2 )
% 5.52/5.90 = ( plus_plus_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.90 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Maclaurin_all_le_objl
% 5.52/5.90 thf(fact_9773_DERIV__odd__real__root,axiom,
% 5.52/5.90 ! [N: nat,X2: real] :
% 5.52/5.90 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.90 => ( ( X2 != zero_zero_real )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_odd_real_root
% 5.52/5.90 thf(fact_9774_Maclaurin,axiom,
% 5.52/5.90 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.52/5.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ( ( Diff @ zero_zero_nat )
% 5.52/5.90 = F )
% 5.52/5.90 => ( ! [M4: nat,T4: real] :
% 5.52/5.90 ( ( ( ord_less_nat @ M4 @ N )
% 5.52/5.90 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.52/5.90 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.52/5.90 => ? [T4: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.52/5.90 & ( ord_less_real @ T4 @ H2 )
% 5.52/5.90 & ( ( F @ H2 )
% 5.52/5.90 = ( plus_plus_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.90 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Maclaurin
% 5.52/5.90 thf(fact_9775_Maclaurin2,axiom,
% 5.52/5.90 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.52/5.90 => ( ( ( Diff @ zero_zero_nat )
% 5.52/5.90 = F )
% 5.52/5.90 => ( ! [M4: nat,T4: real] :
% 5.52/5.90 ( ( ( ord_less_nat @ M4 @ N )
% 5.52/5.90 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.52/5.90 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.52/5.90 => ? [T4: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.52/5.90 & ( ord_less_eq_real @ T4 @ H2 )
% 5.52/5.90 & ( ( F @ H2 )
% 5.52/5.90 = ( plus_plus_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.90 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Maclaurin2
% 5.52/5.90 thf(fact_9776_Maclaurin__minus,axiom,
% 5.52/5.90 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.52/5.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ( ( Diff @ zero_zero_nat )
% 5.52/5.90 = F )
% 5.52/5.90 => ( ! [M4: nat,T4: real] :
% 5.52/5.90 ( ( ( ord_less_nat @ M4 @ N )
% 5.52/5.90 & ( ord_less_eq_real @ H2 @ T4 )
% 5.52/5.90 & ( ord_less_eq_real @ T4 @ zero_zero_real ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.52/5.90 => ? [T4: real] :
% 5.52/5.90 ( ( ord_less_real @ H2 @ T4 )
% 5.52/5.90 & ( ord_less_real @ T4 @ zero_zero_real )
% 5.52/5.90 & ( ( F @ H2 )
% 5.52/5.90 = ( plus_plus_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.90 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Maclaurin_minus
% 5.52/5.90 thf(fact_9777_Maclaurin__all__lt,axiom,
% 5.52/5.90 ! [Diff: nat > real > real,F: real > real,N: nat,X2: real] :
% 5.52/5.90 ( ( ( Diff @ zero_zero_nat )
% 5.52/5.90 = F )
% 5.52/5.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ( X2 != zero_zero_real )
% 5.52/5.90 => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.52/5.90 => ? [T4: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T4 ) )
% 5.52/5.90 & ( ord_less_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.52/5.90 & ( ( F @ X2 )
% 5.52/5.90 = ( plus_plus_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.90 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Maclaurin_all_lt
% 5.52/5.90 thf(fact_9778_Maclaurin__bi__le,axiom,
% 5.52/5.90 ! [Diff: nat > real > real,F: real > real,N: nat,X2: real] :
% 5.52/5.90 ( ( ( Diff @ zero_zero_nat )
% 5.52/5.90 = F )
% 5.52/5.90 => ( ! [M4: nat,T4: real] :
% 5.52/5.90 ( ( ( ord_less_nat @ M4 @ N )
% 5.52/5.90 & ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.52/5.90 => ? [T4: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.52/5.90 & ( ( F @ X2 )
% 5.52/5.90 = ( plus_plus_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.90 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Maclaurin_bi_le
% 5.52/5.90 thf(fact_9779_Taylor,axiom,
% 5.52/5.90 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X2: real] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ( ( Diff @ zero_zero_nat )
% 5.52/5.90 = F )
% 5.52/5.90 => ( ! [M4: nat,T4: real] :
% 5.52/5.90 ( ( ( ord_less_nat @ M4 @ N )
% 5.52/5.90 & ( ord_less_eq_real @ A @ T4 )
% 5.52/5.90 & ( ord_less_eq_real @ T4 @ B ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.52/5.90 => ( ( ord_less_eq_real @ A @ C )
% 5.52/5.90 => ( ( ord_less_eq_real @ C @ B )
% 5.52/5.90 => ( ( ord_less_eq_real @ A @ X2 )
% 5.52/5.90 => ( ( ord_less_eq_real @ X2 @ B )
% 5.52/5.90 => ( ( X2 != C )
% 5.52/5.90 => ? [T4: real] :
% 5.52/5.90 ( ( ( ord_less_real @ X2 @ C )
% 5.52/5.90 => ( ( ord_less_real @ X2 @ T4 )
% 5.52/5.90 & ( ord_less_real @ T4 @ C ) ) )
% 5.52/5.90 & ( ~ ( ord_less_real @ X2 @ C )
% 5.52/5.90 => ( ( ord_less_real @ C @ T4 )
% 5.52/5.90 & ( ord_less_real @ T4 @ X2 ) ) )
% 5.52/5.90 & ( ( F @ X2 )
% 5.52/5.90 = ( plus_plus_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C ) @ M3 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.90 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Taylor
% 5.52/5.90 thf(fact_9780_Taylor__up,axiom,
% 5.52/5.90 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ( ( Diff @ zero_zero_nat )
% 5.52/5.90 = F )
% 5.52/5.90 => ( ! [M4: nat,T4: real] :
% 5.52/5.90 ( ( ( ord_less_nat @ M4 @ N )
% 5.52/5.90 & ( ord_less_eq_real @ A @ T4 )
% 5.52/5.90 & ( ord_less_eq_real @ T4 @ B ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.52/5.90 => ( ( ord_less_eq_real @ A @ C )
% 5.52/5.90 => ( ( ord_less_real @ C @ B )
% 5.52/5.90 => ? [T4: real] :
% 5.52/5.90 ( ( ord_less_real @ C @ T4 )
% 5.52/5.90 & ( ord_less_real @ T4 @ B )
% 5.52/5.90 & ( ( F @ B )
% 5.52/5.90 = ( plus_plus_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M3 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.90 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Taylor_up
% 5.52/5.90 thf(fact_9781_Taylor__down,axiom,
% 5.52/5.90 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ( ( Diff @ zero_zero_nat )
% 5.52/5.90 = F )
% 5.52/5.90 => ( ! [M4: nat,T4: real] :
% 5.52/5.90 ( ( ( ord_less_nat @ M4 @ N )
% 5.52/5.90 & ( ord_less_eq_real @ A @ T4 )
% 5.52/5.90 & ( ord_less_eq_real @ T4 @ B ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.52/5.90 => ( ( ord_less_real @ A @ C )
% 5.52/5.90 => ( ( ord_less_eq_real @ C @ B )
% 5.52/5.90 => ? [T4: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ T4 )
% 5.52/5.90 & ( ord_less_real @ T4 @ C )
% 5.52/5.90 & ( ( F @ A )
% 5.52/5.90 = ( plus_plus_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M3 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ N ) )
% 5.52/5.90 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Taylor_down
% 5.52/5.90 thf(fact_9782_Maclaurin__lemma2,axiom,
% 5.52/5.90 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B4: real] :
% 5.52/5.90 ( ! [M4: nat,T4: real] :
% 5.52/5.90 ( ( ( ord_less_nat @ M4 @ N )
% 5.52/5.90 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.52/5.90 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.52/5.90 => ( ( N
% 5.52/5.90 = ( suc @ K ) )
% 5.52/5.90 => ! [M2: nat,T7: real] :
% 5.52/5.90 ( ( ( ord_less_nat @ M2 @ N )
% 5.52/5.90 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.52/5.90 & ( ord_less_eq_real @ T7 @ H2 ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real
% 5.52/5.90 @ ^ [U2: real] :
% 5.52/5.90 ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 5.52/5.90 @ ( plus_plus_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ U2 @ P4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 5.52/5.90 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 5.52/5.90 @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T7 )
% 5.52/5.90 @ ( plus_plus_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ T7 @ P4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 5.52/5.90 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) ) ) ) )
% 5.52/5.90 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Maclaurin_lemma2
% 5.52/5.90 thf(fact_9783_DERIV__arctan__series,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.52/5.90 => ( has_fi5821293074295781190e_real
% 5.52/5.90 @ ^ [X10: real] :
% 5.52/5.90 ( suminf_real
% 5.52/5.90 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X10 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.52/5.90 @ ( suminf_real
% 5.52/5.90 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( power_power_real @ X2 @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_arctan_series
% 5.52/5.90 thf(fact_9784_DERIV__power__series_H,axiom,
% 5.52/5.90 ! [R2: real,F: nat > real,X0: real] :
% 5.52/5.90 ( ! [X4: real] :
% 5.52/5.90 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 5.52/5.90 => ( summable_real
% 5.52/5.90 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( F @ N3 ) @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ ( power_power_real @ X4 @ N3 ) ) ) )
% 5.52/5.90 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.52/5.90 => ( has_fi5821293074295781190e_real
% 5.52/5.90 @ ^ [X: real] :
% 5.52/5.90 ( suminf_real
% 5.52/5.90 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X @ ( suc @ N3 ) ) ) )
% 5.52/5.90 @ ( suminf_real
% 5.52/5.90 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( F @ N3 ) @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ ( power_power_real @ X0 @ N3 ) ) )
% 5.52/5.90 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_power_series'
% 5.52/5.90 thf(fact_9785_DERIV__isconst3,axiom,
% 5.52/5.90 ! [A: real,B: real,X2: real,Y2: real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.52/5.90 => ( ( member_real @ Y2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.52/5.90 => ( ( F @ X2 )
% 5.52/5.90 = ( F @ Y2 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_isconst3
% 5.52/5.90 thf(fact_9786_UNIV__char__of__nat,axiom,
% 5.52/5.90 ( top_top_set_char
% 5.52/5.90 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % UNIV_char_of_nat
% 5.52/5.90 thf(fact_9787_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.52/5.90 ! [N: nat,J: nat,I: nat] :
% 5.52/5.90 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 5.52/5.90 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 5.52/5.90 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % nth_sorted_list_of_set_greaterThanLessThan
% 5.52/5.90 thf(fact_9788_nat__of__char__less__256,axiom,
% 5.52/5.90 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % nat_of_char_less_256
% 5.52/5.90 thf(fact_9789_range__nat__of__char,axiom,
% 5.52/5.90 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.52/5.90 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % range_nat_of_char
% 5.52/5.90 thf(fact_9790_integer__of__char__code,axiom,
% 5.52/5.90 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.52/5.90 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.52/5.90 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B72 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B62 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % integer_of_char_code
% 5.52/5.90 thf(fact_9791_String_Ochar__of__ascii__of,axiom,
% 5.52/5.90 ! [C: char] :
% 5.52/5.90 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.52/5.90 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % String.char_of_ascii_of
% 5.52/5.90 thf(fact_9792_upt__rec__numeral,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.52/5.90 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.52/5.90 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.52/5.90 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.52/5.90 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.52/5.90 = nil_nat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upt_rec_numeral
% 5.52/5.90 thf(fact_9793_upt__Suc__append,axiom,
% 5.52/5.90 ! [I: nat,J: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ I @ J )
% 5.52/5.90 => ( ( upt @ I @ ( suc @ J ) )
% 5.52/5.90 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upt_Suc_append
% 5.52/5.90 thf(fact_9794_upt__Suc,axiom,
% 5.52/5.90 ! [I: nat,J: nat] :
% 5.52/5.90 ( ( ( ord_less_eq_nat @ I @ J )
% 5.52/5.90 => ( ( upt @ I @ ( suc @ J ) )
% 5.52/5.90 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.52/5.90 & ( ~ ( ord_less_eq_nat @ I @ J )
% 5.52/5.90 => ( ( upt @ I @ ( suc @ J ) )
% 5.52/5.90 = nil_nat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upt_Suc
% 5.52/5.90 thf(fact_9795_upt__add__eq__append,axiom,
% 5.52/5.90 ! [I: nat,J: nat,K: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ I @ J )
% 5.52/5.90 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 5.52/5.90 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upt_add_eq_append
% 5.52/5.90 thf(fact_9796_upt__conv__Cons,axiom,
% 5.52/5.90 ! [I: nat,J: nat] :
% 5.52/5.90 ( ( ord_less_nat @ I @ J )
% 5.52/5.90 => ( ( upt @ I @ J )
% 5.52/5.90 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upt_conv_Cons
% 5.52/5.90 thf(fact_9797_upt__eq__Cons__conv,axiom,
% 5.52/5.90 ! [I: nat,J: nat,X2: nat,Xs2: list_nat] :
% 5.52/5.90 ( ( ( upt @ I @ J )
% 5.52/5.90 = ( cons_nat @ X2 @ Xs2 ) )
% 5.52/5.90 = ( ( ord_less_nat @ I @ J )
% 5.52/5.90 & ( I = X2 )
% 5.52/5.90 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 5.52/5.90 = Xs2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upt_eq_Cons_conv
% 5.52/5.90 thf(fact_9798_upt__rec,axiom,
% 5.52/5.90 ( upt
% 5.52/5.90 = ( ^ [I4: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J3 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upt_rec
% 5.52/5.90 thf(fact_9799_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.52/5.90 ! [I: nat,J: nat] :
% 5.52/5.90 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 5.52/5.90 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 5.52/5.90 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % sorted_list_of_set_greaterThanLessThan
% 5.52/5.90 thf(fact_9800_drop__upt,axiom,
% 5.52/5.90 ! [M: nat,I: nat,J: nat] :
% 5.52/5.90 ( ( drop_nat @ M @ ( upt @ I @ J ) )
% 5.52/5.90 = ( upt @ ( plus_plus_nat @ I @ M ) @ J ) ) ).
% 5.52/5.90
% 5.52/5.90 % drop_upt
% 5.52/5.90 thf(fact_9801_list__encode_Oelims,axiom,
% 5.52/5.90 ! [X2: list_nat,Y2: nat] :
% 5.52/5.90 ( ( ( nat_list_encode @ X2 )
% 5.52/5.90 = Y2 )
% 5.52/5.90 => ( ( ( X2 = nil_nat )
% 5.52/5.90 => ( Y2 != zero_zero_nat ) )
% 5.52/5.90 => ~ ! [X4: nat,Xs3: list_nat] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( cons_nat @ X4 @ Xs3 ) )
% 5.52/5.90 => ( Y2
% 5.52/5.90 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % list_encode.elims
% 5.52/5.90 thf(fact_9802_list__encode_Osimps_I2_J,axiom,
% 5.52/5.90 ! [X2: nat,Xs2: list_nat] :
% 5.52/5.90 ( ( nat_list_encode @ ( cons_nat @ X2 @ Xs2 ) )
% 5.52/5.90 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X2 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % list_encode.simps(2)
% 5.52/5.90 thf(fact_9803_upto__aux__rec,axiom,
% 5.52/5.90 ( upto_aux
% 5.52/5.90 = ( ^ [I4: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I4 ) @ Js @ ( upto_aux @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upto_aux_rec
% 5.52/5.90 thf(fact_9804_upto__rec__numeral_I4_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.90 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.90 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.52/5.90 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.90 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.90 = nil_int ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upto_rec_numeral(4)
% 5.52/5.90 thf(fact_9805_upto__rec__numeral_I3_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.90 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.90 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.52/5.90 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.90 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.90 = nil_int ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upto_rec_numeral(3)
% 5.52/5.90 thf(fact_9806_upto__Nil,axiom,
% 5.52/5.90 ! [I: int,J: int] :
% 5.52/5.90 ( ( ( upto @ I @ J )
% 5.52/5.90 = nil_int )
% 5.52/5.90 = ( ord_less_int @ J @ I ) ) ).
% 5.52/5.90
% 5.52/5.90 % upto_Nil
% 5.52/5.90 thf(fact_9807_upto__Nil2,axiom,
% 5.52/5.90 ! [I: int,J: int] :
% 5.52/5.90 ( ( nil_int
% 5.52/5.90 = ( upto @ I @ J ) )
% 5.52/5.90 = ( ord_less_int @ J @ I ) ) ).
% 5.52/5.90
% 5.52/5.90 % upto_Nil2
% 5.52/5.90 thf(fact_9808_upto__empty,axiom,
% 5.52/5.90 ! [J: int,I: int] :
% 5.52/5.90 ( ( ord_less_int @ J @ I )
% 5.52/5.90 => ( ( upto @ I @ J )
% 5.52/5.90 = nil_int ) ) ).
% 5.52/5.90
% 5.52/5.90 % upto_empty
% 5.52/5.90 thf(fact_9809_upto__rec__numeral_I1_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.90 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.90 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.52/5.90 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.90 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.52/5.90 = nil_int ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upto_rec_numeral(1)
% 5.52/5.90 thf(fact_9810_upto__rec__numeral_I2_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.90 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.90 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.52/5.90 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.90 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.52/5.90 = nil_int ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % upto_rec_numeral(2)
% 5.52/5.90 thf(fact_9811_sorted__wrt__upto,axiom,
% 5.52/5.90 ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 5.52/5.90
% 5.52/5.90 % sorted_wrt_upto
% 5.52/5.90 thf(fact_9812_hd__upt,axiom,
% 5.52/5.90 ! [I: nat,J: nat] :
% 5.52/5.90 ( ( ord_less_nat @ I @ J )
% 5.52/5.90 => ( ( hd_nat @ ( upt @ I @ J ) )
% 5.52/5.90 = I ) ) ).
% 5.52/5.90
% 5.52/5.90 % hd_upt
% 5.52/5.90 thf(fact_9813_LIM__fun__less__zero,axiom,
% 5.52/5.90 ! [F: real > real,L: real,C: real] :
% 5.52/5.90 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.52/5.90 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.52/5.90 => ? [R3: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.52/5.90 & ! [X6: real] :
% 5.52/5.90 ( ( ( X6 != C )
% 5.52/5.90 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X6 ) ) @ R3 ) )
% 5.52/5.90 => ( ord_less_real @ ( F @ X6 ) @ zero_zero_real ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % LIM_fun_less_zero
% 5.52/5.90 thf(fact_9814_LIM__fun__not__zero,axiom,
% 5.52/5.90 ! [F: real > real,L: real,C: real] :
% 5.52/5.90 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.52/5.90 => ( ( L != zero_zero_real )
% 5.52/5.90 => ? [R3: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.52/5.90 & ! [X6: real] :
% 5.52/5.90 ( ( ( X6 != C )
% 5.52/5.90 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X6 ) ) @ R3 ) )
% 5.52/5.90 => ( ( F @ X6 )
% 5.52/5.90 != zero_zero_real ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % LIM_fun_not_zero
% 5.52/5.90 thf(fact_9815_LIM__fun__gt__zero,axiom,
% 5.52/5.90 ! [F: real > real,L: real,C: real] :
% 5.52/5.90 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.52/5.90 => ? [R3: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.52/5.90 & ! [X6: real] :
% 5.52/5.90 ( ( ( X6 != C )
% 5.52/5.90 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X6 ) ) @ R3 ) )
% 5.52/5.90 => ( ord_less_real @ zero_zero_real @ ( F @ X6 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % LIM_fun_gt_zero
% 5.52/5.90 thf(fact_9816_LIM__cos__div__sin,axiom,
% 5.52/5.90 ( filterlim_real_real
% 5.52/5.90 @ ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.52/5.90 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.52/5.90
% 5.52/5.90 % LIM_cos_div_sin
% 5.52/5.90 thf(fact_9817_summable__Leibniz_I2_J,axiom,
% 5.52/5.90 ! [A: nat > real] :
% 5.52/5.90 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.52/5.90 => ( ( topolo6980174941875973593q_real @ A )
% 5.52/5.90 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.52/5.90 => ! [N7: nat] :
% 5.52/5.90 ( member_real
% 5.52/5.90 @ ( suminf_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.52/5.90 @ ( set_or1222579329274155063t_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % summable_Leibniz(2)
% 5.52/5.90 thf(fact_9818_summable__Leibniz_I3_J,axiom,
% 5.52/5.90 ! [A: nat > real] :
% 5.52/5.90 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.52/5.90 => ( ( topolo6980174941875973593q_real @ A )
% 5.52/5.90 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.52/5.90 => ! [N7: nat] :
% 5.52/5.90 ( member_real
% 5.52/5.90 @ ( suminf_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.52/5.90 @ ( set_or1222579329274155063t_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) )
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % summable_Leibniz(3)
% 5.52/5.90 thf(fact_9819_mult__nat__right__at__top,axiom,
% 5.52/5.90 ! [C: nat] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.52/5.90 => ( filterlim_nat_nat
% 5.52/5.90 @ ^ [X: nat] : ( times_times_nat @ X @ C )
% 5.52/5.90 @ at_top_nat
% 5.52/5.90 @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % mult_nat_right_at_top
% 5.52/5.90 thf(fact_9820_mult__nat__left__at__top,axiom,
% 5.52/5.90 ! [C: nat] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.52/5.90 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % mult_nat_left_at_top
% 5.52/5.90 thf(fact_9821_LIMSEQ__root,axiom,
% 5.52/5.90 ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] : ( root @ N3 @ ( semiri5074537144036343181t_real @ N3 ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.52/5.90 @ at_top_nat ) ).
% 5.52/5.90
% 5.52/5.90 % LIMSEQ_root
% 5.52/5.90 thf(fact_9822_LIMSEQ__inverse__zero,axiom,
% 5.52/5.90 ! [X8: nat > real] :
% 5.52/5.90 ( ! [R3: real] :
% 5.52/5.90 ? [N8: nat] :
% 5.52/5.90 ! [N2: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ N8 @ N2 )
% 5.52/5.90 => ( ord_less_real @ R3 @ ( X8 @ N2 ) ) )
% 5.52/5.90 => ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] : ( inverse_inverse_real @ ( X8 @ N3 ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.52/5.90 @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % LIMSEQ_inverse_zero
% 5.52/5.90 thf(fact_9823_LIMSEQ__root__const,axiom,
% 5.52/5.90 ! [C: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ C )
% 5.52/5.90 => ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] : ( root @ N3 @ C )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.52/5.90 @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % LIMSEQ_root_const
% 5.52/5.90 thf(fact_9824_increasing__LIMSEQ,axiom,
% 5.52/5.90 ! [F: nat > real,L: real] :
% 5.52/5.90 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ L )
% 5.52/5.90 => ( ! [E2: real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.52/5.90 => ? [N7: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N7 ) @ E2 ) ) )
% 5.52/5.90 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % increasing_LIMSEQ
% 5.52/5.90 thf(fact_9825_LIMSEQ__realpow__zero,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.90 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.52/5.90 => ( filterlim_nat_real @ ( power_power_real @ X2 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % LIMSEQ_realpow_zero
% 5.52/5.90 thf(fact_9826_LIMSEQ__divide__realpow__zero,axiom,
% 5.52/5.90 ! [X2: real,A: real] :
% 5.52/5.90 ( ( ord_less_real @ one_one_real @ X2 )
% 5.52/5.90 => ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] : ( divide_divide_real @ A @ ( power_power_real @ X2 @ N3 ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.52/5.90 @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % LIMSEQ_divide_realpow_zero
% 5.52/5.90 thf(fact_9827_LIMSEQ__abs__realpow__zero2,axiom,
% 5.52/5.90 ! [C: real] :
% 5.52/5.90 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.52/5.90 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % LIMSEQ_abs_realpow_zero2
% 5.52/5.90 thf(fact_9828_LIMSEQ__abs__realpow__zero,axiom,
% 5.52/5.90 ! [C: real] :
% 5.52/5.90 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.52/5.90 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % LIMSEQ_abs_realpow_zero
% 5.52/5.90 thf(fact_9829_LIMSEQ__inverse__realpow__zero,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_real @ one_one_real @ X2 )
% 5.52/5.90 => ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] : ( inverse_inverse_real @ ( power_power_real @ X2 @ N3 ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.52/5.90 @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % LIMSEQ_inverse_realpow_zero
% 5.52/5.90 thf(fact_9830_tendsto__exp__limit__sequentially,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N3 ) ) ) @ N3 )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.52/5.90 @ at_top_nat ) ).
% 5.52/5.90
% 5.52/5.90 % tendsto_exp_limit_sequentially
% 5.52/5.90 thf(fact_9831_summable__Leibniz_I1_J,axiom,
% 5.52/5.90 ! [A: nat > real] :
% 5.52/5.90 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.52/5.90 => ( ( topolo6980174941875973593q_real @ A )
% 5.52/5.90 => ( summable_real
% 5.52/5.90 @ ^ [N3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( A @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % summable_Leibniz(1)
% 5.52/5.90 thf(fact_9832_summable,axiom,
% 5.52/5.90 ! [A: nat > real] :
% 5.52/5.90 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.52/5.90 => ( summable_real
% 5.52/5.90 @ ^ [N3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( A @ N3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % summable
% 5.52/5.90 thf(fact_9833_cos__diff__limit__1,axiom,
% 5.52/5.90 ! [Theta: nat > real,Theta2: real] :
% 5.52/5.90 ( ( filterlim_nat_real
% 5.52/5.90 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.52/5.90 @ at_top_nat )
% 5.52/5.90 => ~ ! [K3: nat > int] :
% 5.52/5.90 ~ ( filterlim_nat_real
% 5.52/5.90 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.52/5.90 @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % cos_diff_limit_1
% 5.52/5.90 thf(fact_9834_cos__limit__1,axiom,
% 5.52/5.90 ! [Theta: nat > real] :
% 5.52/5.90 ( ( filterlim_nat_real
% 5.52/5.90 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.52/5.90 @ at_top_nat )
% 5.52/5.90 => ? [K3: nat > int] :
% 5.52/5.90 ( filterlim_nat_real
% 5.52/5.90 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.52/5.90 @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % cos_limit_1
% 5.52/5.90 thf(fact_9835_summable__Leibniz_I4_J,axiom,
% 5.52/5.90 ! [A: nat > real] :
% 5.52/5.90 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.52/5.90 => ( ( topolo6980174941875973593q_real @ A )
% 5.52/5.90 => ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] :
% 5.52/5.90 ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real
% 5.52/5.90 @ ( suminf_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.52/5.90 @ at_top_nat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % summable_Leibniz(4)
% 5.52/5.90 thf(fact_9836_zeroseq__arctan__series,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.52/5.90 => ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.52/5.90 @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % zeroseq_arctan_series
% 5.52/5.90 thf(fact_9837_summable__Leibniz_H_I3_J,axiom,
% 5.52/5.90 ! [A: nat > real] :
% 5.52/5.90 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.52/5.90 => ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] :
% 5.52/5.90 ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real
% 5.52/5.90 @ ( suminf_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.52/5.90 @ at_top_nat ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % summable_Leibniz'(3)
% 5.52/5.90 thf(fact_9838_summable__Leibniz_H_I2_J,axiom,
% 5.52/5.90 ! [A: nat > real,N: nat] :
% 5.52/5.90 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.52/5.90 => ( ord_less_eq_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.90 @ ( suminf_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % summable_Leibniz'(2)
% 5.52/5.90 thf(fact_9839_sums__alternating__upper__lower,axiom,
% 5.52/5.90 ! [A: nat > real] :
% 5.52/5.90 ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.52/5.90 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.52/5.90 => ? [L4: real] :
% 5.52/5.90 ( ! [N7: nat] :
% 5.52/5.90 ( ord_less_eq_real
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 5.52/5.90 @ L4 )
% 5.52/5.90 & ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] :
% 5.52/5.90 ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ L4 )
% 5.52/5.90 @ at_top_nat )
% 5.52/5.90 & ! [N7: nat] :
% 5.52/5.90 ( ord_less_eq_real @ L4
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) )
% 5.52/5.90 & ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] :
% 5.52/5.90 ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ L4 )
% 5.52/5.90 @ at_top_nat ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % sums_alternating_upper_lower
% 5.52/5.90 thf(fact_9840_summable__Leibniz_I5_J,axiom,
% 5.52/5.90 ! [A: nat > real] :
% 5.52/5.90 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.52/5.90 => ( ( topolo6980174941875973593q_real @ A )
% 5.52/5.90 => ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] :
% 5.52/5.90 ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real
% 5.52/5.90 @ ( suminf_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.52/5.90 @ at_top_nat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % summable_Leibniz(5)
% 5.52/5.90 thf(fact_9841_summable__Leibniz_H_I5_J,axiom,
% 5.52/5.90 ! [A: nat > real] :
% 5.52/5.90 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.52/5.90 => ( filterlim_nat_real
% 5.52/5.90 @ ^ [N3: nat] :
% 5.52/5.90 ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real
% 5.52/5.90 @ ( suminf_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.52/5.90 @ at_top_nat ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % summable_Leibniz'(5)
% 5.52/5.90 thf(fact_9842_summable__Leibniz_H_I4_J,axiom,
% 5.52/5.90 ! [A: nat > real,N: nat] :
% 5.52/5.90 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.52/5.90 => ( ord_less_eq_real
% 5.52/5.90 @ ( suminf_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.52/5.90 @ ( groups6591440286371151544t_real
% 5.52/5.90 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.52/5.90 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % summable_Leibniz'(4)
% 5.52/5.90 thf(fact_9843_sequentially__offset,axiom,
% 5.52/5.90 ! [P: nat > $o,K: nat] :
% 5.52/5.90 ( ( eventually_nat @ P @ at_top_nat )
% 5.52/5.90 => ( eventually_nat
% 5.52/5.90 @ ^ [I4: nat] : ( P @ ( plus_plus_nat @ I4 @ K ) )
% 5.52/5.90 @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % sequentially_offset
% 5.52/5.90 thf(fact_9844_eventually__sequentially__seg,axiom,
% 5.52/5.90 ! [P: nat > $o,K: nat] :
% 5.52/5.90 ( ( eventually_nat
% 5.52/5.90 @ ^ [N3: nat] : ( P @ ( plus_plus_nat @ N3 @ K ) )
% 5.52/5.90 @ at_top_nat )
% 5.52/5.90 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % eventually_sequentially_seg
% 5.52/5.90 thf(fact_9845_sqrt__at__top,axiom,
% 5.52/5.90 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 5.52/5.90
% 5.52/5.90 % sqrt_at_top
% 5.52/5.90 thf(fact_9846_eventually__at__left__real,axiom,
% 5.52/5.90 ! [B: real,A: real] :
% 5.52/5.90 ( ( ord_less_real @ B @ A )
% 5.52/5.90 => ( eventually_real
% 5.52/5.90 @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ B @ A ) )
% 5.52/5.90 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % eventually_at_left_real
% 5.52/5.90 thf(fact_9847_tendsto__power__div__exp__0,axiom,
% 5.52/5.90 ! [K: nat] :
% 5.52/5.90 ( filterlim_real_real
% 5.52/5.90 @ ^ [X: real] : ( divide_divide_real @ ( power_power_real @ X @ K ) @ ( exp_real @ X ) )
% 5.52/5.90 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.52/5.90 @ at_top_real ) ).
% 5.52/5.90
% 5.52/5.90 % tendsto_power_div_exp_0
% 5.52/5.90 thf(fact_9848_filterlim__tan__at__left,axiom,
% 5.52/5.90 filterlim_real_real @ tan_real @ at_top_real @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( set_or5984915006950818249n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % filterlim_tan_at_left
% 5.52/5.90 thf(fact_9849_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.52/5.90 ! [B: real,F: real > real,Flim: real] :
% 5.52/5.90 ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ B @ X4 )
% 5.52/5.90 => ? [Y4: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.52/5.90 & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 5.52/5.90 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.52/5.90 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_neg_imp_decreasing_at_top
% 5.52/5.90 thf(fact_9850_tendsto__arctan__at__top,axiom,
% 5.52/5.90 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.52/5.90
% 5.52/5.90 % tendsto_arctan_at_top
% 5.52/5.90 thf(fact_9851_eventually__sequentiallyI,axiom,
% 5.52/5.90 ! [C: nat,P: nat > $o] :
% 5.52/5.90 ( ! [X4: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ C @ X4 )
% 5.52/5.90 => ( P @ X4 ) )
% 5.52/5.90 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % eventually_sequentiallyI
% 5.52/5.90 thf(fact_9852_eventually__sequentially,axiom,
% 5.52/5.90 ! [P: nat > $o] :
% 5.52/5.90 ( ( eventually_nat @ P @ at_top_nat )
% 5.52/5.90 = ( ? [N6: nat] :
% 5.52/5.90 ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.52/5.90 => ( P @ N3 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % eventually_sequentially
% 5.52/5.90 thf(fact_9853_le__sequentially,axiom,
% 5.52/5.90 ! [F5: filter_nat] :
% 5.52/5.90 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 5.52/5.90 = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F5 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % le_sequentially
% 5.52/5.90 thf(fact_9854_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.52/5.90 ! [I: nat,J: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 5.52/5.90 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 5.52/5.90 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % sorted_list_of_set_greaterThanAtMost
% 5.52/5.90 thf(fact_9855_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.52/5.90 ! [N: nat,J: nat,I: nat] :
% 5.52/5.90 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 5.52/5.90 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 5.52/5.90 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % nth_sorted_list_of_set_greaterThanAtMost
% 5.52/5.90 thf(fact_9856_filterlim__pow__at__bot__even,axiom,
% 5.52/5.90 ! [N: nat,F: real > real,F5: filter_real] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.52/5.90 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.90 => ( filterlim_real_real
% 5.52/5.90 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 5.52/5.90 @ at_top_real
% 5.52/5.90 @ F5 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % filterlim_pow_at_bot_even
% 5.52/5.90 thf(fact_9857_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.52/5.90 ! [B: real,F: real > real,Flim: real] :
% 5.52/5.90 ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ X4 @ B )
% 5.52/5.90 => ? [Y4: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.52/5.90 & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 5.52/5.90 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.52/5.90 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_pos_imp_increasing_at_bot
% 5.52/5.90 thf(fact_9858_filterlim__pow__at__bot__odd,axiom,
% 5.52/5.90 ! [N: nat,F: real > real,F5: filter_real] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.52/5.90 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.52/5.90 => ( filterlim_real_real
% 5.52/5.90 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 5.52/5.90 @ at_bot_real
% 5.52/5.90 @ F5 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % filterlim_pow_at_bot_odd
% 5.52/5.90 thf(fact_9859_tendsto__arctan__at__bot,axiom,
% 5.52/5.90 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.52/5.90
% 5.52/5.90 % tendsto_arctan_at_bot
% 5.52/5.90 thf(fact_9860_Bseq__realpow,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.90 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.52/5.90 => ( bfun_nat_real @ ( power_power_real @ X2 ) @ at_top_nat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Bseq_realpow
% 5.52/5.90 thf(fact_9861_filterlim__tan__at__right,axiom,
% 5.52/5.90 filterlim_real_real @ tan_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % filterlim_tan_at_right
% 5.52/5.90 thf(fact_9862_eventually__at__right__real,axiom,
% 5.52/5.90 ! [A: real,B: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( eventually_real
% 5.52/5.90 @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.52/5.90 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % eventually_at_right_real
% 5.52/5.90 thf(fact_9863_Real_Opositive_Orep__eq,axiom,
% 5.52/5.90 ( positive2
% 5.52/5.90 = ( ^ [X: real] :
% 5.52/5.90 ? [R5: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.52/5.90 & ? [K2: nat] :
% 5.52/5.90 ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K2 @ N3 )
% 5.52/5.90 => ( ord_less_rat @ R5 @ ( rep_real2 @ X @ N3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Real.positive.rep_eq
% 5.52/5.90 thf(fact_9864_inverse__real__def,axiom,
% 5.52/5.90 ( inverse_inverse_real
% 5.52/5.90 = ( map_fu7146612038024189824t_real @ rep_real2 @ real2
% 5.52/5.90 @ ^ [X7: nat > rat] :
% 5.52/5.90 ( if_nat_rat @ ( vanishes @ X7 )
% 5.52/5.90 @ ^ [N3: nat] : zero_zero_rat
% 5.52/5.90 @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X7 @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % inverse_real_def
% 5.52/5.90 thf(fact_9865_uminus__real__def,axiom,
% 5.52/5.90 ( uminus_uminus_real
% 5.52/5.90 = ( map_fu7146612038024189824t_real @ rep_real2 @ real2
% 5.52/5.90 @ ^ [X7: nat > rat,N3: nat] : ( uminus_uminus_rat @ ( X7 @ N3 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % uminus_real_def
% 5.52/5.90 thf(fact_9866_inf__enat__def,axiom,
% 5.52/5.90 inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 5.52/5.90
% 5.52/5.90 % inf_enat_def
% 5.52/5.90 thf(fact_9867_inf__nat__def,axiom,
% 5.52/5.90 inf_inf_nat = ord_min_nat ).
% 5.52/5.90
% 5.52/5.90 % inf_nat_def
% 5.52/5.90 thf(fact_9868_times__real__def,axiom,
% 5.52/5.90 ( times_times_real
% 5.52/5.90 = ( map_fu1532550112467129777l_real @ rep_real2 @ ( map_fu7146612038024189824t_real @ rep_real2 @ real2 )
% 5.52/5.90 @ ^ [X7: nat > rat,Y7: nat > rat,N3: nat] : ( times_times_rat @ ( X7 @ N3 ) @ ( Y7 @ N3 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % times_real_def
% 5.52/5.90 thf(fact_9869_plus__real__def,axiom,
% 5.52/5.90 ( plus_plus_real
% 5.52/5.90 = ( map_fu1532550112467129777l_real @ rep_real2 @ ( map_fu7146612038024189824t_real @ rep_real2 @ real2 )
% 5.52/5.90 @ ^ [X7: nat > rat,Y7: nat > rat,N3: nat] : ( plus_plus_rat @ ( X7 @ N3 ) @ ( Y7 @ N3 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % plus_real_def
% 5.52/5.90 thf(fact_9870_isCont__real__sqrt,axiom,
% 5.52/5.90 ! [X2: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ sqrt ) ).
% 5.52/5.90
% 5.52/5.90 % isCont_real_sqrt
% 5.52/5.90 thf(fact_9871_isCont__real__root,axiom,
% 5.52/5.90 ! [X2: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ ( root @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % isCont_real_root
% 5.52/5.90 thf(fact_9872_isCont__inverse__function2,axiom,
% 5.52/5.90 ! [A: real,X2: real,B: real,G: real > real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ X2 )
% 5.52/5.90 => ( ( ord_less_real @ X2 @ B )
% 5.52/5.90 => ( ! [Z3: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ A @ Z3 )
% 5.52/5.90 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.52/5.90 => ( ( G @ ( F @ Z3 ) )
% 5.52/5.90 = Z3 ) ) )
% 5.52/5.90 => ( ! [Z3: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ A @ Z3 )
% 5.52/5.90 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.52/5.90 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 5.52/5.90 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X2 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % isCont_inverse_function2
% 5.52/5.90 thf(fact_9873_isCont__arcosh,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_real @ one_one_real @ X2 )
% 5.52/5.90 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.52/5.90
% 5.52/5.90 % isCont_arcosh
% 5.52/5.90 thf(fact_9874_DERIV__inverse__function,axiom,
% 5.52/5.90 ! [F: real > real,D4: real,G: real > real,X2: real,A: real,B: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X2 ) @ top_top_set_real ) )
% 5.52/5.90 => ( ( D4 != zero_zero_real )
% 5.52/5.90 => ( ( ord_less_real @ A @ X2 )
% 5.52/5.90 => ( ( ord_less_real @ X2 @ B )
% 5.52/5.90 => ( ! [Y3: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ Y3 )
% 5.52/5.90 => ( ( ord_less_real @ Y3 @ B )
% 5.52/5.90 => ( ( F @ ( G @ Y3 ) )
% 5.52/5.90 = Y3 ) ) )
% 5.52/5.90 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ G )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_inverse_function
% 5.52/5.90 thf(fact_9875_isCont__arccos,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.90 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.52/5.90 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arccos ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % isCont_arccos
% 5.52/5.90 thf(fact_9876_isCont__arcsin,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.90 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.52/5.90 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % isCont_arcsin
% 5.52/5.90 thf(fact_9877_LIM__less__bound,axiom,
% 5.52/5.90 ! [B: real,X2: real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ B @ X2 )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ B @ X2 ) )
% 5.52/5.90 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.52/5.90 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ F )
% 5.52/5.90 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X2 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % LIM_less_bound
% 5.52/5.90 thf(fact_9878_isCont__artanh,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.52/5.90 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.52/5.90 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % isCont_artanh
% 5.52/5.90 thf(fact_9879_isCont__inverse__function,axiom,
% 5.52/5.90 ! [D2: real,X2: real,G: real > real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.52/5.90 => ( ! [Z3: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X2 ) ) @ D2 )
% 5.52/5.90 => ( ( G @ ( F @ Z3 ) )
% 5.52/5.90 = Z3 ) )
% 5.52/5.90 => ( ! [Z3: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X2 ) ) @ D2 )
% 5.52/5.90 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 5.52/5.90 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X2 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % isCont_inverse_function
% 5.52/5.90 thf(fact_9880_GMVT_H,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ! [Z3: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ A @ Z3 )
% 5.52/5.90 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.52/5.90 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 5.52/5.90 => ( ! [Z3: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ A @ Z3 )
% 5.52/5.90 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.52/5.90 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 5.52/5.90 => ( ! [Z3: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ Z3 )
% 5.52/5.90 => ( ( ord_less_real @ Z3 @ B )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 5.52/5.90 => ( ! [Z3: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ Z3 )
% 5.52/5.90 => ( ( ord_less_real @ Z3 @ B )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 5.52/5.90 => ? [C2: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ C2 )
% 5.52/5.90 & ( ord_less_real @ C2 @ B )
% 5.52/5.90 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 5.52/5.90 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C2 ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % GMVT'
% 5.52/5.90 thf(fact_9881_GMVT,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ( ord_less_eq_real @ A @ X4 )
% 5.52/5.90 & ( ord_less_eq_real @ X4 @ B ) )
% 5.52/5.90 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ( ord_less_real @ A @ X4 )
% 5.52/5.90 & ( ord_less_real @ X4 @ B ) )
% 5.52/5.90 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ( ord_less_eq_real @ A @ X4 )
% 5.52/5.90 & ( ord_less_eq_real @ X4 @ B ) )
% 5.52/5.90 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G ) )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ( ord_less_real @ A @ X4 )
% 5.52/5.90 & ( ord_less_real @ X4 @ B ) )
% 5.52/5.90 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.52/5.90 => ? [G_c: real,F_c: real,C2: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.52/5.90 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.52/5.90 & ( ord_less_real @ A @ C2 )
% 5.52/5.90 & ( ord_less_real @ C2 @ B )
% 5.52/5.90 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.52/5.90 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % GMVT
% 5.52/5.90 thf(fact_9882_mono__Suc,axiom,
% 5.52/5.90 order_mono_nat_nat @ suc ).
% 5.52/5.90
% 5.52/5.90 % mono_Suc
% 5.52/5.90 thf(fact_9883_mono__times__nat,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % mono_times_nat
% 5.52/5.90 thf(fact_9884_mono__ge2__power__minus__self,axiom,
% 5.52/5.90 ! [K: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.52/5.90 => ( order_mono_nat_nat
% 5.52/5.90 @ ^ [M3: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M3 ) @ M3 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % mono_ge2_power_minus_self
% 5.52/5.90 thf(fact_9885_MVT,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ X4 )
% 5.52/5.90 => ( ( ord_less_real @ X4 @ B )
% 5.52/5.90 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.52/5.90 => ? [L4: real,Z3: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ Z3 )
% 5.52/5.90 & ( ord_less_real @ Z3 @ B )
% 5.52/5.90 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) )
% 5.52/5.90 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.52/5.90 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % MVT
% 5.52/5.90 thf(fact_9886_Rolle__deriv,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ( ( F @ A )
% 5.52/5.90 = ( F @ B ) )
% 5.52/5.90 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ X4 )
% 5.52/5.90 => ( ( ord_less_real @ X4 @ B )
% 5.52/5.90 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.52/5.90 => ? [Z3: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ Z3 )
% 5.52/5.90 & ( ord_less_real @ Z3 @ B )
% 5.52/5.90 & ( ( F4 @ Z3 )
% 5.52/5.90 = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rolle_deriv
% 5.52/5.90 thf(fact_9887_mvt,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ X4 )
% 5.52/5.90 => ( ( ord_less_real @ X4 @ B )
% 5.52/5.90 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.52/5.90 => ~ ! [Xi: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ Xi )
% 5.52/5.90 => ( ( ord_less_real @ Xi @ B )
% 5.52/5.90 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.52/5.90 != ( F4 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % mvt
% 5.52/5.90 thf(fact_9888_DERIV__isconst__end,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ X4 )
% 5.52/5.90 => ( ( ord_less_real @ X4 @ B )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.52/5.90 => ( ( F @ B )
% 5.52/5.90 = ( F @ A ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_isconst_end
% 5.52/5.90 thf(fact_9889_DERIV__neg__imp__decreasing__open,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ X4 )
% 5.52/5.90 => ( ( ord_less_real @ X4 @ B )
% 5.52/5.90 => ? [Y4: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.52/5.90 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 5.52/5.90 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.52/5.90 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_neg_imp_decreasing_open
% 5.52/5.90 thf(fact_9890_DERIV__pos__imp__increasing__open,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ X4 )
% 5.52/5.90 => ( ( ord_less_real @ X4 @ B )
% 5.52/5.90 => ? [Y4: real] :
% 5.52/5.90 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.52/5.90 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 5.52/5.90 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.52/5.90 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_pos_imp_increasing_open
% 5.52/5.90 thf(fact_9891_DERIV__isconst2,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real,X2: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ X4 )
% 5.52/5.90 => ( ( ord_less_real @ X4 @ B )
% 5.52/5.90 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.52/5.90 => ( ( ord_less_eq_real @ A @ X2 )
% 5.52/5.90 => ( ( ord_less_eq_real @ X2 @ B )
% 5.52/5.90 => ( ( F @ X2 )
% 5.52/5.90 = ( F @ A ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DERIV_isconst2
% 5.52/5.90 thf(fact_9892_Rolle,axiom,
% 5.52/5.90 ! [A: real,B: real,F: real > real] :
% 5.52/5.90 ( ( ord_less_real @ A @ B )
% 5.52/5.90 => ( ( ( F @ A )
% 5.52/5.90 = ( F @ B ) )
% 5.52/5.90 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.52/5.90 => ( ! [X4: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ X4 )
% 5.52/5.90 => ( ( ord_less_real @ X4 @ B )
% 5.52/5.90 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.52/5.90 => ? [Z3: real] :
% 5.52/5.90 ( ( ord_less_real @ A @ Z3 )
% 5.52/5.90 & ( ord_less_real @ Z3 @ B )
% 5.52/5.90 & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rolle
% 5.52/5.90 thf(fact_9893_inj__sgn__power,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( inj_on_real_real
% 5.52/5.90 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.52/5.90 @ top_top_set_real ) ) ).
% 5.52/5.90
% 5.52/5.90 % inj_sgn_power
% 5.52/5.90 thf(fact_9894_log__inj,axiom,
% 5.52/5.90 ! [B: real] :
% 5.52/5.90 ( ( ord_less_real @ one_one_real @ B )
% 5.52/5.90 => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % log_inj
% 5.52/5.90 thf(fact_9895_inj__Suc,axiom,
% 5.52/5.90 ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 5.52/5.90
% 5.52/5.90 % inj_Suc
% 5.52/5.90 thf(fact_9896_inj__on__diff__nat,axiom,
% 5.52/5.90 ! [N4: set_nat,K: nat] :
% 5.52/5.90 ( ! [N2: nat] :
% 5.52/5.90 ( ( member_nat @ N2 @ N4 )
% 5.52/5.90 => ( ord_less_eq_nat @ K @ N2 ) )
% 5.52/5.90 => ( inj_on_nat_nat
% 5.52/5.90 @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ K )
% 5.52/5.90 @ N4 ) ) ).
% 5.52/5.90
% 5.52/5.90 % inj_on_diff_nat
% 5.52/5.90 thf(fact_9897_powr__real__of__int_H,axiom,
% 5.52/5.90 ! [X2: real,N: int] :
% 5.52/5.90 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.90 => ( ( ( X2 != zero_zero_real )
% 5.52/5.90 | ( ord_less_int @ zero_zero_int @ N ) )
% 5.52/5.90 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.52/5.90 = ( power_int_real @ X2 @ N ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % powr_real_of_int'
% 5.52/5.90 thf(fact_9898_inj__on__char__of__nat,axiom,
% 5.52/5.90 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % inj_on_char_of_nat
% 5.52/5.90 thf(fact_9899_atLeastLessThan__add__Un,axiom,
% 5.52/5.90 ! [I: nat,J: nat,K: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ I @ J )
% 5.52/5.90 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 5.52/5.90 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % atLeastLessThan_add_Un
% 5.52/5.90 thf(fact_9900_Code__Target__Int_Onegative__def,axiom,
% 5.52/5.90 ( code_Target_negative
% 5.52/5.90 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 5.52/5.90
% 5.52/5.90 % Code_Target_Int.negative_def
% 5.52/5.90 thf(fact_9901_sup__nat__def,axiom,
% 5.52/5.90 sup_sup_nat = ord_max_nat ).
% 5.52/5.90
% 5.52/5.90 % sup_nat_def
% 5.52/5.90 thf(fact_9902_sup__enat__def,axiom,
% 5.52/5.90 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.52/5.90
% 5.52/5.90 % sup_enat_def
% 5.52/5.90 thf(fact_9903_pos__deriv__imp__strict__mono,axiom,
% 5.52/5.90 ! [F: real > real,F4: real > real] :
% 5.52/5.90 ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.52/5.90 => ( ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( F4 @ X4 ) )
% 5.52/5.90 => ( order_7092887310737990675l_real @ F ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % pos_deriv_imp_strict_mono
% 5.52/5.90 thf(fact_9904_list__encode_Opelims,axiom,
% 5.52/5.90 ! [X2: list_nat,Y2: nat] :
% 5.52/5.90 ( ( ( nat_list_encode @ X2 )
% 5.52/5.90 = Y2 )
% 5.52/5.90 => ( ( accp_list_nat @ nat_list_encode_rel @ X2 )
% 5.52/5.90 => ( ( ( X2 = nil_nat )
% 5.52/5.90 => ( ( Y2 = zero_zero_nat )
% 5.52/5.90 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.52/5.90 => ~ ! [X4: nat,Xs3: list_nat] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( cons_nat @ X4 @ Xs3 ) )
% 5.52/5.90 => ( ( Y2
% 5.52/5.90 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 5.52/5.90 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X4 @ Xs3 ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % list_encode.pelims
% 5.52/5.90 thf(fact_9905_strict__mono__imp__increasing,axiom,
% 5.52/5.90 ! [F: nat > nat,N: nat] :
% 5.52/5.90 ( ( order_5726023648592871131at_nat @ F )
% 5.52/5.90 => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % strict_mono_imp_increasing
% 5.52/5.90 thf(fact_9906_inverse__real_Oabs__eq,axiom,
% 5.52/5.90 ! [X2: nat > rat] :
% 5.52/5.90 ( ( realrel @ X2 @ X2 )
% 5.52/5.90 => ( ( inverse_inverse_real @ ( real2 @ X2 ) )
% 5.52/5.90 = ( real2
% 5.52/5.90 @ ( if_nat_rat @ ( vanishes @ X2 )
% 5.52/5.90 @ ^ [N3: nat] : zero_zero_rat
% 5.52/5.90 @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X2 @ N3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % inverse_real.abs_eq
% 5.52/5.90 thf(fact_9907_real_Oabs__induct,axiom,
% 5.52/5.90 ! [P: real > $o,X2: real] :
% 5.52/5.90 ( ! [Y3: nat > rat] :
% 5.52/5.90 ( ( realrel @ Y3 @ Y3 )
% 5.52/5.90 => ( P @ ( real2 @ Y3 ) ) )
% 5.52/5.90 => ( P @ X2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % real.abs_induct
% 5.52/5.90 thf(fact_9908_zero__real_Orsp,axiom,
% 5.52/5.90 ( realrel
% 5.52/5.90 @ ^ [N3: nat] : zero_zero_rat
% 5.52/5.90 @ ^ [N3: nat] : zero_zero_rat ) ).
% 5.52/5.90
% 5.52/5.90 % zero_real.rsp
% 5.52/5.90 thf(fact_9909_one__real_Orsp,axiom,
% 5.52/5.90 ( realrel
% 5.52/5.90 @ ^ [N3: nat] : one_one_rat
% 5.52/5.90 @ ^ [N3: nat] : one_one_rat ) ).
% 5.52/5.90
% 5.52/5.90 % one_real.rsp
% 5.52/5.90 thf(fact_9910_realrel__refl,axiom,
% 5.52/5.90 ! [X8: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( realrel @ X8 @ X8 ) ) ).
% 5.52/5.90
% 5.52/5.90 % realrel_refl
% 5.52/5.90 thf(fact_9911_uminus__real_Oabs__eq,axiom,
% 5.52/5.90 ! [X2: nat > rat] :
% 5.52/5.90 ( ( realrel @ X2 @ X2 )
% 5.52/5.90 => ( ( uminus_uminus_real @ ( real2 @ X2 ) )
% 5.52/5.90 = ( real2
% 5.52/5.90 @ ^ [N3: nat] : ( uminus_uminus_rat @ ( X2 @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % uminus_real.abs_eq
% 5.52/5.90 thf(fact_9912_plus__real_Oabs__eq,axiom,
% 5.52/5.90 ! [Xa2: nat > rat,X2: nat > rat] :
% 5.52/5.90 ( ( realrel @ Xa2 @ Xa2 )
% 5.52/5.90 => ( ( realrel @ X2 @ X2 )
% 5.52/5.90 => ( ( plus_plus_real @ ( real2 @ Xa2 ) @ ( real2 @ X2 ) )
% 5.52/5.90 = ( real2
% 5.52/5.90 @ ^ [N3: nat] : ( plus_plus_rat @ ( Xa2 @ N3 ) @ ( X2 @ N3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % plus_real.abs_eq
% 5.52/5.90 thf(fact_9913_times__real_Oabs__eq,axiom,
% 5.52/5.90 ! [Xa2: nat > rat,X2: nat > rat] :
% 5.52/5.90 ( ( realrel @ Xa2 @ Xa2 )
% 5.52/5.90 => ( ( realrel @ X2 @ X2 )
% 5.52/5.90 => ( ( times_times_real @ ( real2 @ Xa2 ) @ ( real2 @ X2 ) )
% 5.52/5.90 = ( real2
% 5.52/5.90 @ ^ [N3: nat] : ( times_times_rat @ ( Xa2 @ N3 ) @ ( X2 @ N3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % times_real.abs_eq
% 5.52/5.90 thf(fact_9914_realrelI,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y6: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ( cauchy @ Y6 )
% 5.52/5.90 => ( ( vanishes
% 5.52/5.90 @ ^ [N3: nat] : ( minus_minus_rat @ ( X8 @ N3 ) @ ( Y6 @ N3 ) ) )
% 5.52/5.90 => ( realrel @ X8 @ Y6 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % realrelI
% 5.52/5.90 thf(fact_9915_realrel__def,axiom,
% 5.52/5.90 ( realrel
% 5.52/5.90 = ( ^ [X7: nat > rat,Y7: nat > rat] :
% 5.52/5.90 ( ( cauchy @ X7 )
% 5.52/5.90 & ( cauchy @ Y7 )
% 5.52/5.90 & ( vanishes
% 5.52/5.90 @ ^ [N3: nat] : ( minus_minus_rat @ ( X7 @ N3 ) @ ( Y7 @ N3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % realrel_def
% 5.52/5.90 thf(fact_9916_Real_Opositive_Oabs__eq,axiom,
% 5.52/5.90 ! [X2: nat > rat] :
% 5.52/5.90 ( ( realrel @ X2 @ X2 )
% 5.52/5.90 => ( ( positive2 @ ( real2 @ X2 ) )
% 5.52/5.90 = ( ? [R5: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.52/5.90 & ? [K2: nat] :
% 5.52/5.90 ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K2 @ N3 )
% 5.52/5.90 => ( ord_less_rat @ R5 @ ( X2 @ N3 ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Real.positive.abs_eq
% 5.52/5.90 thf(fact_9917_Field__natLeq__on,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( ( field_nat
% 5.52/5.90 @ ( collec3392354462482085612at_nat
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( ( ord_less_nat @ X @ N )
% 5.52/5.90 & ( ord_less_nat @ Y @ N )
% 5.52/5.90 & ( ord_less_eq_nat @ X @ Y ) ) ) ) )
% 5.52/5.90 = ( collect_nat
% 5.52/5.90 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Field_natLeq_on
% 5.52/5.90 thf(fact_9918_cr__real__def,axiom,
% 5.52/5.90 ( cr_real
% 5.52/5.90 = ( ^ [X: nat > rat,Y: real] :
% 5.52/5.90 ( ( realrel @ X @ X )
% 5.52/5.90 & ( ( real2 @ X )
% 5.52/5.90 = Y ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % cr_real_def
% 5.52/5.90 thf(fact_9919_natLess__def,axiom,
% 5.52/5.90 ( bNF_Ca8459412986667044542atLess
% 5.52/5.90 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % natLess_def
% 5.52/5.90 thf(fact_9920_Real_Opositive_Orsp,axiom,
% 5.52/5.90 ( bNF_re728719798268516973at_o_o @ realrel
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [X7: nat > rat] :
% 5.52/5.90 ? [R5: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.52/5.90 & ? [K2: nat] :
% 5.52/5.90 ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K2 @ N3 )
% 5.52/5.90 => ( ord_less_rat @ R5 @ ( X7 @ N3 ) ) ) )
% 5.52/5.90 @ ^ [X7: nat > rat] :
% 5.52/5.90 ? [R5: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.52/5.90 & ? [K2: nat] :
% 5.52/5.90 ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K2 @ N3 )
% 5.52/5.90 => ( ord_less_rat @ R5 @ ( X7 @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Real.positive.rsp
% 5.52/5.90 thf(fact_9921_less__eq__natural_Orsp,axiom,
% 5.52/5.90 ( bNF_re578469030762574527_nat_o
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ( bNF_re4705727531993890431at_o_o
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.52/5.90 @ ord_less_eq_nat
% 5.52/5.90 @ ord_less_eq_nat ) ).
% 5.52/5.90
% 5.52/5.90 % less_eq_natural.rsp
% 5.52/5.90 thf(fact_9922_less__integer_Orsp,axiom,
% 5.52/5.90 ( bNF_re3403563459893282935_int_o
% 5.52/5.90 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.52/5.90 @ ( bNF_re5089333283451836215nt_o_o
% 5.52/5.90 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.52/5.90 @ ord_less_int
% 5.52/5.90 @ ord_less_int ) ).
% 5.52/5.90
% 5.52/5.90 % less_integer.rsp
% 5.52/5.90 thf(fact_9923_less__natural_Orsp,axiom,
% 5.52/5.90 ( bNF_re578469030762574527_nat_o
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ( bNF_re4705727531993890431at_o_o
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.52/5.90 @ ord_less_nat
% 5.52/5.90 @ ord_less_nat ) ).
% 5.52/5.90
% 5.52/5.90 % less_natural.rsp
% 5.52/5.90 thf(fact_9924_times__natural_Orsp,axiom,
% 5.52/5.90 ( bNF_re1345281282404953727at_nat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ( bNF_re5653821019739307937at_nat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.52/5.90 @ times_times_nat
% 5.52/5.90 @ times_times_nat ) ).
% 5.52/5.90
% 5.52/5.90 % times_natural.rsp
% 5.52/5.90 thf(fact_9925_sub_Orsp,axiom,
% 5.52/5.90 ( bNF_re8402795839162346335um_int
% 5.52/5.90 @ ^ [Y5: num,Z4: num] : ( Y5 = Z4 )
% 5.52/5.90 @ ( bNF_re1822329894187522285nt_int
% 5.52/5.90 @ ^ [Y5: num,Z4: num] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.52/5.90 @ ^ [M3: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) )
% 5.52/5.90 @ ^ [M3: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % sub.rsp
% 5.52/5.90 thf(fact_9926_divide__integer_Orsp,axiom,
% 5.52/5.90 ( bNF_re711492959462206631nt_int
% 5.52/5.90 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.52/5.90 @ ( bNF_re4712519889275205905nt_int
% 5.52/5.90 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.52/5.90 @ divide_divide_int
% 5.52/5.90 @ divide_divide_int ) ).
% 5.52/5.90
% 5.52/5.90 % divide_integer.rsp
% 5.52/5.90 thf(fact_9927_divide__natural_Orsp,axiom,
% 5.52/5.90 ( bNF_re1345281282404953727at_nat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ( bNF_re5653821019739307937at_nat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.52/5.90 @ divide_divide_nat
% 5.52/5.90 @ divide_divide_nat ) ).
% 5.52/5.90
% 5.52/5.90 % divide_natural.rsp
% 5.52/5.90 thf(fact_9928_plus__natural_Orsp,axiom,
% 5.52/5.90 ( bNF_re1345281282404953727at_nat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ( bNF_re5653821019739307937at_nat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.52/5.90 @ plus_plus_nat
% 5.52/5.90 @ plus_plus_nat ) ).
% 5.52/5.90
% 5.52/5.90 % plus_natural.rsp
% 5.52/5.90 thf(fact_9929_plus__real_Orsp,axiom,
% 5.52/5.90 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.52/5.90 @ ^ [X7: nat > rat,Y7: nat > rat,N3: nat] : ( plus_plus_rat @ ( X7 @ N3 ) @ ( Y7 @ N3 ) )
% 5.52/5.90 @ ^ [X7: nat > rat,Y7: nat > rat,N3: nat] : ( plus_plus_rat @ ( X7 @ N3 ) @ ( Y7 @ N3 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % plus_real.rsp
% 5.52/5.90 thf(fact_9930_uminus__real_Orsp,axiom,
% 5.52/5.90 ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 5.52/5.90 @ ^ [X7: nat > rat,N3: nat] : ( uminus_uminus_rat @ ( X7 @ N3 ) )
% 5.52/5.90 @ ^ [X7: nat > rat,N3: nat] : ( uminus_uminus_rat @ ( X7 @ N3 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % uminus_real.rsp
% 5.52/5.90 thf(fact_9931_times__real_Orsp,axiom,
% 5.52/5.90 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.52/5.90 @ ^ [X7: nat > rat,Y7: nat > rat,N3: nat] : ( times_times_rat @ ( X7 @ N3 ) @ ( Y7 @ N3 ) )
% 5.52/5.90 @ ^ [X7: nat > rat,Y7: nat > rat,N3: nat] : ( times_times_rat @ ( X7 @ N3 ) @ ( Y7 @ N3 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % times_real.rsp
% 5.52/5.90 thf(fact_9932_inverse__real_Orsp,axiom,
% 5.52/5.90 ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 5.52/5.90 @ ^ [X7: nat > rat] :
% 5.52/5.90 ( if_nat_rat @ ( vanishes @ X7 )
% 5.52/5.90 @ ^ [N3: nat] : zero_zero_rat
% 5.52/5.90 @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X7 @ N3 ) ) )
% 5.52/5.90 @ ^ [X7: nat > rat] :
% 5.52/5.90 ( if_nat_rat @ ( vanishes @ X7 )
% 5.52/5.90 @ ^ [N3: nat] : zero_zero_rat
% 5.52/5.90 @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X7 @ N3 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % inverse_real.rsp
% 5.52/5.90 thf(fact_9933_Real_Opositive_Otransfer,axiom,
% 5.52/5.90 ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [X7: nat > rat] :
% 5.52/5.90 ? [R5: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.52/5.90 & ? [K2: nat] :
% 5.52/5.90 ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K2 @ N3 )
% 5.52/5.90 => ( ord_less_rat @ R5 @ ( X7 @ N3 ) ) ) )
% 5.52/5.90 @ positive2 ) ).
% 5.52/5.90
% 5.52/5.90 % Real.positive.transfer
% 5.52/5.90 thf(fact_9934_Rat_Opositive_Otransfer,axiom,
% 5.52/5.90 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 5.52/5.90 @ positive ) ).
% 5.52/5.90
% 5.52/5.90 % Rat.positive.transfer
% 5.52/5.90 thf(fact_9935_real_Orel__eq__transfer,axiom,
% 5.52/5.90 ( bNF_re4521903465945308077real_o @ pcr_real
% 5.52/5.90 @ ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.52/5.90 @ realrel
% 5.52/5.90 @ ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) ) ).
% 5.52/5.90
% 5.52/5.90 % real.rel_eq_transfer
% 5.52/5.90 thf(fact_9936_real_Opcr__cr__eq,axiom,
% 5.52/5.90 pcr_real = cr_real ).
% 5.52/5.90
% 5.52/5.90 % real.pcr_cr_eq
% 5.52/5.90 thf(fact_9937_zero__real_Otransfer,axiom,
% 5.52/5.90 ( pcr_real
% 5.52/5.90 @ ^ [N3: nat] : zero_zero_rat
% 5.52/5.90 @ zero_zero_real ) ).
% 5.52/5.90
% 5.52/5.90 % zero_real.transfer
% 5.52/5.90 thf(fact_9938_one__real_Otransfer,axiom,
% 5.52/5.90 ( pcr_real
% 5.52/5.90 @ ^ [N3: nat] : one_one_rat
% 5.52/5.90 @ one_one_real ) ).
% 5.52/5.90
% 5.52/5.90 % one_real.transfer
% 5.52/5.90 thf(fact_9939_cr__real__eq,axiom,
% 5.52/5.90 ( pcr_real
% 5.52/5.90 = ( ^ [X: nat > rat,Y: real] :
% 5.52/5.90 ( ( cauchy @ X )
% 5.52/5.90 & ( ( real2 @ X )
% 5.52/5.90 = Y ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % cr_real_eq
% 5.52/5.90 thf(fact_9940_uminus__real_Otransfer,axiom,
% 5.52/5.90 ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 5.52/5.90 @ ^ [X7: nat > rat,N3: nat] : ( uminus_uminus_rat @ ( X7 @ N3 ) )
% 5.52/5.90 @ uminus_uminus_real ) ).
% 5.52/5.90
% 5.52/5.90 % uminus_real.transfer
% 5.52/5.90 thf(fact_9941_plus__real_Otransfer,axiom,
% 5.52/5.90 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.52/5.90 @ ^ [X7: nat > rat,Y7: nat > rat,N3: nat] : ( plus_plus_rat @ ( X7 @ N3 ) @ ( Y7 @ N3 ) )
% 5.52/5.90 @ plus_plus_real ) ).
% 5.52/5.90
% 5.52/5.90 % plus_real.transfer
% 5.52/5.90 thf(fact_9942_times__real_Otransfer,axiom,
% 5.52/5.90 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.52/5.90 @ ^ [X7: nat > rat,Y7: nat > rat,N3: nat] : ( times_times_rat @ ( X7 @ N3 ) @ ( Y7 @ N3 ) )
% 5.52/5.90 @ times_times_real ) ).
% 5.52/5.90
% 5.52/5.90 % times_real.transfer
% 5.52/5.90 thf(fact_9943_inverse__real_Otransfer,axiom,
% 5.52/5.90 ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 5.52/5.90 @ ^ [X7: nat > rat] :
% 5.52/5.90 ( if_nat_rat @ ( vanishes @ X7 )
% 5.52/5.90 @ ^ [N3: nat] : zero_zero_rat
% 5.52/5.90 @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X7 @ N3 ) ) )
% 5.52/5.90 @ inverse_inverse_real ) ).
% 5.52/5.90
% 5.52/5.90 % inverse_real.transfer
% 5.52/5.90 thf(fact_9944_times__int_Otransfer,axiom,
% 5.52/5.90 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.52/5.90 @ ( produc27273713700761075at_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc2626176000494625587at_nat
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) )
% 5.52/5.90 @ times_times_int ) ).
% 5.52/5.90
% 5.52/5.90 % times_int.transfer
% 5.52/5.90 thf(fact_9945_zero__int_Otransfer,axiom,
% 5.52/5.90 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 5.52/5.90
% 5.52/5.90 % zero_int.transfer
% 5.52/5.90 thf(fact_9946_int__transfer,axiom,
% 5.52/5.90 ( bNF_re6830278522597306478at_int
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ pcr_int
% 5.52/5.90 @ ^ [N3: nat] : ( product_Pair_nat_nat @ N3 @ zero_zero_nat )
% 5.52/5.90 @ semiri1314217659103216013at_int ) ).
% 5.52/5.90
% 5.52/5.90 % int_transfer
% 5.52/5.90 thf(fact_9947_uminus__int_Otransfer,axiom,
% 5.52/5.90 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 5.52/5.90 @ ( produc2626176000494625587at_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) )
% 5.52/5.90 @ uminus_uminus_int ) ).
% 5.52/5.90
% 5.52/5.90 % uminus_int.transfer
% 5.52/5.90 thf(fact_9948_one__int_Otransfer,axiom,
% 5.52/5.90 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 5.52/5.90
% 5.52/5.90 % one_int.transfer
% 5.52/5.90 thf(fact_9949_less__int_Otransfer,axiom,
% 5.52/5.90 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.52/5.90 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.52/5.90 @ ( produc8739625826339149834_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.52/5.90 @ ord_less_int ) ).
% 5.52/5.90
% 5.52/5.90 % less_int.transfer
% 5.52/5.90 thf(fact_9950_less__eq__int_Otransfer,axiom,
% 5.52/5.90 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.52/5.90 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.52/5.90 @ ( produc8739625826339149834_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.52/5.90 @ ord_less_eq_int ) ).
% 5.52/5.90
% 5.52/5.90 % less_eq_int.transfer
% 5.52/5.90 thf(fact_9951_plus__int_Otransfer,axiom,
% 5.52/5.90 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.52/5.90 @ ( produc27273713700761075at_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc2626176000494625587at_nat
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 5.52/5.90 @ plus_plus_int ) ).
% 5.52/5.90
% 5.52/5.90 % plus_int.transfer
% 5.52/5.90 thf(fact_9952_minus__int_Otransfer,axiom,
% 5.52/5.90 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.52/5.90 @ ( produc27273713700761075at_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc2626176000494625587at_nat
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) )
% 5.52/5.90 @ minus_minus_int ) ).
% 5.52/5.90
% 5.52/5.90 % minus_int.transfer
% 5.52/5.90 thf(fact_9953_of__rat__dense,axiom,
% 5.52/5.90 ! [X2: real,Y2: real] :
% 5.52/5.90 ( ( ord_less_real @ X2 @ Y2 )
% 5.52/5.90 => ? [Q3: rat] :
% 5.52/5.90 ( ( ord_less_real @ X2 @ ( field_7254667332652039916t_real @ Q3 ) )
% 5.52/5.90 & ( ord_less_real @ ( field_7254667332652039916t_real @ Q3 ) @ Y2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % of_rat_dense
% 5.52/5.90 thf(fact_9954_of__rat__Real,axiom,
% 5.52/5.90 ( field_7254667332652039916t_real
% 5.52/5.90 = ( ^ [X: rat] :
% 5.52/5.90 ( real2
% 5.52/5.90 @ ^ [N3: nat] : X ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % of_rat_Real
% 5.52/5.90 thf(fact_9955_wf__less,axiom,
% 5.52/5.90 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % wf_less
% 5.52/5.90 thf(fact_9956_less__RealD,axiom,
% 5.52/5.90 ! [Y6: nat > rat,X2: real] :
% 5.52/5.90 ( ( cauchy @ Y6 )
% 5.52/5.90 => ( ( ord_less_real @ X2 @ ( real2 @ Y6 ) )
% 5.52/5.90 => ? [N2: nat] : ( ord_less_real @ X2 @ ( field_7254667332652039916t_real @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_RealD
% 5.52/5.90 thf(fact_9957_Real__leI,axiom,
% 5.52/5.90 ! [X8: nat > rat,Y2: real] :
% 5.52/5.90 ( ( cauchy @ X8 )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ ( field_7254667332652039916t_real @ ( X8 @ N2 ) ) @ Y2 )
% 5.52/5.90 => ( ord_less_eq_real @ ( real2 @ X8 ) @ Y2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Real_leI
% 5.52/5.90 thf(fact_9958_le__RealI,axiom,
% 5.52/5.90 ! [Y6: nat > rat,X2: real] :
% 5.52/5.90 ( ( cauchy @ Y6 )
% 5.52/5.90 => ( ! [N2: nat] : ( ord_less_eq_real @ X2 @ ( field_7254667332652039916t_real @ ( Y6 @ N2 ) ) )
% 5.52/5.90 => ( ord_less_eq_real @ X2 @ ( real2 @ Y6 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % le_RealI
% 5.52/5.90 thf(fact_9959_times__int_Orsp,axiom,
% 5.52/5.90 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.52/5.90 @ ( produc27273713700761075at_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc2626176000494625587at_nat
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) )
% 5.52/5.90 @ ( produc27273713700761075at_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc2626176000494625587at_nat
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % times_int.rsp
% 5.52/5.90 thf(fact_9960_intrel__iff,axiom,
% 5.52/5.90 ! [X2: nat,Y2: nat,U: nat,V: nat] :
% 5.52/5.90 ( ( intrel @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ ( product_Pair_nat_nat @ U @ V ) )
% 5.52/5.90 = ( ( plus_plus_nat @ X2 @ V )
% 5.52/5.90 = ( plus_plus_nat @ U @ Y2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % intrel_iff
% 5.52/5.90 thf(fact_9961_zero__int_Orsp,axiom,
% 5.52/5.90 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.52/5.90
% 5.52/5.90 % zero_int.rsp
% 5.52/5.90 thf(fact_9962_uminus__int_Orsp,axiom,
% 5.52/5.90 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 5.52/5.90 @ ( produc2626176000494625587at_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) )
% 5.52/5.90 @ ( produc2626176000494625587at_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % uminus_int.rsp
% 5.52/5.90 thf(fact_9963_one__int_Orsp,axiom,
% 5.52/5.90 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.52/5.90
% 5.52/5.90 % one_int.rsp
% 5.52/5.90 thf(fact_9964_intrel__def,axiom,
% 5.52/5.90 ( intrel
% 5.52/5.90 = ( produc8739625826339149834_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [U2: nat,V4: nat] :
% 5.52/5.90 ( ( plus_plus_nat @ X @ V4 )
% 5.52/5.90 = ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % intrel_def
% 5.52/5.90 thf(fact_9965_less__int_Orsp,axiom,
% 5.52/5.90 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.52/5.90 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.52/5.90 @ ( produc8739625826339149834_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.52/5.90 @ ( produc8739625826339149834_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_int.rsp
% 5.52/5.90 thf(fact_9966_less__eq__int_Orsp,axiom,
% 5.52/5.90 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.52/5.90 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.52/5.90 @ ( produc8739625826339149834_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.52/5.90 @ ( produc8739625826339149834_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_eq_int.rsp
% 5.52/5.90 thf(fact_9967_minus__int_Orsp,axiom,
% 5.52/5.90 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.52/5.90 @ ( produc27273713700761075at_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc2626176000494625587at_nat
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) )
% 5.52/5.90 @ ( produc27273713700761075at_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc2626176000494625587at_nat
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % minus_int.rsp
% 5.52/5.90 thf(fact_9968_plus__int_Orsp,axiom,
% 5.52/5.90 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.52/5.90 @ ( produc27273713700761075at_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc2626176000494625587at_nat
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 5.52/5.90 @ ( produc27273713700761075at_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc2626176000494625587at_nat
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % plus_int.rsp
% 5.52/5.90 thf(fact_9969_le__enumerate,axiom,
% 5.52/5.90 ! [S3: set_nat,N: nat] :
% 5.52/5.90 ( ~ ( finite_finite_nat @ S3 )
% 5.52/5.90 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % le_enumerate
% 5.52/5.90 thf(fact_9970_finite__le__enumerate,axiom,
% 5.52/5.90 ! [S3: set_nat,N: nat] :
% 5.52/5.90 ( ( finite_finite_nat @ S3 )
% 5.52/5.90 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 5.52/5.90 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % finite_le_enumerate
% 5.52/5.90 thf(fact_9971_DeMoivre2,axiom,
% 5.52/5.90 ! [R: real,A: real,N: nat] :
% 5.52/5.90 ( ( power_power_complex @ ( rcis @ R @ A ) @ N )
% 5.52/5.90 = ( rcis @ ( power_power_real @ R @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % DeMoivre2
% 5.52/5.90 thf(fact_9972_Least__eq__0,axiom,
% 5.52/5.90 ! [P: nat > $o] :
% 5.52/5.90 ( ( P @ zero_zero_nat )
% 5.52/5.90 => ( ( ord_Least_nat @ P )
% 5.52/5.90 = zero_zero_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % Least_eq_0
% 5.52/5.90 thf(fact_9973_Least__Suc2,axiom,
% 5.52/5.90 ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 5.52/5.90 ( ( P @ N )
% 5.52/5.90 => ( ( Q @ M )
% 5.52/5.90 => ( ~ ( P @ zero_zero_nat )
% 5.52/5.90 => ( ! [K3: nat] :
% 5.52/5.90 ( ( P @ ( suc @ K3 ) )
% 5.52/5.90 = ( Q @ K3 ) )
% 5.52/5.90 => ( ( ord_Least_nat @ P )
% 5.52/5.90 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Least_Suc2
% 5.52/5.90 thf(fact_9974_Least__Suc,axiom,
% 5.52/5.90 ! [P: nat > $o,N: nat] :
% 5.52/5.90 ( ( P @ N )
% 5.52/5.90 => ( ~ ( P @ zero_zero_nat )
% 5.52/5.90 => ( ( ord_Least_nat @ P )
% 5.52/5.90 = ( suc
% 5.52/5.90 @ ( ord_Least_nat
% 5.52/5.90 @ ^ [M3: nat] : ( P @ ( suc @ M3 ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Least_Suc
% 5.52/5.90 thf(fact_9975_Sup__real__def,axiom,
% 5.52/5.90 ( comple1385675409528146559p_real
% 5.52/5.90 = ( ^ [X7: set_real] :
% 5.52/5.90 ( ord_Least_real
% 5.52/5.90 @ ^ [Z2: real] :
% 5.52/5.90 ! [X: real] :
% 5.52/5.90 ( ( member_real @ X @ X7 )
% 5.52/5.90 => ( ord_less_eq_real @ X @ Z2 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Sup_real_def
% 5.52/5.90 thf(fact_9976_uniformity__complex__def,axiom,
% 5.52/5.90 ( topolo896644834953643431omplex
% 5.52/5.90 = ( comple8358262395181532106omplex
% 5.52/5.90 @ ( image_5971271580939081552omplex
% 5.52/5.90 @ ^ [E3: real] :
% 5.52/5.90 ( princi3496590319149328850omplex
% 5.52/5.90 @ ( collec8663557070575231912omplex
% 5.52/5.90 @ ( produc6771430404735790350plex_o
% 5.52/5.90 @ ^ [X: complex,Y: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X @ Y ) @ E3 ) ) ) )
% 5.52/5.90 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % uniformity_complex_def
% 5.52/5.90 thf(fact_9977_uniformity__real__def,axiom,
% 5.52/5.90 ( topolo1511823702728130853y_real
% 5.52/5.90 = ( comple2936214249959783750l_real
% 5.52/5.90 @ ( image_2178119161166701260l_real
% 5.52/5.90 @ ^ [E3: real] :
% 5.52/5.90 ( princi6114159922880469582l_real
% 5.52/5.90 @ ( collec3799799289383736868l_real
% 5.52/5.90 @ ( produc5414030515140494994real_o
% 5.52/5.90 @ ^ [X: real,Y: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X @ Y ) @ E3 ) ) ) )
% 5.52/5.90 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % uniformity_real_def
% 5.52/5.90 thf(fact_9978_eventually__prod__sequentially,axiom,
% 5.52/5.90 ! [P: product_prod_nat_nat > $o] :
% 5.52/5.90 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 5.52/5.90 = ( ? [N6: nat] :
% 5.52/5.90 ! [M3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ N6 @ M3 )
% 5.52/5.90 => ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.52/5.90 => ( P @ ( product_Pair_nat_nat @ N3 @ M3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % eventually_prod_sequentially
% 5.52/5.90 thf(fact_9979_pairs__le__eq__Sigma,axiom,
% 5.52/5.90 ! [M: nat] :
% 5.52/5.90 ( ( collec3392354462482085612at_nat
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ M ) ) )
% 5.52/5.90 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 5.52/5.90 @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % pairs_le_eq_Sigma
% 5.52/5.90 thf(fact_9980_of__nat__eq__id,axiom,
% 5.52/5.90 semiri1316708129612266289at_nat = id_nat ).
% 5.52/5.90
% 5.52/5.90 % of_nat_eq_id
% 5.52/5.90 thf(fact_9981_set__decode__div__2,axiom,
% 5.52/5.90 ! [X2: nat] :
% 5.52/5.90 ( ( nat_set_decode @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.52/5.90 = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % set_decode_div_2
% 5.52/5.90 thf(fact_9982_set__encode__vimage__Suc,axiom,
% 5.52/5.90 ! [A2: set_nat] :
% 5.52/5.90 ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A2 ) )
% 5.52/5.90 = ( divide_divide_nat @ ( nat_set_encode @ A2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % set_encode_vimage_Suc
% 5.52/5.90 thf(fact_9983_Real_Opositive__def,axiom,
% 5.52/5.90 ( positive2
% 5.52/5.90 = ( map_fu1856342031159181835at_o_o @ rep_real2 @ id_o
% 5.52/5.90 @ ^ [X7: nat > rat] :
% 5.52/5.90 ? [R5: rat] :
% 5.52/5.90 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.52/5.90 & ? [K2: nat] :
% 5.52/5.90 ! [N3: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ K2 @ N3 )
% 5.52/5.90 => ( ord_less_rat @ R5 @ ( X7 @ N3 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Real.positive_def
% 5.52/5.90 thf(fact_9984_Rat_Opositive__def,axiom,
% 5.52/5.90 ( positive
% 5.52/5.90 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.52/5.90 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rat.positive_def
% 5.52/5.90 thf(fact_9985_Restr__natLeq,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.52/5.90 @ ( produc457027306803732586at_nat
% 5.52/5.90 @ ( collect_nat
% 5.52/5.90 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) )
% 5.52/5.90 @ ^ [Uu3: nat] :
% 5.52/5.90 ( collect_nat
% 5.52/5.90 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) )
% 5.52/5.90 = ( collec3392354462482085612at_nat
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( ( ord_less_nat @ X @ N )
% 5.52/5.90 & ( ord_less_nat @ Y @ N )
% 5.52/5.90 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Restr_natLeq
% 5.52/5.90 thf(fact_9986_natLeq__def,axiom,
% 5.52/5.90 ( bNF_Ca8665028551170535155natLeq
% 5.52/5.90 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % natLeq_def
% 5.52/5.90 thf(fact_9987_Restr__natLeq2,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.52/5.90 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 5.52/5.90 @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 5.52/5.90 = ( collec3392354462482085612at_nat
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( ( ord_less_nat @ X @ N )
% 5.52/5.90 & ( ord_less_nat @ Y @ N )
% 5.52/5.90 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Restr_natLeq2
% 5.52/5.90 thf(fact_9988_natLeq__underS__less,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 5.52/5.90 = ( collect_nat
% 5.52/5.90 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % natLeq_underS_less
% 5.52/5.90 thf(fact_9989_Rat_Opositive_Orsp,axiom,
% 5.52/5.90 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 5.52/5.90 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rat.positive.rsp
% 5.52/5.90 thf(fact_9990_Rat_Opositive_Oabs__eq,axiom,
% 5.52/5.90 ! [X2: product_prod_int_int] :
% 5.52/5.90 ( ( ratrel @ X2 @ X2 )
% 5.52/5.90 => ( ( positive @ ( abs_Rat @ X2 ) )
% 5.52/5.90 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rat.positive.abs_eq
% 5.52/5.90 thf(fact_9991_last__upt,axiom,
% 5.52/5.90 ! [I: nat,J: nat] :
% 5.52/5.90 ( ( ord_less_nat @ I @ J )
% 5.52/5.90 => ( ( last_nat @ ( upt @ I @ J ) )
% 5.52/5.90 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % last_upt
% 5.52/5.90 thf(fact_9992_natLeq__on__wo__rel,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( bNF_We3818239936649020644el_nat
% 5.52/5.90 @ ( collec3392354462482085612at_nat
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( ( ord_less_nat @ X @ N )
% 5.52/5.90 & ( ord_less_nat @ Y @ N )
% 5.52/5.90 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % natLeq_on_wo_rel
% 5.52/5.90 thf(fact_9993_pred__nat__trancl__eq__le,axiom,
% 5.52/5.90 ! [M: nat,N: nat] :
% 5.52/5.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.52/5.90 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % pred_nat_trancl_eq_le
% 5.52/5.90 thf(fact_9994_less__eq,axiom,
% 5.52/5.90 ! [M: nat,N: nat] :
% 5.52/5.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.52/5.90 = ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_eq
% 5.52/5.90 thf(fact_9995_Bseq__monoseq__convergent_H__inc,axiom,
% 5.52/5.90 ! [F: nat > real,M7: nat] :
% 5.52/5.90 ( ( bfun_nat_real
% 5.52/5.90 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ M7 ) )
% 5.52/5.90 @ at_top_nat )
% 5.52/5.90 => ( ! [M4: nat,N2: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ M7 @ M4 )
% 5.52/5.90 => ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.90 => ( ord_less_eq_real @ ( F @ M4 ) @ ( F @ N2 ) ) ) )
% 5.52/5.90 => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Bseq_monoseq_convergent'_inc
% 5.52/5.90 thf(fact_9996_Bseq__mono__convergent,axiom,
% 5.52/5.90 ! [X8: nat > real] :
% 5.52/5.90 ( ( bfun_nat_real @ X8 @ at_top_nat )
% 5.52/5.90 => ( ! [M4: nat,N2: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.90 => ( ord_less_eq_real @ ( X8 @ M4 ) @ ( X8 @ N2 ) ) )
% 5.52/5.90 => ( topolo7531315842566124627t_real @ X8 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Bseq_mono_convergent
% 5.52/5.90 thf(fact_9997_convergent__realpow,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.52/5.90 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.52/5.90 => ( topolo7531315842566124627t_real @ ( power_power_real @ X2 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % convergent_realpow
% 5.52/5.90 thf(fact_9998_Bseq__monoseq__convergent_H__dec,axiom,
% 5.52/5.90 ! [F: nat > real,M7: nat] :
% 5.52/5.90 ( ( bfun_nat_real
% 5.52/5.90 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ M7 ) )
% 5.52/5.90 @ at_top_nat )
% 5.52/5.90 => ( ! [M4: nat,N2: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ M7 @ M4 )
% 5.52/5.90 => ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.52/5.90 => ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ M4 ) ) ) )
% 5.52/5.90 => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Bseq_monoseq_convergent'_dec
% 5.52/5.90 thf(fact_9999_pair__lessI2,axiom,
% 5.52/5.90 ! [A: nat,B: nat,S: nat,T: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ A @ B )
% 5.52/5.90 => ( ( ord_less_nat @ S @ T )
% 5.52/5.90 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % pair_lessI2
% 5.52/5.90 thf(fact_10000_pair__less__iff1,axiom,
% 5.52/5.90 ! [X2: nat,Y2: nat,Z: nat] :
% 5.52/5.90 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ ( product_Pair_nat_nat @ X2 @ Z ) ) @ fun_pair_less )
% 5.52/5.90 = ( ord_less_nat @ Y2 @ Z ) ) ).
% 5.52/5.90
% 5.52/5.90 % pair_less_iff1
% 5.52/5.90 thf(fact_10001_pair__lessI1,axiom,
% 5.52/5.90 ! [A: nat,B: nat,S: nat,T: nat] :
% 5.52/5.90 ( ( ord_less_nat @ A @ B )
% 5.52/5.90 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ).
% 5.52/5.90
% 5.52/5.90 % pair_lessI1
% 5.52/5.90 thf(fact_10002_pair__leqI2,axiom,
% 5.52/5.90 ! [A: nat,B: nat,S: nat,T: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ A @ B )
% 5.52/5.90 => ( ( ord_less_eq_nat @ S @ T )
% 5.52/5.90 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % pair_leqI2
% 5.52/5.90 thf(fact_10003_pair__leqI1,axiom,
% 5.52/5.90 ! [A: nat,B: nat,S: nat,T: nat] :
% 5.52/5.90 ( ( ord_less_nat @ A @ B )
% 5.52/5.90 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ).
% 5.52/5.90
% 5.52/5.90 % pair_leqI1
% 5.52/5.90 thf(fact_10004_bot__nat__0_Oordering__top__axioms,axiom,
% 5.52/5.90 ( ordering_top_nat
% 5.52/5.90 @ ^ [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X )
% 5.52/5.90 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 5.52/5.90 @ zero_zero_nat ) ).
% 5.52/5.90
% 5.52/5.90 % bot_nat_0.ordering_top_axioms
% 5.52/5.90 thf(fact_10005_euclidean__size__nat__def,axiom,
% 5.52/5.90 euclid4777050414544973029ze_nat = id_nat ).
% 5.52/5.90
% 5.52/5.90 % euclidean_size_nat_def
% 5.52/5.90 thf(fact_10006_euclidean__size__int__def,axiom,
% 5.52/5.90 ( euclid4774559944035922753ze_int
% 5.52/5.90 = ( comp_int_nat_int @ nat2 @ abs_abs_int ) ) ).
% 5.52/5.90
% 5.52/5.90 % euclidean_size_int_def
% 5.52/5.90 thf(fact_10007_abs__division__segment,axiom,
% 5.52/5.90 ! [K: int] :
% 5.52/5.90 ( ( abs_abs_int @ ( euclid3395696857347342551nt_int @ K ) )
% 5.52/5.90 = one_one_int ) ).
% 5.52/5.90
% 5.52/5.90 % abs_division_segment
% 5.52/5.90 thf(fact_10008_division__segment__eq__sgn,axiom,
% 5.52/5.90 ! [K: int] :
% 5.52/5.90 ( ( K != zero_zero_int )
% 5.52/5.90 => ( ( euclid3395696857347342551nt_int @ K )
% 5.52/5.90 = ( sgn_sgn_int @ K ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % division_segment_eq_sgn
% 5.52/5.90 thf(fact_10009_division__segment__nat__def,axiom,
% 5.52/5.90 ( euclid3398187327856392827nt_nat
% 5.52/5.90 = ( ^ [N3: nat] : one_one_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % division_segment_nat_def
% 5.52/5.90 thf(fact_10010_division__segment__int__def,axiom,
% 5.52/5.90 ( euclid3395696857347342551nt_int
% 5.52/5.90 = ( ^ [K2: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K2 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % division_segment_int_def
% 5.52/5.90 thf(fact_10011_less__eq__enat__def,axiom,
% 5.52/5.90 ( ord_le2932123472753598470d_enat
% 5.52/5.90 = ( ^ [M3: extended_enat] :
% 5.52/5.90 ( extended_case_enat_o
% 5.52/5.90 @ ^ [N1: nat] :
% 5.52/5.90 ( extended_case_enat_o
% 5.52/5.90 @ ^ [M1: nat] : ( ord_less_eq_nat @ M1 @ N1 )
% 5.52/5.90 @ $false
% 5.52/5.90 @ M3 )
% 5.52/5.90 @ $true ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_eq_enat_def
% 5.52/5.90 thf(fact_10012_less__enat__def,axiom,
% 5.52/5.90 ( ord_le72135733267957522d_enat
% 5.52/5.90 = ( ^ [M3: extended_enat,N3: extended_enat] :
% 5.52/5.90 ( extended_case_enat_o
% 5.52/5.90 @ ^ [M1: nat] : ( extended_case_enat_o @ ( ord_less_nat @ M1 ) @ $true @ N3 )
% 5.52/5.90 @ $false
% 5.52/5.90 @ M3 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_enat_def
% 5.52/5.90 thf(fact_10013_transp__realrel,axiom,
% 5.52/5.90 transp_nat_rat @ realrel ).
% 5.52/5.90
% 5.52/5.90 % transp_realrel
% 5.52/5.90 thf(fact_10014_natLeq__on__well__order__on,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( order_2888998067076097458on_nat
% 5.52/5.90 @ ( collect_nat
% 5.52/5.90 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) )
% 5.52/5.90 @ ( collec3392354462482085612at_nat
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( ( ord_less_nat @ X @ N )
% 5.52/5.90 & ( ord_less_nat @ Y @ N )
% 5.52/5.90 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % natLeq_on_well_order_on
% 5.52/5.90 thf(fact_10015_natLeq__on__Well__order,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( order_2888998067076097458on_nat
% 5.52/5.90 @ ( field_nat
% 5.52/5.90 @ ( collec3392354462482085612at_nat
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( ( ord_less_nat @ X @ N )
% 5.52/5.90 & ( ord_less_nat @ Y @ N )
% 5.52/5.90 & ( ord_less_eq_nat @ X @ Y ) ) ) ) )
% 5.52/5.90 @ ( collec3392354462482085612at_nat
% 5.52/5.90 @ ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( ( ord_less_nat @ X @ N )
% 5.52/5.90 & ( ord_less_nat @ Y @ N )
% 5.52/5.90 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % natLeq_on_Well_order
% 5.52/5.90 thf(fact_10016_prod__decode__triangle__add,axiom,
% 5.52/5.90 ! [K: nat,M: nat] :
% 5.52/5.90 ( ( nat_prod_decode @ ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) )
% 5.52/5.90 = ( nat_prod_decode_aux @ K @ M ) ) ).
% 5.52/5.90
% 5.52/5.90 % prod_decode_triangle_add
% 5.52/5.90 thf(fact_10017_list__decode_Opinduct,axiom,
% 5.52/5.90 ! [A0: nat,P: nat > $o] :
% 5.52/5.90 ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 5.52/5.90 => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 5.52/5.90 => ( P @ zero_zero_nat ) )
% 5.52/5.90 => ( ! [N2: nat] :
% 5.52/5.90 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) )
% 5.52/5.90 => ( ! [X6: nat,Y4: nat] :
% 5.52/5.90 ( ( ( product_Pair_nat_nat @ X6 @ Y4 )
% 5.52/5.90 = ( nat_prod_decode @ N2 ) )
% 5.52/5.90 => ( P @ Y4 ) )
% 5.52/5.90 => ( P @ ( suc @ N2 ) ) ) )
% 5.52/5.90 => ( P @ A0 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % list_decode.pinduct
% 5.52/5.90 thf(fact_10018_compute__powr__real,axiom,
% 5.52/5.90 ( powr_real2
% 5.52/5.90 = ( ^ [B3: real,I4: real] :
% 5.52/5.90 ( if_real @ ( ord_less_eq_real @ B3 @ zero_zero_real )
% 5.52/5.90 @ ( abort_real @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.52/5.90 @ ^ [Uu3: product_unit] : ( powr_real2 @ B3 @ I4 ) )
% 5.52/5.90 @ ( if_real
% 5.52/5.90 @ ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ I4 ) )
% 5.52/5.90 = I4 )
% 5.52/5.90 @ ( if_real @ ( ord_less_eq_real @ zero_zero_real @ I4 ) @ ( power_power_real @ B3 @ ( nat2 @ ( archim6058952711729229775r_real @ I4 ) ) ) @ ( divide_divide_real @ one_one_real @ ( power_power_real @ B3 @ ( nat2 @ ( archim6058952711729229775r_real @ ( uminus_uminus_real @ I4 ) ) ) ) ) )
% 5.52/5.90 @ ( abort_real @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.52/5.90 @ ^ [Uu3: product_unit] : ( powr_real2 @ B3 @ I4 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % compute_powr_real
% 5.52/5.90 thf(fact_10019_numeral__le__enat__iff,axiom,
% 5.52/5.90 ! [M: num,N: nat] :
% 5.52/5.90 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( extended_enat2 @ N ) )
% 5.52/5.90 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % numeral_le_enat_iff
% 5.52/5.90 thf(fact_10020_enat_Oinject,axiom,
% 5.52/5.90 ! [Nat: nat,Nat2: nat] :
% 5.52/5.90 ( ( ( extended_enat2 @ Nat )
% 5.52/5.90 = ( extended_enat2 @ Nat2 ) )
% 5.52/5.90 = ( Nat = Nat2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat.inject
% 5.52/5.90 thf(fact_10021_enat__ord__simps_I2_J,axiom,
% 5.52/5.90 ! [M: nat,N: nat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.52/5.90 = ( ord_less_nat @ M @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_ord_simps(2)
% 5.52/5.90 thf(fact_10022_plus__enat__simps_I1_J,axiom,
% 5.52/5.90 ! [M: nat,N: nat] :
% 5.52/5.90 ( ( plus_p3455044024723400733d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.52/5.90 = ( extended_enat2 @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % plus_enat_simps(1)
% 5.52/5.90 thf(fact_10023_enat__ord__simps_I1_J,axiom,
% 5.52/5.90 ! [M: nat,N: nat] :
% 5.52/5.90 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.52/5.90 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_ord_simps(1)
% 5.52/5.90 thf(fact_10024_idiff__enat__0__right,axiom,
% 5.52/5.90 ! [N: extended_enat] :
% 5.52/5.90 ( ( minus_3235023915231533773d_enat @ N @ ( extended_enat2 @ zero_zero_nat ) )
% 5.52/5.90 = N ) ).
% 5.52/5.90
% 5.52/5.90 % idiff_enat_0_right
% 5.52/5.90 thf(fact_10025_idiff__enat__0,axiom,
% 5.52/5.90 ! [N: extended_enat] :
% 5.52/5.90 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ zero_zero_nat ) @ N )
% 5.52/5.90 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % idiff_enat_0
% 5.52/5.90 thf(fact_10026_idiff__enat__enat,axiom,
% 5.52/5.90 ! [A: nat,B: nat] :
% 5.52/5.90 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
% 5.52/5.90 = ( extended_enat2 @ ( minus_minus_nat @ A @ B ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % idiff_enat_enat
% 5.52/5.90 thf(fact_10027_times__enat__simps_I1_J,axiom,
% 5.52/5.90 ! [M: nat,N: nat] :
% 5.52/5.90 ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.52/5.90 = ( extended_enat2 @ ( times_times_nat @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % times_enat_simps(1)
% 5.52/5.90 thf(fact_10028_max__enat__simps_I1_J,axiom,
% 5.52/5.90 ! [M: nat,N: nat] :
% 5.52/5.90 ( ( ord_ma741700101516333627d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.52/5.90 = ( extended_enat2 @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % max_enat_simps(1)
% 5.52/5.90 thf(fact_10029_min__enat__simps_I1_J,axiom,
% 5.52/5.90 ! [M: nat,N: nat] :
% 5.52/5.90 ( ( ord_mi8085742599997312461d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.52/5.90 = ( extended_enat2 @ ( ord_min_nat @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % min_enat_simps(1)
% 5.52/5.90 thf(fact_10030_numeral__less__enat__iff,axiom,
% 5.52/5.90 ! [M: num,N: nat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( extended_enat2 @ N ) )
% 5.52/5.90 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % numeral_less_enat_iff
% 5.52/5.90 thf(fact_10031_Suc__ile__eq,axiom,
% 5.52/5.90 ! [M: nat,N: extended_enat] :
% 5.52/5.90 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ ( suc @ M ) ) @ N )
% 5.52/5.90 = ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % Suc_ile_eq
% 5.52/5.90 thf(fact_10032_enat__ile,axiom,
% 5.52/5.90 ! [N: extended_enat,M: nat] :
% 5.52/5.90 ( ( ord_le2932123472753598470d_enat @ N @ ( extended_enat2 @ M ) )
% 5.52/5.90 => ? [K3: nat] :
% 5.52/5.90 ( N
% 5.52/5.90 = ( extended_enat2 @ K3 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_ile
% 5.52/5.90 thf(fact_10033_finite__enat__bounded,axiom,
% 5.52/5.90 ! [A2: set_Extended_enat,N: nat] :
% 5.52/5.90 ( ! [Y3: extended_enat] :
% 5.52/5.90 ( ( member_Extended_enat @ Y3 @ A2 )
% 5.52/5.90 => ( ord_le2932123472753598470d_enat @ Y3 @ ( extended_enat2 @ N ) ) )
% 5.52/5.90 => ( finite4001608067531595151d_enat @ A2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % finite_enat_bounded
% 5.52/5.90 thf(fact_10034_enat__1__iff_I2_J,axiom,
% 5.52/5.90 ! [X2: nat] :
% 5.52/5.90 ( ( one_on7984719198319812577d_enat
% 5.52/5.90 = ( extended_enat2 @ X2 ) )
% 5.52/5.90 = ( X2 = one_one_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_1_iff(2)
% 5.52/5.90 thf(fact_10035_enat__1__iff_I1_J,axiom,
% 5.52/5.90 ! [X2: nat] :
% 5.52/5.90 ( ( ( extended_enat2 @ X2 )
% 5.52/5.90 = one_on7984719198319812577d_enat )
% 5.52/5.90 = ( X2 = one_one_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_1_iff(1)
% 5.52/5.90 thf(fact_10036_one__enat__def,axiom,
% 5.52/5.90 ( one_on7984719198319812577d_enat
% 5.52/5.90 = ( extended_enat2 @ one_one_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % one_enat_def
% 5.52/5.90 thf(fact_10037_of__nat__eq__enat,axiom,
% 5.52/5.90 semiri4216267220026989637d_enat = extended_enat2 ).
% 5.52/5.90
% 5.52/5.90 % of_nat_eq_enat
% 5.52/5.90 thf(fact_10038_numeral__eq__enat,axiom,
% 5.52/5.90 ( numera1916890842035813515d_enat
% 5.52/5.90 = ( ^ [K2: num] : ( extended_enat2 @ ( numeral_numeral_nat @ K2 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % numeral_eq_enat
% 5.52/5.90 thf(fact_10039_enat__iless,axiom,
% 5.52/5.90 ! [N: extended_enat,M: nat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ N @ ( extended_enat2 @ M ) )
% 5.52/5.90 => ? [K3: nat] :
% 5.52/5.90 ( N
% 5.52/5.90 = ( extended_enat2 @ K3 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_iless
% 5.52/5.90 thf(fact_10040_less__enatE,axiom,
% 5.52/5.90 ! [N: extended_enat,M: nat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ N @ ( extended_enat2 @ M ) )
% 5.52/5.90 => ~ ! [K3: nat] :
% 5.52/5.90 ( ( N
% 5.52/5.90 = ( extended_enat2 @ K3 ) )
% 5.52/5.90 => ~ ( ord_less_nat @ K3 @ M ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_enatE
% 5.52/5.90 thf(fact_10041_zero__enat__def,axiom,
% 5.52/5.90 ( zero_z5237406670263579293d_enat
% 5.52/5.90 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % zero_enat_def
% 5.52/5.90 thf(fact_10042_enat__0__iff_I1_J,axiom,
% 5.52/5.90 ! [X2: nat] :
% 5.52/5.90 ( ( ( extended_enat2 @ X2 )
% 5.52/5.90 = zero_z5237406670263579293d_enat )
% 5.52/5.90 = ( X2 = zero_zero_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_0_iff(1)
% 5.52/5.90 thf(fact_10043_enat__0__iff_I2_J,axiom,
% 5.52/5.90 ! [X2: nat] :
% 5.52/5.90 ( ( zero_z5237406670263579293d_enat
% 5.52/5.90 = ( extended_enat2 @ X2 ) )
% 5.52/5.90 = ( X2 = zero_zero_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_0_iff(2)
% 5.52/5.90 thf(fact_10044_iadd__le__enat__iff,axiom,
% 5.52/5.90 ! [X2: extended_enat,Y2: extended_enat,N: nat] :
% 5.52/5.90 ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ X2 @ Y2 ) @ ( extended_enat2 @ N ) )
% 5.52/5.90 = ( ? [Y8: nat,X10: nat] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( extended_enat2 @ X10 ) )
% 5.52/5.90 & ( Y2
% 5.52/5.90 = ( extended_enat2 @ Y8 ) )
% 5.52/5.90 & ( ord_less_eq_nat @ ( plus_plus_nat @ X10 @ Y8 ) @ N ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % iadd_le_enat_iff
% 5.52/5.90 thf(fact_10045_elimnum,axiom,
% 5.52/5.90 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.52/5.90 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.52/5.90 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.52/5.90 = ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % elimnum
% 5.52/5.90 thf(fact_10046_VEBT__internal_Oelim__dead_Osimps_I3_J,axiom,
% 5.52/5.90 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,L: nat] :
% 5.52/5.90 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ ( extended_enat2 @ L ) )
% 5.52/5.90 = ( vEBT_Node @ Info @ Deg
% 5.52/5.90 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 @ ( map_VE8901447254227204932T_VEBT
% 5.52/5.90 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 @ TreeList ) )
% 5.52/5.90 @ ( vEBT_VEBT_elim_dead @ Summary @ ( extended_enat2 @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT_internal.elim_dead.simps(3)
% 5.52/5.90 thf(fact_10047_VEBT__internal_Oelim__dead_Oelims,axiom,
% 5.52/5.90 ! [X2: vEBT_VEBT,Xa2: extended_enat,Y2: vEBT_VEBT] :
% 5.52/5.90 ( ( ( vEBT_VEBT_elim_dead @ X2 @ Xa2 )
% 5.52/5.90 = Y2 )
% 5.52/5.90 => ( ! [A3: $o,B2: $o] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.90 => ( Y2
% 5.52/5.90 != ( vEBT_Leaf @ A3 @ B2 ) ) )
% 5.52/5.90 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.90 => ( ( Xa2 = extend5688581933313929465d_enat )
% 5.52/5.90 => ( Y2
% 5.52/5.90 != ( vEBT_Node @ Info2 @ Deg2
% 5.52/5.90 @ ( map_VE8901447254227204932T_VEBT
% 5.52/5.90 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 @ TreeList2 )
% 5.52/5.90 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) ) ) )
% 5.52/5.90 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.90 => ! [L4: nat] :
% 5.52/5.90 ( ( Xa2
% 5.52/5.90 = ( extended_enat2 @ L4 ) )
% 5.52/5.90 => ( Y2
% 5.52/5.90 != ( vEBT_Node @ Info2 @ Deg2
% 5.52/5.90 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 @ ( map_VE8901447254227204932T_VEBT
% 5.52/5.90 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 @ TreeList2 ) )
% 5.52/5.90 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT_internal.elim_dead.elims
% 5.52/5.90 thf(fact_10048_VEBT__internal_Oelim__dead_Osimps_I2_J,axiom,
% 5.52/5.90 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.52/5.90 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ extend5688581933313929465d_enat )
% 5.52/5.90 = ( vEBT_Node @ Info @ Deg
% 5.52/5.90 @ ( map_VE8901447254227204932T_VEBT
% 5.52/5.90 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 @ TreeList )
% 5.52/5.90 @ ( vEBT_VEBT_elim_dead @ Summary @ extend5688581933313929465d_enat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT_internal.elim_dead.simps(2)
% 5.52/5.90 thf(fact_10049_elimcomplete,axiom,
% 5.52/5.90 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.52/5.90 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.52/5.90 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ extend5688581933313929465d_enat )
% 5.52/5.90 = ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % elimcomplete
% 5.52/5.90 thf(fact_10050_not__infinity__eq,axiom,
% 5.52/5.90 ! [X2: extended_enat] :
% 5.52/5.90 ( ( X2 != extend5688581933313929465d_enat )
% 5.52/5.90 = ( ? [I4: nat] :
% 5.52/5.90 ( X2
% 5.52/5.90 = ( extended_enat2 @ I4 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % not_infinity_eq
% 5.52/5.90 thf(fact_10051_not__enat__eq,axiom,
% 5.52/5.90 ! [X2: extended_enat] :
% 5.52/5.90 ( ( ! [Y: nat] :
% 5.52/5.90 ( X2
% 5.52/5.90 != ( extended_enat2 @ Y ) ) )
% 5.52/5.90 = ( X2 = extend5688581933313929465d_enat ) ) ).
% 5.52/5.90
% 5.52/5.90 % not_enat_eq
% 5.52/5.90 thf(fact_10052_enat__ord__simps_I4_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ Q2 @ extend5688581933313929465d_enat )
% 5.52/5.90 = ( Q2 != extend5688581933313929465d_enat ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_ord_simps(4)
% 5.52/5.90 thf(fact_10053_enat__ord__simps_I6_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] :
% 5.52/5.90 ~ ( ord_le72135733267957522d_enat @ extend5688581933313929465d_enat @ Q2 ) ).
% 5.52/5.90
% 5.52/5.90 % enat_ord_simps(6)
% 5.52/5.90 thf(fact_10054_plus__enat__simps_I2_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] :
% 5.52/5.90 ( ( plus_p3455044024723400733d_enat @ extend5688581933313929465d_enat @ Q2 )
% 5.52/5.90 = extend5688581933313929465d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % plus_enat_simps(2)
% 5.52/5.90 thf(fact_10055_plus__enat__simps_I3_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] :
% 5.52/5.90 ( ( plus_p3455044024723400733d_enat @ Q2 @ extend5688581933313929465d_enat )
% 5.52/5.90 = extend5688581933313929465d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % plus_enat_simps(3)
% 5.52/5.90 thf(fact_10056_enat__ord__code_I3_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] : ( ord_le2932123472753598470d_enat @ Q2 @ extend5688581933313929465d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % enat_ord_code(3)
% 5.52/5.90 thf(fact_10057_enat__ord__simps_I5_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] :
% 5.52/5.90 ( ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ Q2 )
% 5.52/5.90 = ( Q2 = extend5688581933313929465d_enat ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_ord_simps(5)
% 5.52/5.90 thf(fact_10058_idiff__infinity,axiom,
% 5.52/5.90 ! [N: extended_enat] :
% 5.52/5.90 ( ( minus_3235023915231533773d_enat @ extend5688581933313929465d_enat @ N )
% 5.52/5.90 = extend5688581933313929465d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % idiff_infinity
% 5.52/5.90 thf(fact_10059_times__enat__simps_I2_J,axiom,
% 5.52/5.90 ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ extend5688581933313929465d_enat )
% 5.52/5.90 = extend5688581933313929465d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % times_enat_simps(2)
% 5.52/5.90 thf(fact_10060_max__enat__simps_I4_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] :
% 5.52/5.90 ( ( ord_ma741700101516333627d_enat @ Q2 @ extend5688581933313929465d_enat )
% 5.52/5.90 = extend5688581933313929465d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % max_enat_simps(4)
% 5.52/5.90 thf(fact_10061_max__enat__simps_I5_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] :
% 5.52/5.90 ( ( ord_ma741700101516333627d_enat @ extend5688581933313929465d_enat @ Q2 )
% 5.52/5.90 = extend5688581933313929465d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % max_enat_simps(5)
% 5.52/5.90 thf(fact_10062_min__enat__simps_I5_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] :
% 5.52/5.90 ( ( ord_mi8085742599997312461d_enat @ extend5688581933313929465d_enat @ Q2 )
% 5.52/5.90 = Q2 ) ).
% 5.52/5.90
% 5.52/5.90 % min_enat_simps(5)
% 5.52/5.90 thf(fact_10063_min__enat__simps_I4_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] :
% 5.52/5.90 ( ( ord_mi8085742599997312461d_enat @ Q2 @ extend5688581933313929465d_enat )
% 5.52/5.90 = Q2 ) ).
% 5.52/5.90
% 5.52/5.90 % min_enat_simps(4)
% 5.52/5.90 thf(fact_10064_idiff__self,axiom,
% 5.52/5.90 ! [N: extended_enat] :
% 5.52/5.90 ( ( N != extend5688581933313929465d_enat )
% 5.52/5.90 => ( ( minus_3235023915231533773d_enat @ N @ N )
% 5.52/5.90 = zero_z5237406670263579293d_enat ) ) ).
% 5.52/5.90
% 5.52/5.90 % idiff_self
% 5.52/5.90 thf(fact_10065_add__diff__cancel__enat,axiom,
% 5.52/5.90 ! [X2: extended_enat,Y2: extended_enat] :
% 5.52/5.90 ( ( X2 != extend5688581933313929465d_enat )
% 5.52/5.90 => ( ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X2 @ Y2 ) @ X2 )
% 5.52/5.90 = Y2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % add_diff_cancel_enat
% 5.52/5.90 thf(fact_10066_idiff__infinity__right,axiom,
% 5.52/5.90 ! [A: nat] :
% 5.52/5.90 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ A ) @ extend5688581933313929465d_enat )
% 5.52/5.90 = zero_z5237406670263579293d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % idiff_infinity_right
% 5.52/5.90 thf(fact_10067_times__enat__simps_I3_J,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( ( ( N = zero_zero_nat )
% 5.52/5.90 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 5.52/5.90 = zero_z5237406670263579293d_enat ) )
% 5.52/5.90 & ( ( N != zero_zero_nat )
% 5.52/5.90 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 5.52/5.90 = extend5688581933313929465d_enat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % times_enat_simps(3)
% 5.52/5.90 thf(fact_10068_times__enat__simps_I4_J,axiom,
% 5.52/5.90 ! [M: nat] :
% 5.52/5.90 ( ( ( M = zero_zero_nat )
% 5.52/5.90 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat )
% 5.52/5.90 = zero_z5237406670263579293d_enat ) )
% 5.52/5.90 & ( ( M != zero_zero_nat )
% 5.52/5.90 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat )
% 5.52/5.90 = extend5688581933313929465d_enat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % times_enat_simps(4)
% 5.52/5.90 thf(fact_10069_Sup__enat__def,axiom,
% 5.52/5.90 ( comple4398354569131411667d_enat
% 5.52/5.90 = ( ^ [A6: set_Extended_enat] : ( if_Extended_enat @ ( A6 = bot_bo7653980558646680370d_enat ) @ zero_z5237406670263579293d_enat @ ( if_Extended_enat @ ( finite4001608067531595151d_enat @ A6 ) @ ( lattic921264341876707157d_enat @ A6 ) @ extend5688581933313929465d_enat ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Sup_enat_def
% 5.52/5.90 thf(fact_10070_enat__add__left__cancel__le,axiom,
% 5.52/5.90 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.52/5.90 ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( plus_p3455044024723400733d_enat @ A @ C ) )
% 5.52/5.90 = ( ( A = extend5688581933313929465d_enat )
% 5.52/5.90 | ( ord_le2932123472753598470d_enat @ B @ C ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_add_left_cancel_le
% 5.52/5.90 thf(fact_10071_enat__ord__simps_I3_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] : ( ord_le2932123472753598470d_enat @ Q2 @ extend5688581933313929465d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % enat_ord_simps(3)
% 5.52/5.90 thf(fact_10072_Inf__enat__def,axiom,
% 5.52/5.90 ( comple2295165028678016749d_enat
% 5.52/5.90 = ( ^ [A6: set_Extended_enat] :
% 5.52/5.90 ( if_Extended_enat @ ( A6 = bot_bo7653980558646680370d_enat ) @ extend5688581933313929465d_enat
% 5.52/5.90 @ ( ord_Le1955565732374568822d_enat
% 5.52/5.90 @ ^ [X: extended_enat] : ( member_Extended_enat @ X @ A6 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Inf_enat_def
% 5.52/5.90 thf(fact_10073_numeral__ne__infinity,axiom,
% 5.52/5.90 ! [K: num] :
% 5.52/5.90 ( ( numera1916890842035813515d_enat @ K )
% 5.52/5.90 != extend5688581933313929465d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % numeral_ne_infinity
% 5.52/5.90 thf(fact_10074_infinity__ne__i1,axiom,
% 5.52/5.90 extend5688581933313929465d_enat != one_on7984719198319812577d_enat ).
% 5.52/5.90
% 5.52/5.90 % infinity_ne_i1
% 5.52/5.90 thf(fact_10075_enat__add__left__cancel,axiom,
% 5.52/5.90 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.52/5.90 ( ( ( plus_p3455044024723400733d_enat @ A @ B )
% 5.52/5.90 = ( plus_p3455044024723400733d_enat @ A @ C ) )
% 5.52/5.90 = ( ( A = extend5688581933313929465d_enat )
% 5.52/5.90 | ( B = C ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_add_left_cancel
% 5.52/5.90 thf(fact_10076_plus__eq__infty__iff__enat,axiom,
% 5.52/5.90 ! [M: extended_enat,N: extended_enat] :
% 5.52/5.90 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.52/5.90 = extend5688581933313929465d_enat )
% 5.52/5.90 = ( ( M = extend5688581933313929465d_enat )
% 5.52/5.90 | ( N = extend5688581933313929465d_enat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % plus_eq_infty_iff_enat
% 5.52/5.90 thf(fact_10077_enat__add__left__cancel__less,axiom,
% 5.52/5.90 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( plus_p3455044024723400733d_enat @ A @ C ) )
% 5.52/5.90 = ( ( A != extend5688581933313929465d_enat )
% 5.52/5.90 & ( ord_le72135733267957522d_enat @ B @ C ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_add_left_cancel_less
% 5.52/5.90 thf(fact_10078_imult__is__infinity,axiom,
% 5.52/5.90 ! [A: extended_enat,B: extended_enat] :
% 5.52/5.90 ( ( ( times_7803423173614009249d_enat @ A @ B )
% 5.52/5.90 = extend5688581933313929465d_enat )
% 5.52/5.90 = ( ( ( A = extend5688581933313929465d_enat )
% 5.52/5.90 & ( B != zero_z5237406670263579293d_enat ) )
% 5.52/5.90 | ( ( B = extend5688581933313929465d_enat )
% 5.52/5.90 & ( A != zero_z5237406670263579293d_enat ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % imult_is_infinity
% 5.52/5.90 thf(fact_10079_infinity__ne__i0,axiom,
% 5.52/5.90 extend5688581933313929465d_enat != zero_z5237406670263579293d_enat ).
% 5.52/5.90
% 5.52/5.90 % infinity_ne_i0
% 5.52/5.90 thf(fact_10080_top__enat__def,axiom,
% 5.52/5.90 top_to3028658606643905974d_enat = extend5688581933313929465d_enat ).
% 5.52/5.90
% 5.52/5.90 % top_enat_def
% 5.52/5.90 thf(fact_10081_VEBT__internal_Oelim__dead_Ocases,axiom,
% 5.52/5.90 ! [X2: produc7272778201969148633d_enat] :
% 5.52/5.90 ( ! [A3: $o,B2: $o,Uu2: extended_enat] :
% 5.52/5.90 ( X2
% 5.52/5.90 != ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A3 @ B2 ) @ Uu2 ) )
% 5.52/5.90 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.90 ( X2
% 5.52/5.90 != ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ extend5688581933313929465d_enat ) )
% 5.52/5.90 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,L4: nat] :
% 5.52/5.90 ( X2
% 5.52/5.90 != ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ ( extended_enat2 @ L4 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT_internal.elim_dead.cases
% 5.52/5.90 thf(fact_10082_infinity__ilessE,axiom,
% 5.52/5.90 ! [M: nat] :
% 5.52/5.90 ~ ( ord_le72135733267957522d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ M ) ) ).
% 5.52/5.90
% 5.52/5.90 % infinity_ilessE
% 5.52/5.90 thf(fact_10083_less__infinityE,axiom,
% 5.52/5.90 ! [N: extended_enat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ N @ extend5688581933313929465d_enat )
% 5.52/5.90 => ~ ! [K3: nat] :
% 5.52/5.90 ( N
% 5.52/5.90 != ( extended_enat2 @ K3 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_infinityE
% 5.52/5.90 thf(fact_10084_enat__ord__code_I4_J,axiom,
% 5.52/5.90 ! [M: nat] : ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % enat_ord_code(4)
% 5.52/5.90 thf(fact_10085_enat__ex__split,axiom,
% 5.52/5.90 ( ( ^ [P2: extended_enat > $o] :
% 5.52/5.90 ? [X5: extended_enat] : ( P2 @ X5 ) )
% 5.52/5.90 = ( ^ [P3: extended_enat > $o] :
% 5.52/5.90 ( ( P3 @ extend5688581933313929465d_enat )
% 5.52/5.90 | ? [X: nat] : ( P3 @ ( extended_enat2 @ X ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_ex_split
% 5.52/5.90 thf(fact_10086_enat3__cases,axiom,
% 5.52/5.90 ! [Y2: extended_enat,Ya: extended_enat,Yb: extended_enat] :
% 5.52/5.90 ( ( ? [Nat3: nat] :
% 5.52/5.90 ( Y2
% 5.52/5.90 = ( extended_enat2 @ Nat3 ) )
% 5.52/5.90 => ( ? [Nata: nat] :
% 5.52/5.90 ( Ya
% 5.52/5.90 = ( extended_enat2 @ Nata ) )
% 5.52/5.90 => ! [Natb: nat] :
% 5.52/5.90 ( Yb
% 5.52/5.90 != ( extended_enat2 @ Natb ) ) ) )
% 5.52/5.90 => ( ( ? [Nat3: nat] :
% 5.52/5.90 ( Y2
% 5.52/5.90 = ( extended_enat2 @ Nat3 ) )
% 5.52/5.90 => ( ? [Nata: nat] :
% 5.52/5.90 ( Ya
% 5.52/5.90 = ( extended_enat2 @ Nata ) )
% 5.52/5.90 => ( Yb != extend5688581933313929465d_enat ) ) )
% 5.52/5.90 => ( ( ? [Nat3: nat] :
% 5.52/5.90 ( Y2
% 5.52/5.90 = ( extended_enat2 @ Nat3 ) )
% 5.52/5.90 => ( ( Ya = extend5688581933313929465d_enat )
% 5.52/5.90 => ! [Nata: nat] :
% 5.52/5.90 ( Yb
% 5.52/5.90 != ( extended_enat2 @ Nata ) ) ) )
% 5.52/5.90 => ( ( ? [Nat3: nat] :
% 5.52/5.90 ( Y2
% 5.52/5.90 = ( extended_enat2 @ Nat3 ) )
% 5.52/5.90 => ( ( Ya = extend5688581933313929465d_enat )
% 5.52/5.90 => ( Yb != extend5688581933313929465d_enat ) ) )
% 5.52/5.90 => ( ( ( Y2 = extend5688581933313929465d_enat )
% 5.52/5.90 => ( ? [Nat3: nat] :
% 5.52/5.90 ( Ya
% 5.52/5.90 = ( extended_enat2 @ Nat3 ) )
% 5.52/5.90 => ! [Nata: nat] :
% 5.52/5.90 ( Yb
% 5.52/5.90 != ( extended_enat2 @ Nata ) ) ) )
% 5.52/5.90 => ( ( ( Y2 = extend5688581933313929465d_enat )
% 5.52/5.90 => ( ? [Nat3: nat] :
% 5.52/5.90 ( Ya
% 5.52/5.90 = ( extended_enat2 @ Nat3 ) )
% 5.52/5.90 => ( Yb != extend5688581933313929465d_enat ) ) )
% 5.52/5.90 => ( ( ( Y2 = extend5688581933313929465d_enat )
% 5.52/5.90 => ( ( Ya = extend5688581933313929465d_enat )
% 5.52/5.90 => ! [Nat3: nat] :
% 5.52/5.90 ( Yb
% 5.52/5.90 != ( extended_enat2 @ Nat3 ) ) ) )
% 5.52/5.90 => ~ ( ( Y2 = extend5688581933313929465d_enat )
% 5.52/5.90 => ( ( Ya = extend5688581933313929465d_enat )
% 5.52/5.90 => ( Yb != extend5688581933313929465d_enat ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat3_cases
% 5.52/5.90 thf(fact_10087_enat2__cases,axiom,
% 5.52/5.90 ! [Y2: extended_enat,Ya: extended_enat] :
% 5.52/5.90 ( ( ? [Nat3: nat] :
% 5.52/5.90 ( Y2
% 5.52/5.90 = ( extended_enat2 @ Nat3 ) )
% 5.52/5.90 => ! [Nata: nat] :
% 5.52/5.90 ( Ya
% 5.52/5.90 != ( extended_enat2 @ Nata ) ) )
% 5.52/5.90 => ( ( ? [Nat3: nat] :
% 5.52/5.90 ( Y2
% 5.52/5.90 = ( extended_enat2 @ Nat3 ) )
% 5.52/5.90 => ( Ya != extend5688581933313929465d_enat ) )
% 5.52/5.90 => ( ( ( Y2 = extend5688581933313929465d_enat )
% 5.52/5.90 => ! [Nat3: nat] :
% 5.52/5.90 ( Ya
% 5.52/5.90 != ( extended_enat2 @ Nat3 ) ) )
% 5.52/5.90 => ~ ( ( Y2 = extend5688581933313929465d_enat )
% 5.52/5.90 => ( Ya != extend5688581933313929465d_enat ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat2_cases
% 5.52/5.90 thf(fact_10088_enat_Oexhaust,axiom,
% 5.52/5.90 ! [Y2: extended_enat] :
% 5.52/5.90 ( ! [Nat3: nat] :
% 5.52/5.90 ( Y2
% 5.52/5.90 != ( extended_enat2 @ Nat3 ) )
% 5.52/5.90 => ( Y2 = extend5688581933313929465d_enat ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat.exhaust
% 5.52/5.90 thf(fact_10089_enat_Odistinct_I1_J,axiom,
% 5.52/5.90 ! [Nat: nat] :
% 5.52/5.90 ( ( extended_enat2 @ Nat )
% 5.52/5.90 != extend5688581933313929465d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % enat.distinct(1)
% 5.52/5.90 thf(fact_10090_enat_Odistinct_I2_J,axiom,
% 5.52/5.90 ! [Nat: nat] :
% 5.52/5.90 ( extend5688581933313929465d_enat
% 5.52/5.90 != ( extended_enat2 @ Nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat.distinct(2)
% 5.52/5.90 thf(fact_10091_infinity__ileE,axiom,
% 5.52/5.90 ! [M: nat] :
% 5.52/5.90 ~ ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ M ) ) ).
% 5.52/5.90
% 5.52/5.90 % infinity_ileE
% 5.52/5.90 thf(fact_10092_enat__ord__code_I5_J,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ~ ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_ord_code(5)
% 5.52/5.90 thf(fact_10093_imult__infinity,axiom,
% 5.52/5.90 ! [N: extended_enat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.52/5.90 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ N )
% 5.52/5.90 = extend5688581933313929465d_enat ) ) ).
% 5.52/5.90
% 5.52/5.90 % imult_infinity
% 5.52/5.90 thf(fact_10094_imult__infinity__right,axiom,
% 5.52/5.90 ! [N: extended_enat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.52/5.90 => ( ( times_7803423173614009249d_enat @ N @ extend5688581933313929465d_enat )
% 5.52/5.90 = extend5688581933313929465d_enat ) ) ).
% 5.52/5.90
% 5.52/5.90 % imult_infinity_right
% 5.52/5.90 thf(fact_10095_plus__enat__def,axiom,
% 5.52/5.90 ( plus_p3455044024723400733d_enat
% 5.52/5.90 = ( ^ [M3: extended_enat,N3: extended_enat] :
% 5.52/5.90 ( extend3600170679010898289d_enat
% 5.52/5.90 @ ^ [O: nat] :
% 5.52/5.90 ( extend3600170679010898289d_enat
% 5.52/5.90 @ ^ [P4: nat] : ( extended_enat2 @ ( plus_plus_nat @ O @ P4 ) )
% 5.52/5.90 @ extend5688581933313929465d_enat
% 5.52/5.90 @ N3 )
% 5.52/5.90 @ extend5688581933313929465d_enat
% 5.52/5.90 @ M3 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % plus_enat_def
% 5.52/5.90 thf(fact_10096_diff__enat__def,axiom,
% 5.52/5.90 ( minus_3235023915231533773d_enat
% 5.52/5.90 = ( ^ [A4: extended_enat,B3: extended_enat] :
% 5.52/5.90 ( extend3600170679010898289d_enat
% 5.52/5.90 @ ^ [X: nat] :
% 5.52/5.90 ( extend3600170679010898289d_enat
% 5.52/5.90 @ ^ [Y: nat] : ( extended_enat2 @ ( minus_minus_nat @ X @ Y ) )
% 5.52/5.90 @ zero_z5237406670263579293d_enat
% 5.52/5.90 @ B3 )
% 5.52/5.90 @ extend5688581933313929465d_enat
% 5.52/5.90 @ A4 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % diff_enat_def
% 5.52/5.90 thf(fact_10097_times__enat__def,axiom,
% 5.52/5.90 ( times_7803423173614009249d_enat
% 5.52/5.90 = ( ^ [M3: extended_enat,N3: extended_enat] :
% 5.52/5.90 ( extend3600170679010898289d_enat
% 5.52/5.90 @ ^ [O: nat] :
% 5.52/5.90 ( extend3600170679010898289d_enat
% 5.52/5.90 @ ^ [P4: nat] : ( extended_enat2 @ ( times_times_nat @ O @ P4 ) )
% 5.52/5.90 @ ( if_Extended_enat @ ( O = zero_zero_nat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 5.52/5.90 @ N3 )
% 5.52/5.90 @ ( if_Extended_enat @ ( N3 = zero_z5237406670263579293d_enat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 5.52/5.90 @ M3 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % times_enat_def
% 5.52/5.90 thf(fact_10098_VEBT__internal_Oelim__dead_Opelims,axiom,
% 5.52/5.90 ! [X2: vEBT_VEBT,Xa2: extended_enat,Y2: vEBT_VEBT] :
% 5.52/5.90 ( ( ( vEBT_VEBT_elim_dead @ X2 @ Xa2 )
% 5.52/5.90 = Y2 )
% 5.52/5.90 => ( ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ X2 @ Xa2 ) )
% 5.52/5.90 => ( ! [A3: $o,B2: $o] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.90 => ( ( Y2
% 5.52/5.90 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.52/5.90 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.52/5.90 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.90 => ( ( Xa2 = extend5688581933313929465d_enat )
% 5.52/5.90 => ( ( Y2
% 5.52/5.90 = ( vEBT_Node @ Info2 @ Deg2
% 5.52/5.90 @ ( map_VE8901447254227204932T_VEBT
% 5.52/5.90 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 @ TreeList2 )
% 5.52/5.90 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) )
% 5.52/5.90 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ extend5688581933313929465d_enat ) ) ) ) )
% 5.52/5.90 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.52/5.90 => ! [L4: nat] :
% 5.52/5.90 ( ( Xa2
% 5.52/5.90 = ( extended_enat2 @ L4 ) )
% 5.52/5.90 => ( ( Y2
% 5.52/5.90 = ( vEBT_Node @ Info2 @ Deg2
% 5.52/5.90 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.52/5.90 @ ( map_VE8901447254227204932T_VEBT
% 5.52/5.90 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.52/5.90 @ TreeList2 ) )
% 5.52/5.90 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.52/5.90 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ ( extended_enat2 @ L4 ) ) ) ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % VEBT_internal.elim_dead.pelims
% 5.52/5.90 thf(fact_10099_the__enat_Osimps,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( ( extended_the_enat @ ( extended_enat2 @ N ) )
% 5.52/5.90 = N ) ).
% 5.52/5.90
% 5.52/5.90 % the_enat.simps
% 5.52/5.90 thf(fact_10100_eSuc__Max,axiom,
% 5.52/5.90 ! [A2: set_Extended_enat] :
% 5.52/5.90 ( ( finite4001608067531595151d_enat @ A2 )
% 5.52/5.90 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 5.52/5.90 => ( ( extended_eSuc @ ( lattic921264341876707157d_enat @ A2 ) )
% 5.52/5.90 = ( lattic921264341876707157d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A2 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_Max
% 5.52/5.90 thf(fact_10101_eSuc__inject,axiom,
% 5.52/5.90 ! [M: extended_enat,N: extended_enat] :
% 5.52/5.90 ( ( ( extended_eSuc @ M )
% 5.52/5.90 = ( extended_eSuc @ N ) )
% 5.52/5.90 = ( M = N ) ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_inject
% 5.52/5.90 thf(fact_10102_eSuc__infinity,axiom,
% 5.52/5.90 ( ( extended_eSuc @ extend5688581933313929465d_enat )
% 5.52/5.90 = extend5688581933313929465d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_infinity
% 5.52/5.90 thf(fact_10103_eSuc__mono,axiom,
% 5.52/5.90 ! [N: extended_enat,M: extended_enat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 5.52/5.90 = ( ord_le72135733267957522d_enat @ N @ M ) ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_mono
% 5.52/5.90 thf(fact_10104_eSuc__ile__mono,axiom,
% 5.52/5.90 ! [N: extended_enat,M: extended_enat] :
% 5.52/5.90 ( ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 5.52/5.90 = ( ord_le2932123472753598470d_enat @ N @ M ) ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_ile_mono
% 5.52/5.90 thf(fact_10105_eSuc__minus__eSuc,axiom,
% 5.52/5.90 ! [N: extended_enat,M: extended_enat] :
% 5.52/5.90 ( ( minus_3235023915231533773d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 5.52/5.90 = ( minus_3235023915231533773d_enat @ N @ M ) ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_minus_eSuc
% 5.52/5.90 thf(fact_10106_iless__eSuc0,axiom,
% 5.52/5.90 ! [N: extended_enat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ N @ ( extended_eSuc @ zero_z5237406670263579293d_enat ) )
% 5.52/5.90 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.52/5.90
% 5.52/5.90 % iless_eSuc0
% 5.52/5.90 thf(fact_10107_eSuc__minus__1,axiom,
% 5.52/5.90 ! [N: extended_enat] :
% 5.52/5.90 ( ( minus_3235023915231533773d_enat @ ( extended_eSuc @ N ) @ one_on7984719198319812577d_enat )
% 5.52/5.90 = N ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_minus_1
% 5.52/5.90 thf(fact_10108_eSuc__numeral,axiom,
% 5.52/5.90 ! [K: num] :
% 5.52/5.90 ( ( extended_eSuc @ ( numera1916890842035813515d_enat @ K ) )
% 5.52/5.90 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ K @ one ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_numeral
% 5.52/5.90 thf(fact_10109_iless__Suc__eq,axiom,
% 5.52/5.90 ! [M: nat,N: extended_enat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ ( extended_eSuc @ N ) )
% 5.52/5.90 = ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M ) @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % iless_Suc_eq
% 5.52/5.90 thf(fact_10110_ileI1,axiom,
% 5.52/5.90 ! [M: extended_enat,N: extended_enat] :
% 5.52/5.90 ( ( ord_le72135733267957522d_enat @ M @ N )
% 5.52/5.90 => ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ M ) @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % ileI1
% 5.52/5.90 thf(fact_10111_mono__eSuc,axiom,
% 5.52/5.90 order_4130057895858720880d_enat @ extended_eSuc ).
% 5.52/5.90
% 5.52/5.90 % mono_eSuc
% 5.52/5.90 thf(fact_10112_ile__eSuc,axiom,
% 5.52/5.90 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ N @ ( extended_eSuc @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % ile_eSuc
% 5.52/5.90 thf(fact_10113_mult__eSuc,axiom,
% 5.52/5.90 ! [M: extended_enat,N: extended_enat] :
% 5.52/5.90 ( ( times_7803423173614009249d_enat @ ( extended_eSuc @ M ) @ N )
% 5.52/5.90 = ( plus_p3455044024723400733d_enat @ N @ ( times_7803423173614009249d_enat @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % mult_eSuc
% 5.52/5.90 thf(fact_10114_mult__eSuc__right,axiom,
% 5.52/5.90 ! [M: extended_enat,N: extended_enat] :
% 5.52/5.90 ( ( times_7803423173614009249d_enat @ M @ ( extended_eSuc @ N ) )
% 5.52/5.90 = ( plus_p3455044024723400733d_enat @ M @ ( times_7803423173614009249d_enat @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % mult_eSuc_right
% 5.52/5.90 thf(fact_10115_iadd__Suc__right,axiom,
% 5.52/5.90 ! [M: extended_enat,N: extended_enat] :
% 5.52/5.90 ( ( plus_p3455044024723400733d_enat @ M @ ( extended_eSuc @ N ) )
% 5.52/5.90 = ( extended_eSuc @ ( plus_p3455044024723400733d_enat @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % iadd_Suc_right
% 5.52/5.90 thf(fact_10116_iadd__Suc,axiom,
% 5.52/5.90 ! [M: extended_enat,N: extended_enat] :
% 5.52/5.90 ( ( plus_p3455044024723400733d_enat @ ( extended_eSuc @ M ) @ N )
% 5.52/5.90 = ( extended_eSuc @ ( plus_p3455044024723400733d_enat @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % iadd_Suc
% 5.52/5.90 thf(fact_10117_eSuc__max,axiom,
% 5.52/5.90 ! [X2: extended_enat,Y2: extended_enat] :
% 5.52/5.90 ( ( extended_eSuc @ ( ord_ma741700101516333627d_enat @ X2 @ Y2 ) )
% 5.52/5.90 = ( ord_ma741700101516333627d_enat @ ( extended_eSuc @ X2 ) @ ( extended_eSuc @ Y2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_max
% 5.52/5.90 thf(fact_10118_eSuc__plus__1,axiom,
% 5.52/5.90 ( extended_eSuc
% 5.52/5.90 = ( ^ [N3: extended_enat] : ( plus_p3455044024723400733d_enat @ N3 @ one_on7984719198319812577d_enat ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_plus_1
% 5.52/5.90 thf(fact_10119_plus__1__eSuc_I1_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] :
% 5.52/5.90 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ Q2 )
% 5.52/5.90 = ( extended_eSuc @ Q2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % plus_1_eSuc(1)
% 5.52/5.90 thf(fact_10120_plus__1__eSuc_I2_J,axiom,
% 5.52/5.90 ! [Q2: extended_enat] :
% 5.52/5.90 ( ( plus_p3455044024723400733d_enat @ Q2 @ one_on7984719198319812577d_enat )
% 5.52/5.90 = ( extended_eSuc @ Q2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % plus_1_eSuc(2)
% 5.52/5.90 thf(fact_10121_i0__iless__eSuc,axiom,
% 5.52/5.90 ! [N: extended_enat] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( extended_eSuc @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % i0_iless_eSuc
% 5.52/5.90 thf(fact_10122_one__eSuc,axiom,
% 5.52/5.90 ( one_on7984719198319812577d_enat
% 5.52/5.90 = ( extended_eSuc @ zero_z5237406670263579293d_enat ) ) ).
% 5.52/5.90
% 5.52/5.90 % one_eSuc
% 5.52/5.90 thf(fact_10123_zero__ne__eSuc,axiom,
% 5.52/5.90 ! [N: extended_enat] :
% 5.52/5.90 ( zero_z5237406670263579293d_enat
% 5.52/5.90 != ( extended_eSuc @ N ) ) ).
% 5.52/5.90
% 5.52/5.90 % zero_ne_eSuc
% 5.52/5.90 thf(fact_10124_not__eSuc__ilei0,axiom,
% 5.52/5.90 ! [N: extended_enat] :
% 5.52/5.90 ~ ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ N ) @ zero_z5237406670263579293d_enat ) ).
% 5.52/5.90
% 5.52/5.90 % not_eSuc_ilei0
% 5.52/5.90 thf(fact_10125_eSuc__enat,axiom,
% 5.52/5.90 ! [N: nat] :
% 5.52/5.90 ( ( extended_eSuc @ ( extended_enat2 @ N ) )
% 5.52/5.90 = ( extended_enat2 @ ( suc @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_enat
% 5.52/5.90 thf(fact_10126_eSuc__enat__iff,axiom,
% 5.52/5.90 ! [X2: extended_enat,Y2: nat] :
% 5.52/5.90 ( ( ( extended_eSuc @ X2 )
% 5.52/5.90 = ( extended_enat2 @ Y2 ) )
% 5.52/5.90 = ( ? [N3: nat] :
% 5.52/5.90 ( ( Y2
% 5.52/5.90 = ( suc @ N3 ) )
% 5.52/5.90 & ( X2
% 5.52/5.90 = ( extended_enat2 @ N3 ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_enat_iff
% 5.52/5.90 thf(fact_10127_enat__eSuc__iff,axiom,
% 5.52/5.90 ! [Y2: nat,X2: extended_enat] :
% 5.52/5.90 ( ( ( extended_enat2 @ Y2 )
% 5.52/5.90 = ( extended_eSuc @ X2 ) )
% 5.52/5.90 = ( ? [N3: nat] :
% 5.52/5.90 ( ( Y2
% 5.52/5.90 = ( suc @ N3 ) )
% 5.52/5.90 & ( ( extended_enat2 @ N3 )
% 5.52/5.90 = X2 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_eSuc_iff
% 5.52/5.90 thf(fact_10128_eSuc__Sup,axiom,
% 5.52/5.90 ! [A2: set_Extended_enat] :
% 5.52/5.90 ( ( A2 != bot_bo7653980558646680370d_enat )
% 5.52/5.90 => ( ( extended_eSuc @ ( comple4398354569131411667d_enat @ A2 ) )
% 5.52/5.90 = ( comple4398354569131411667d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A2 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_Sup
% 5.52/5.90 thf(fact_10129_eSuc__def,axiom,
% 5.52/5.90 ( extended_eSuc
% 5.52/5.90 = ( extend3600170679010898289d_enat
% 5.52/5.90 @ ^ [N3: nat] : ( extended_enat2 @ ( suc @ N3 ) )
% 5.52/5.90 @ extend5688581933313929465d_enat ) ) ).
% 5.52/5.90
% 5.52/5.90 % eSuc_def
% 5.52/5.90 thf(fact_10130_less__than__iff,axiom,
% 5.52/5.90 ! [X2: nat,Y2: nat] :
% 5.52/5.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ less_than )
% 5.52/5.90 = ( ord_less_nat @ X2 @ Y2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_than_iff
% 5.52/5.90 thf(fact_10131_Quotient__real,axiom,
% 5.52/5.90 quotie3684837364556693515t_real @ realrel @ real2 @ rep_real2 @ cr_real ).
% 5.52/5.90
% 5.52/5.90 % Quotient_real
% 5.52/5.90 thf(fact_10132_max__nat_Osemilattice__neutr__axioms,axiom,
% 5.52/5.90 semila9081495762789891438tr_nat @ ord_max_nat @ zero_zero_nat ).
% 5.52/5.90
% 5.52/5.90 % max_nat.semilattice_neutr_axioms
% 5.52/5.90 thf(fact_10133_less__eq__int__def,axiom,
% 5.52/5.90 ( ord_less_eq_int
% 5.52/5.90 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.52/5.90 @ ( produc8739625826339149834_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_eq_int_def
% 5.52/5.90 thf(fact_10134_less__int__def,axiom,
% 5.52/5.90 ( ord_less_int
% 5.52/5.90 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.52/5.90 @ ( produc8739625826339149834_nat_o
% 5.52/5.90 @ ^ [X: nat,Y: nat] :
% 5.52/5.90 ( produc6081775807080527818_nat_o
% 5.52/5.90 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_int_def
% 5.52/5.90 thf(fact_10135_sub_Oabs__eq,axiom,
% 5.52/5.90 ( code_sub
% 5.52/5.90 = ( ^ [Xa4: num,X: num] : ( code_integer_of_int @ ( minus_minus_int @ ( numeral_numeral_int @ Xa4 ) @ ( numeral_numeral_int @ X ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % sub.abs_eq
% 5.52/5.90 thf(fact_10136_Code__Numeral_Osub__code_I1_J,axiom,
% 5.52/5.90 ( ( code_sub @ one @ one )
% 5.52/5.90 = zero_z3403309356797280102nteger ) ).
% 5.52/5.90
% 5.52/5.90 % Code_Numeral.sub_code(1)
% 5.52/5.90 thf(fact_10137_sub_Orep__eq,axiom,
% 5.52/5.90 ! [X2: num,Xa2: num] :
% 5.52/5.90 ( ( code_int_of_integer @ ( code_sub @ X2 @ Xa2 ) )
% 5.52/5.90 = ( minus_minus_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Xa2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % sub.rep_eq
% 5.52/5.90 thf(fact_10138_Code__Numeral_Osub__code_I9_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( code_sub @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.52/5.90 = ( minus_8373710615458151222nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 5.52/5.90
% 5.52/5.90 % Code_Numeral.sub_code(9)
% 5.52/5.90 thf(fact_10139_Code__Numeral_Osub__code_I8_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( code_sub @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.52/5.90 = ( plus_p5714425477246183910nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 5.52/5.90
% 5.52/5.90 % Code_Numeral.sub_code(8)
% 5.52/5.90 thf(fact_10140_Code__Numeral_Osub__code_I6_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( code_sub @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.52/5.90 = ( code_dup @ ( code_sub @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Code_Numeral.sub_code(6)
% 5.52/5.90 thf(fact_10141_Code__Numeral_Osub__code_I7_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( code_sub @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.52/5.90 = ( code_dup @ ( code_sub @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Code_Numeral.sub_code(7)
% 5.52/5.90 thf(fact_10142_Code__Numeral_Osub__code_I4_J,axiom,
% 5.52/5.90 ! [N: num] :
% 5.52/5.90 ( ( code_sub @ one @ ( bit0 @ N ) )
% 5.52/5.90 = ( code_Neg @ ( bitM @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Code_Numeral.sub_code(4)
% 5.52/5.90 thf(fact_10143_Code__Numeral_Osub__code_I2_J,axiom,
% 5.52/5.90 ! [M: num] :
% 5.52/5.90 ( ( code_sub @ ( bit0 @ M ) @ one )
% 5.52/5.90 = ( code_Pos @ ( bitM @ M ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Code_Numeral.sub_code(2)
% 5.52/5.90 thf(fact_10144_Code__Numeral_Odup__code_I3_J,axiom,
% 5.52/5.90 ! [N: num] :
% 5.52/5.90 ( ( code_dup @ ( code_Neg @ N ) )
% 5.52/5.90 = ( code_Neg @ ( bit0 @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Code_Numeral.dup_code(3)
% 5.52/5.90 thf(fact_10145_Code__Numeral_Odup__code_I2_J,axiom,
% 5.52/5.90 ! [N: num] :
% 5.52/5.90 ( ( code_dup @ ( code_Pos @ N ) )
% 5.52/5.90 = ( code_Pos @ ( bit0 @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Code_Numeral.dup_code(2)
% 5.52/5.90 thf(fact_10146_less__integer__code_I3_J,axiom,
% 5.52/5.90 ! [L: num] :
% 5.52/5.90 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_integer_code(3)
% 5.52/5.90 thf(fact_10147_less__integer__code_I7_J,axiom,
% 5.52/5.90 ! [K: num] : ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 5.52/5.90
% 5.52/5.90 % less_integer_code(7)
% 5.52/5.90 thf(fact_10148_less__integer__code_I2_J,axiom,
% 5.52/5.90 ! [L: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( code_Pos @ L ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_integer_code(2)
% 5.52/5.90 thf(fact_10149_less__integer__code_I4_J,axiom,
% 5.52/5.90 ! [K: num] :
% 5.52/5.90 ~ ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ zero_z3403309356797280102nteger ) ).
% 5.52/5.90
% 5.52/5.90 % less_integer_code(4)
% 5.52/5.90 thf(fact_10150_less__integer__code_I6_J,axiom,
% 5.52/5.90 ! [K: num,L: num] :
% 5.52/5.90 ~ ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ ( code_Neg @ L ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_integer_code(6)
% 5.52/5.90 thf(fact_10151_less__integer__code_I8_J,axiom,
% 5.52/5.90 ! [K: num,L: num] : ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ ( code_Pos @ L ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_integer_code(8)
% 5.52/5.90 thf(fact_10152_less__integer__code_I5_J,axiom,
% 5.52/5.90 ! [K: num,L: num] :
% 5.52/5.90 ( ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ ( code_Pos @ L ) )
% 5.52/5.90 = ( ord_less_num @ K @ L ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_integer_code(5)
% 5.52/5.90 thf(fact_10153_less__integer__code_I9_J,axiom,
% 5.52/5.90 ! [K: num,L: num] :
% 5.52/5.90 ( ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 5.52/5.90 = ( ord_less_num @ L @ K ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_integer_code(9)
% 5.52/5.90 thf(fact_10154_plus__integer__code_I6_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( plus_p5714425477246183910nteger @ ( code_Neg @ M ) @ ( code_Neg @ N ) )
% 5.52/5.90 = ( code_Neg @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % plus_integer_code(6)
% 5.52/5.90 thf(fact_10155_Pos__fold_I3_J,axiom,
% 5.52/5.90 ! [K: num] :
% 5.52/5.90 ( ( numera6620942414471956472nteger @ ( bit1 @ K ) )
% 5.52/5.90 = ( code_Pos @ ( bit1 @ K ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Pos_fold(3)
% 5.52/5.90 thf(fact_10156_Pos__fold_I2_J,axiom,
% 5.52/5.90 ! [K: num] :
% 5.52/5.90 ( ( numera6620942414471956472nteger @ ( bit0 @ K ) )
% 5.52/5.90 = ( code_Pos @ ( bit0 @ K ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Pos_fold(2)
% 5.52/5.90 thf(fact_10157_Pos__fold_I1_J,axiom,
% 5.52/5.90 ( ( numera6620942414471956472nteger @ one )
% 5.52/5.90 = ( code_Pos @ one ) ) ).
% 5.52/5.90
% 5.52/5.90 % Pos_fold(1)
% 5.52/5.90 thf(fact_10158_times__integer__code_I6_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( times_3573771949741848930nteger @ ( code_Neg @ M ) @ ( code_Neg @ N ) )
% 5.52/5.90 = ( code_Pos @ ( times_times_num @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % times_integer_code(6)
% 5.52/5.90 thf(fact_10159_times__integer__code_I5_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( times_3573771949741848930nteger @ ( code_Neg @ M ) @ ( code_Pos @ N ) )
% 5.52/5.90 = ( code_Neg @ ( times_times_num @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % times_integer_code(5)
% 5.52/5.90 thf(fact_10160_times__integer__code_I4_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( times_3573771949741848930nteger @ ( code_Pos @ M ) @ ( code_Neg @ N ) )
% 5.52/5.90 = ( code_Neg @ ( times_times_num @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % times_integer_code(4)
% 5.52/5.90 thf(fact_10161_one__integer__code,axiom,
% 5.52/5.90 ( one_one_Code_integer
% 5.52/5.90 = ( code_Pos @ one ) ) ).
% 5.52/5.90
% 5.52/5.90 % one_integer_code
% 5.52/5.90 thf(fact_10162_plus__integer__code_I3_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( plus_p5714425477246183910nteger @ ( code_Pos @ M ) @ ( code_Pos @ N ) )
% 5.52/5.90 = ( code_Pos @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % plus_integer_code(3)
% 5.52/5.90 thf(fact_10163_times__integer__code_I3_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( times_3573771949741848930nteger @ ( code_Pos @ M ) @ ( code_Pos @ N ) )
% 5.52/5.90 = ( code_Pos @ ( times_times_num @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % times_integer_code(3)
% 5.52/5.90 thf(fact_10164_minus__integer__code_I5_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( minus_8373710615458151222nteger @ ( code_Neg @ M ) @ ( code_Pos @ N ) )
% 5.52/5.90 = ( code_Neg @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % minus_integer_code(5)
% 5.52/5.90 thf(fact_10165_minus__integer__code_I4_J,axiom,
% 5.52/5.90 ! [M: num,N: num] :
% 5.52/5.90 ( ( minus_8373710615458151222nteger @ ( code_Pos @ M ) @ ( code_Neg @ N ) )
% 5.52/5.90 = ( code_Pos @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % minus_integer_code(4)
% 5.52/5.90 thf(fact_10166_less__eq__integer__code_I5_J,axiom,
% 5.52/5.90 ! [K: num,L: num] :
% 5.52/5.90 ( ( ord_le3102999989581377725nteger @ ( code_Pos @ K ) @ ( code_Pos @ L ) )
% 5.52/5.90 = ( ord_less_eq_num @ K @ L ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_eq_integer_code(5)
% 5.52/5.90 thf(fact_10167_less__eq__integer__code_I9_J,axiom,
% 5.52/5.90 ! [K: num,L: num] :
% 5.52/5.90 ( ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 5.52/5.90 = ( ord_less_eq_num @ L @ K ) ) ).
% 5.52/5.90
% 5.52/5.90 % less_eq_integer_code(9)
% 5.52/5.90 thf(fact_10168_Code__Numeral_Osub__code_I3_J,axiom,
% 5.52/5.90 ! [M: num] :
% 5.52/5.90 ( ( code_sub @ ( bit1 @ M ) @ one )
% 5.52/5.90 = ( code_Pos @ ( bit0 @ M ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Code_Numeral.sub_code(3)
% 5.52/5.90 thf(fact_10169_Code__Numeral_Osub__code_I5_J,axiom,
% 5.52/5.90 ! [N: num] :
% 5.52/5.90 ( ( code_sub @ one @ ( bit1 @ N ) )
% 5.52/5.90 = ( code_Neg @ ( bit0 @ N ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Code_Numeral.sub_code(5)
% 5.52/5.90 thf(fact_10170_max__nat_Omonoid__axioms,axiom,
% 5.52/5.90 monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 5.52/5.90
% 5.52/5.90 % max_nat.monoid_axioms
% 5.52/5.90 thf(fact_10171_sum__decode__def,axiom,
% 5.52/5.90 ( nat_sum_decode
% 5.52/5.90 = ( ^ [N3: nat] : ( if_Sum_sum_nat_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ ( sum_Inl_nat_nat @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( sum_Inr_nat_nat @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % sum_decode_def
% 5.52/5.90 thf(fact_10172_nth__item_Opinduct,axiom,
% 5.52/5.90 ! [A0: nat,P: nat > $o] :
% 5.52/5.90 ( ( accp_nat @ nth_item_rel @ A0 )
% 5.52/5.90 => ( ( ( accp_nat @ nth_item_rel @ zero_zero_nat )
% 5.52/5.90 => ( P @ zero_zero_nat ) )
% 5.52/5.90 => ( ! [N2: nat] :
% 5.52/5.90 ( ( accp_nat @ nth_item_rel @ ( suc @ N2 ) )
% 5.52/5.90 => ( ! [A8: nat,Aa: nat] :
% 5.52/5.90 ( ( ( nat_sum_decode @ N2 )
% 5.52/5.90 = ( sum_Inl_nat_nat @ A8 ) )
% 5.52/5.90 => ( ( ( nat_sum_decode @ A8 )
% 5.52/5.90 = ( sum_Inl_nat_nat @ Aa ) )
% 5.52/5.90 => ( P @ Aa ) ) )
% 5.52/5.90 => ( ! [A8: nat,B10: nat] :
% 5.52/5.90 ( ( ( nat_sum_decode @ N2 )
% 5.52/5.90 = ( sum_Inl_nat_nat @ A8 ) )
% 5.52/5.90 => ( ( ( nat_sum_decode @ A8 )
% 5.52/5.90 = ( sum_Inr_nat_nat @ B10 ) )
% 5.52/5.90 => ( P @ B10 ) ) )
% 5.52/5.90 => ( ! [B10: nat,Ba: nat,X6: nat,Y4: nat] :
% 5.52/5.90 ( ( ( nat_sum_decode @ N2 )
% 5.52/5.90 = ( sum_Inr_nat_nat @ B10 ) )
% 5.52/5.90 => ( ( ( nat_sum_decode @ B10 )
% 5.52/5.90 = ( sum_Inr_nat_nat @ Ba ) )
% 5.52/5.90 => ( ( ( product_Pair_nat_nat @ X6 @ Y4 )
% 5.52/5.90 = ( nat_prod_decode @ Ba ) )
% 5.52/5.90 => ( P @ X6 ) ) ) )
% 5.52/5.90 => ( ! [B10: nat,Ba: nat,X6: nat,Y4: nat] :
% 5.52/5.90 ( ( ( nat_sum_decode @ N2 )
% 5.52/5.90 = ( sum_Inr_nat_nat @ B10 ) )
% 5.52/5.90 => ( ( ( nat_sum_decode @ B10 )
% 5.52/5.90 = ( sum_Inr_nat_nat @ Ba ) )
% 5.52/5.90 => ( ( ( product_Pair_nat_nat @ X6 @ Y4 )
% 5.52/5.90 = ( nat_prod_decode @ Ba ) )
% 5.52/5.90 => ( P @ Y4 ) ) ) )
% 5.52/5.90 => ( P @ ( suc @ N2 ) ) ) ) ) ) )
% 5.52/5.90 => ( P @ A0 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % nth_item.pinduct
% 5.52/5.90 thf(fact_10173_le__sum__encode__Inl,axiom,
% 5.52/5.90 ! [X2: nat,Y2: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 5.52/5.90 => ( ord_less_eq_nat @ X2 @ ( nat_sum_encode @ ( sum_Inl_nat_nat @ Y2 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % le_sum_encode_Inl
% 5.52/5.90 thf(fact_10174_le__sum__encode__Inr,axiom,
% 5.52/5.90 ! [X2: nat,Y2: nat] :
% 5.52/5.90 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 5.52/5.90 => ( ord_less_eq_nat @ X2 @ ( nat_sum_encode @ ( sum_Inr_nat_nat @ Y2 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % le_sum_encode_Inr
% 5.52/5.90 thf(fact_10175_sum__encode__def,axiom,
% 5.52/5.90 ( nat_sum_encode
% 5.52/5.90 = ( sum_ca6763686470577984908at_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.52/5.90 @ ^ [B3: nat] : ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % sum_encode_def
% 5.52/5.90 thf(fact_10176_infinity__enat__def,axiom,
% 5.52/5.90 ( extend5688581933313929465d_enat
% 5.52/5.90 = ( extended_Abs_enat @ none_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % infinity_enat_def
% 5.52/5.90 thf(fact_10177_Abs__enat__cases,axiom,
% 5.52/5.90 ! [X2: extended_enat] :
% 5.52/5.90 ~ ! [Y3: option_nat] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( extended_Abs_enat @ Y3 ) )
% 5.52/5.90 => ~ ( member_option_nat @ Y3 @ top_to8920198386146353926on_nat ) ) ).
% 5.52/5.90
% 5.52/5.90 % Abs_enat_cases
% 5.52/5.90 thf(fact_10178_Abs__enat__induct,axiom,
% 5.52/5.90 ! [P: extended_enat > $o,X2: extended_enat] :
% 5.52/5.90 ( ! [Y3: option_nat] :
% 5.52/5.90 ( ( member_option_nat @ Y3 @ top_to8920198386146353926on_nat )
% 5.52/5.90 => ( P @ ( extended_Abs_enat @ Y3 ) ) )
% 5.52/5.90 => ( P @ X2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % Abs_enat_induct
% 5.52/5.90 thf(fact_10179_Abs__enat__inject,axiom,
% 5.52/5.90 ! [X2: option_nat,Y2: option_nat] :
% 5.52/5.90 ( ( member_option_nat @ X2 @ top_to8920198386146353926on_nat )
% 5.52/5.90 => ( ( member_option_nat @ Y2 @ top_to8920198386146353926on_nat )
% 5.52/5.90 => ( ( ( extended_Abs_enat @ X2 )
% 5.52/5.90 = ( extended_Abs_enat @ Y2 ) )
% 5.52/5.90 = ( X2 = Y2 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Abs_enat_inject
% 5.52/5.90 thf(fact_10180_enat__def,axiom,
% 5.52/5.90 ( extended_enat2
% 5.52/5.90 = ( ^ [N3: nat] : ( extended_Abs_enat @ ( some_nat @ N3 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % enat_def
% 5.52/5.90 thf(fact_10181_Abs__enat__inverse,axiom,
% 5.52/5.90 ! [Y2: option_nat] :
% 5.52/5.90 ( ( member_option_nat @ Y2 @ top_to8920198386146353926on_nat )
% 5.52/5.90 => ( ( extended_Rep_enat @ ( extended_Abs_enat @ Y2 ) )
% 5.52/5.90 = Y2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % Abs_enat_inverse
% 5.52/5.90 thf(fact_10182_Rep__enat__induct,axiom,
% 5.52/5.90 ! [Y2: option_nat,P: option_nat > $o] :
% 5.52/5.90 ( ( member_option_nat @ Y2 @ top_to8920198386146353926on_nat )
% 5.52/5.90 => ( ! [X4: extended_enat] : ( P @ ( extended_Rep_enat @ X4 ) )
% 5.52/5.90 => ( P @ Y2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rep_enat_induct
% 5.52/5.90 thf(fact_10183_Rep__enat__cases,axiom,
% 5.52/5.90 ! [Y2: option_nat] :
% 5.52/5.90 ( ( member_option_nat @ Y2 @ top_to8920198386146353926on_nat )
% 5.52/5.90 => ~ ! [X4: extended_enat] :
% 5.52/5.90 ( Y2
% 5.52/5.90 != ( extended_Rep_enat @ X4 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rep_enat_cases
% 5.52/5.90 thf(fact_10184_Rep__enat,axiom,
% 5.52/5.90 ! [X2: extended_enat] : ( member_option_nat @ ( extended_Rep_enat @ X2 ) @ top_to8920198386146353926on_nat ) ).
% 5.52/5.90
% 5.52/5.90 % Rep_enat
% 5.52/5.90 thf(fact_10185_Rep__enat__inject,axiom,
% 5.52/5.90 ! [X2: extended_enat,Y2: extended_enat] :
% 5.52/5.90 ( ( ( extended_Rep_enat @ X2 )
% 5.52/5.90 = ( extended_Rep_enat @ Y2 ) )
% 5.52/5.90 = ( X2 = Y2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rep_enat_inject
% 5.52/5.90 thf(fact_10186_Rep__enat__inverse,axiom,
% 5.52/5.90 ! [X2: extended_enat] :
% 5.52/5.90 ( ( extended_Abs_enat @ ( extended_Rep_enat @ X2 ) )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 % Rep_enat_inverse
% 5.52/5.90 thf(fact_10187_type__definition__enat,axiom,
% 5.52/5.90 type_d7649664348572268762on_nat @ extended_Rep_enat @ extended_Abs_enat @ top_to8920198386146353926on_nat ).
% 5.52/5.90
% 5.52/5.90 % type_definition_enat
% 5.52/5.90 thf(fact_10188_pcr__real__def,axiom,
% 5.52/5.90 ( pcr_real
% 5.52/5.90 = ( relcom2856161143838007533t_real
% 5.52/5.90 @ ( bNF_re4702136315717946289at_rat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.52/5.90 @ cr_real ) ) ).
% 5.52/5.90
% 5.52/5.90 % pcr_real_def
% 5.52/5.90 thf(fact_10189_real_Odomain,axiom,
% 5.52/5.90 ( ( domainp_nat_rat_real @ pcr_real )
% 5.52/5.90 = ( ^ [X: nat > rat] :
% 5.52/5.90 ? [Y: nat > rat] :
% 5.52/5.90 ( ( bNF_re4702136315717946289at_rat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 )
% 5.52/5.90 @ X
% 5.52/5.90 @ Y )
% 5.52/5.90 & ( realrel @ Y @ Y ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % real.domain
% 5.52/5.90 thf(fact_10190_lcm__altdef__int,axiom,
% 5.52/5.90 ( gcd_lcm_int
% 5.52/5.90 = ( ^ [A4: int,B3: int] : ( divide_divide_int @ ( times_times_int @ ( abs_abs_int @ A4 ) @ ( abs_abs_int @ B3 ) ) @ ( gcd_gcd_int @ A4 @ B3 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % lcm_altdef_int
% 5.52/5.90 thf(fact_10191_Domainp__pcr__real,axiom,
% 5.52/5.90 ( ( domainp_nat_rat_real @ pcr_real )
% 5.52/5.90 = cauchy ) ).
% 5.52/5.90
% 5.52/5.90 % Domainp_pcr_real
% 5.52/5.90 thf(fact_10192_real_Odomain__eq,axiom,
% 5.52/5.90 ( ( domainp_nat_rat_real @ pcr_real )
% 5.52/5.90 = ( ^ [X: nat > rat] : ( realrel @ X @ X ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % real.domain_eq
% 5.52/5.90 thf(fact_10193_lcm__pos__int,axiom,
% 5.52/5.90 ! [M: int,N: int] :
% 5.52/5.90 ( ( M != zero_zero_int )
% 5.52/5.90 => ( ( N != zero_zero_int )
% 5.52/5.90 => ( ord_less_int @ zero_zero_int @ ( gcd_lcm_int @ M @ N ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % lcm_pos_int
% 5.52/5.90 thf(fact_10194_real_Odomain__par__left__total,axiom,
% 5.52/5.90 ! [P5: ( nat > rat ) > $o] :
% 5.52/5.90 ( ( left_t2768085380646472630at_rat
% 5.52/5.90 @ ( bNF_re4702136315717946289at_rat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) ) )
% 5.52/5.90 => ( ( bNF_re728719798268516973at_o_o
% 5.52/5.90 @ ( bNF_re4702136315717946289at_rat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 5.52/5.90 @ P5
% 5.52/5.90 @ ^ [X: nat > rat] : ( realrel @ X @ X ) )
% 5.52/5.90 => ( ( domainp_nat_rat_real @ pcr_real )
% 5.52/5.90 = P5 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % real.domain_par_left_total
% 5.52/5.90 thf(fact_10195_lcm__nat__def,axiom,
% 5.52/5.90 ( gcd_lcm_nat
% 5.52/5.90 = ( ^ [X: nat,Y: nat] : ( divide_divide_nat @ ( times_times_nat @ X @ Y ) @ ( gcd_gcd_nat @ X @ Y ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % lcm_nat_def
% 5.52/5.90 thf(fact_10196_prod__gcd__lcm__nat,axiom,
% 5.52/5.90 ( times_times_nat
% 5.52/5.90 = ( ^ [M3: nat,N3: nat] : ( times_times_nat @ ( gcd_gcd_nat @ M3 @ N3 ) @ ( gcd_lcm_nat @ M3 @ N3 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % prod_gcd_lcm_nat
% 5.52/5.90 thf(fact_10197_lcm__pos__nat,axiom,
% 5.52/5.90 ! [M: nat,N: nat] :
% 5.52/5.90 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.52/5.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.52/5.90 => ( ord_less_nat @ zero_zero_nat @ ( gcd_lcm_nat @ M @ N ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % lcm_pos_nat
% 5.52/5.90 thf(fact_10198_Rep__real__induct,axiom,
% 5.52/5.90 ! [Y2: set_nat_rat,P: set_nat_rat > $o] :
% 5.52/5.90 ( ( member_set_nat_rat @ Y2
% 5.52/5.90 @ ( collect_set_nat_rat
% 5.52/5.90 @ ^ [C3: set_nat_rat] :
% 5.52/5.90 ? [X: nat > rat] :
% 5.52/5.90 ( ( realrel @ X @ X )
% 5.52/5.90 & ( C3
% 5.52/5.90 = ( collect_nat_rat @ ( realrel @ X ) ) ) ) ) )
% 5.52/5.90 => ( ! [X4: real] : ( P @ ( rep_real @ X4 ) )
% 5.52/5.90 => ( P @ Y2 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rep_real_induct
% 5.52/5.90 thf(fact_10199_Rep__real__cases,axiom,
% 5.52/5.90 ! [Y2: set_nat_rat] :
% 5.52/5.90 ( ( member_set_nat_rat @ Y2
% 5.52/5.90 @ ( collect_set_nat_rat
% 5.52/5.90 @ ^ [C3: set_nat_rat] :
% 5.52/5.90 ? [X: nat > rat] :
% 5.52/5.90 ( ( realrel @ X @ X )
% 5.52/5.90 & ( C3
% 5.52/5.90 = ( collect_nat_rat @ ( realrel @ X ) ) ) ) ) )
% 5.52/5.90 => ~ ! [X4: real] :
% 5.52/5.90 ( Y2
% 5.52/5.90 != ( rep_real @ X4 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rep_real_cases
% 5.52/5.90 thf(fact_10200_Rep__real__inject,axiom,
% 5.52/5.90 ! [X2: real,Y2: real] :
% 5.52/5.90 ( ( ( rep_real @ X2 )
% 5.52/5.90 = ( rep_real @ Y2 ) )
% 5.52/5.90 = ( X2 = Y2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rep_real_inject
% 5.52/5.90 thf(fact_10201_Rep__real,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( member_set_nat_rat @ ( rep_real @ X2 )
% 5.52/5.90 @ ( collect_set_nat_rat
% 5.52/5.90 @ ^ [C3: set_nat_rat] :
% 5.52/5.90 ? [X: nat > rat] :
% 5.52/5.90 ( ( realrel @ X @ X )
% 5.52/5.90 & ( C3
% 5.52/5.90 = ( collect_nat_rat @ ( realrel @ X ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Rep_real
% 5.52/5.90 thf(fact_10202_Abs__real__inverse,axiom,
% 5.52/5.90 ! [Y2: set_nat_rat] :
% 5.52/5.90 ( ( member_set_nat_rat @ Y2
% 5.52/5.90 @ ( collect_set_nat_rat
% 5.52/5.90 @ ^ [C3: set_nat_rat] :
% 5.52/5.90 ? [X: nat > rat] :
% 5.52/5.90 ( ( realrel @ X @ X )
% 5.52/5.90 & ( C3
% 5.52/5.90 = ( collect_nat_rat @ ( realrel @ X ) ) ) ) ) )
% 5.52/5.90 => ( ( rep_real @ ( abs_real @ Y2 ) )
% 5.52/5.90 = Y2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % Abs_real_inverse
% 5.52/5.90 thf(fact_10203_rep__real__def,axiom,
% 5.52/5.90 ( rep_real2
% 5.52/5.90 = ( quot_r1730120044975580712at_rat @ rep_real ) ) ).
% 5.52/5.90
% 5.52/5.90 % rep_real_def
% 5.52/5.90 thf(fact_10204_Rep__real__inverse,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ( ( abs_real @ ( rep_real @ X2 ) )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 % Rep_real_inverse
% 5.52/5.90 thf(fact_10205_Abs__real__inject,axiom,
% 5.52/5.90 ! [X2: set_nat_rat,Y2: set_nat_rat] :
% 5.52/5.90 ( ( member_set_nat_rat @ X2
% 5.52/5.90 @ ( collect_set_nat_rat
% 5.52/5.90 @ ^ [C3: set_nat_rat] :
% 5.52/5.90 ? [X: nat > rat] :
% 5.52/5.90 ( ( realrel @ X @ X )
% 5.52/5.90 & ( C3
% 5.52/5.90 = ( collect_nat_rat @ ( realrel @ X ) ) ) ) ) )
% 5.52/5.90 => ( ( member_set_nat_rat @ Y2
% 5.52/5.90 @ ( collect_set_nat_rat
% 5.52/5.90 @ ^ [C3: set_nat_rat] :
% 5.52/5.90 ? [X: nat > rat] :
% 5.52/5.90 ( ( realrel @ X @ X )
% 5.52/5.90 & ( C3
% 5.52/5.90 = ( collect_nat_rat @ ( realrel @ X ) ) ) ) ) )
% 5.52/5.90 => ( ( ( abs_real @ X2 )
% 5.52/5.90 = ( abs_real @ Y2 ) )
% 5.52/5.90 = ( X2 = Y2 ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Abs_real_inject
% 5.52/5.90 thf(fact_10206_Abs__real__induct,axiom,
% 5.52/5.90 ! [P: real > $o,X2: real] :
% 5.52/5.90 ( ! [Y3: set_nat_rat] :
% 5.52/5.90 ( ( member_set_nat_rat @ Y3
% 5.52/5.90 @ ( collect_set_nat_rat
% 5.52/5.90 @ ^ [C3: set_nat_rat] :
% 5.52/5.90 ? [X: nat > rat] :
% 5.52/5.90 ( ( realrel @ X @ X )
% 5.52/5.90 & ( C3
% 5.52/5.90 = ( collect_nat_rat @ ( realrel @ X ) ) ) ) ) )
% 5.52/5.90 => ( P @ ( abs_real @ Y3 ) ) )
% 5.52/5.90 => ( P @ X2 ) ) ).
% 5.52/5.90
% 5.52/5.90 % Abs_real_induct
% 5.52/5.90 thf(fact_10207_Abs__real__cases,axiom,
% 5.52/5.90 ! [X2: real] :
% 5.52/5.90 ~ ! [Y3: set_nat_rat] :
% 5.52/5.90 ( ( X2
% 5.52/5.90 = ( abs_real @ Y3 ) )
% 5.52/5.90 => ~ ( member_set_nat_rat @ Y3
% 5.52/5.90 @ ( collect_set_nat_rat
% 5.52/5.90 @ ^ [C3: set_nat_rat] :
% 5.52/5.90 ? [X: nat > rat] :
% 5.52/5.90 ( ( realrel @ X @ X )
% 5.52/5.90 & ( C3
% 5.52/5.90 = ( collect_nat_rat @ ( realrel @ X ) ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % Abs_real_cases
% 5.52/5.90 thf(fact_10208_Real__def,axiom,
% 5.52/5.90 ( real2
% 5.52/5.90 = ( quot_a3129823074075660125t_real @ realrel @ abs_real ) ) ).
% 5.52/5.90
% 5.52/5.90 % Real_def
% 5.52/5.90 thf(fact_10209_type__definition__real,axiom,
% 5.52/5.90 ( type_d8072115097938612567at_rat @ rep_real @ abs_real
% 5.52/5.90 @ ( collect_set_nat_rat
% 5.52/5.90 @ ^ [C3: set_nat_rat] :
% 5.52/5.90 ? [X: nat > rat] :
% 5.52/5.90 ( ( realrel @ X @ X )
% 5.52/5.90 & ( C3
% 5.52/5.90 = ( collect_nat_rat @ ( realrel @ X ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % type_definition_real
% 5.52/5.90 thf(fact_10210_real_Odomain__par,axiom,
% 5.52/5.90 ! [DT: nat > $o,DS: rat > $o,P22: ( nat > rat ) > $o] :
% 5.52/5.90 ( ( ( domainp_nat_nat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.52/5.90 = DT )
% 5.52/5.90 => ( ( ( domainp_rat_rat
% 5.52/5.90 @ ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.52/5.90 = DS )
% 5.52/5.90 => ( ( left_unique_nat_nat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.52/5.90 => ( ( bNF_re728719798268516973at_o_o
% 5.52/5.90 @ ( bNF_re4702136315717946289at_rat
% 5.52/5.90 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.52/5.90 @ ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.52/5.90 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 5.52/5.90 @ P22
% 5.52/5.90 @ ^ [X: nat > rat] : ( realrel @ X @ X ) )
% 5.52/5.90 => ( ( domainp_nat_rat_real @ pcr_real )
% 5.52/5.90 = ( inf_inf_nat_rat_o @ ( basic_208271146493774413at_rat @ DT @ DS ) @ P22 ) ) ) ) ) ) ).
% 5.52/5.90
% 5.52/5.90 % real.domain_par
% 5.52/5.90
% 5.52/5.90 % Helper facts (50)
% 5.52/5.90 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.52/5.90 ! [X2: int,Y2: int] :
% 5.52/5.90 ( ( if_int @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.52/5.90 ! [X2: int,Y2: int] :
% 5.52/5.90 ( ( if_int @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.52/5.90 ! [X2: nat,Y2: nat] :
% 5.52/5.90 ( ( if_nat @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.52/5.90 ! [X2: nat,Y2: nat] :
% 5.52/5.90 ( ( if_nat @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.52/5.90 ! [X2: num,Y2: num] :
% 5.52/5.90 ( ( if_num @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.52/5.90 ! [X2: num,Y2: num] :
% 5.52/5.90 ( ( if_num @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.52/5.90 ! [X2: rat,Y2: rat] :
% 5.52/5.90 ( ( if_rat @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.52/5.90 ! [X2: rat,Y2: rat] :
% 5.52/5.90 ( ( if_rat @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.52/5.90 ! [X2: real,Y2: real] :
% 5.52/5.90 ( ( if_real @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.52/5.90 ! [X2: real,Y2: real] :
% 5.52/5.90 ( ( if_real @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.52/5.90 ! [P: real > $o] :
% 5.52/5.90 ( ( P @ ( fChoice_real @ P ) )
% 5.52/5.90 = ( ? [X7: real] : ( P @ X7 ) ) ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.52/5.90 ! [X2: complex,Y2: complex] :
% 5.52/5.90 ( ( if_complex @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.52/5.90 ! [X2: complex,Y2: complex] :
% 5.52/5.90 ( ( if_complex @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.52/5.90 ! [X2: extended_enat,Y2: extended_enat] :
% 5.52/5.90 ( ( if_Extended_enat @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.52/5.90 ! [X2: extended_enat,Y2: extended_enat] :
% 5.52/5.90 ( ( if_Extended_enat @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.52/5.90 ! [X2: code_integer,Y2: code_integer] :
% 5.52/5.90 ( ( if_Code_integer @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.52/5.90 ! [X2: code_integer,Y2: code_integer] :
% 5.52/5.90 ( ( if_Code_integer @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.52/5.90 ! [X2: set_int,Y2: set_int] :
% 5.52/5.90 ( ( if_set_int @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.52/5.90 ! [X2: set_int,Y2: set_int] :
% 5.52/5.90 ( ( if_set_int @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.52/5.90 ! [X2: set_nat,Y2: set_nat] :
% 5.52/5.90 ( ( if_set_nat @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.52/5.90 ! [X2: set_nat,Y2: set_nat] :
% 5.52/5.90 ( ( if_set_nat @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.52/5.90 ! [X2: vEBT_VEBT,Y2: vEBT_VEBT] :
% 5.52/5.90 ( ( if_VEBT_VEBT @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.52/5.90 ! [X2: vEBT_VEBT,Y2: vEBT_VEBT] :
% 5.52/5.90 ( ( if_VEBT_VEBT @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.52/5.90 ! [X2: list_int,Y2: list_int] :
% 5.52/5.90 ( ( if_list_int @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.52/5.90 ! [X2: list_int,Y2: list_int] :
% 5.52/5.90 ( ( if_list_int @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.52/5.90 ! [X2: list_nat,Y2: list_nat] :
% 5.52/5.90 ( ( if_list_nat @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.52/5.90 ! [X2: list_nat,Y2: list_nat] :
% 5.52/5.90 ( ( if_list_nat @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.52/5.90 ! [X2: int > int,Y2: int > int] :
% 5.52/5.90 ( ( if_int_int @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.52/5.90 ! [X2: int > int,Y2: int > int] :
% 5.52/5.90 ( ( if_int_int @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.52/5.90 ! [X2: nat > rat,Y2: nat > rat] :
% 5.52/5.90 ( ( if_nat_rat @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.52/5.90 ! [X2: nat > rat,Y2: nat > rat] :
% 5.52/5.90 ( ( if_nat_rat @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.52/5.90 ! [X2: option_nat,Y2: option_nat] :
% 5.52/5.90 ( ( if_option_nat @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.52/5.90 ! [X2: option_nat,Y2: option_nat] :
% 5.52/5.90 ( ( if_option_nat @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.52/5.90 ! [X2: option_num,Y2: option_num] :
% 5.52/5.90 ( ( if_option_num @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.52/5.90 ! [X2: option_num,Y2: option_num] :
% 5.52/5.90 ( ( if_option_num @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.52/5.90 ! [X2: sum_sum_nat_nat,Y2: sum_sum_nat_nat] :
% 5.52/5.90 ( ( if_Sum_sum_nat_nat @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.52/5.90 ! [X2: sum_sum_nat_nat,Y2: sum_sum_nat_nat] :
% 5.52/5.90 ( ( if_Sum_sum_nat_nat @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.52/5.90 ! [X2: product_prod_int_int,Y2: product_prod_int_int] :
% 5.52/5.90 ( ( if_Pro3027730157355071871nt_int @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.52/5.90 ! [X2: product_prod_int_int,Y2: product_prod_int_int] :
% 5.52/5.90 ( ( if_Pro3027730157355071871nt_int @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.52/5.90 ! [X2: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 5.52/5.90 ( ( if_Pro6206227464963214023at_nat @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.52/5.90 ! [X2: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 5.52/5.90 ( ( if_Pro6206227464963214023at_nat @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 5.52/5.90 ! [X2: nat > int > int,Y2: nat > int > int] :
% 5.52/5.90 ( ( if_nat_int_int @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 5.52/5.90 ! [X2: nat > int > int,Y2: nat > int > int] :
% 5.52/5.90 ( ( if_nat_int_int @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 5.52/5.90 ! [X2: nat > nat > nat,Y2: nat > nat > nat] :
% 5.52/5.90 ( ( if_nat_nat_nat @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 5.52/5.90 ! [X2: nat > nat > nat,Y2: nat > nat > nat] :
% 5.52/5.90 ( ( if_nat_nat_nat @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.52/5.90 ! [X2: produc6271795597528267376eger_o,Y2: produc6271795597528267376eger_o] :
% 5.52/5.90 ( ( if_Pro5737122678794959658eger_o @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.52/5.90 ! [X2: produc6271795597528267376eger_o,Y2: produc6271795597528267376eger_o] :
% 5.52/5.90 ( ( if_Pro5737122678794959658eger_o @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.52/5.90 ! [P: $o] :
% 5.52/5.90 ( ( P = $true )
% 5.52/5.90 | ( P = $false ) ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.52/5.90 ! [X2: produc8923325533196201883nteger,Y2: produc8923325533196201883nteger] :
% 5.52/5.90 ( ( if_Pro6119634080678213985nteger @ $false @ X2 @ Y2 )
% 5.52/5.90 = Y2 ) ).
% 5.52/5.90
% 5.52/5.90 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.52/5.90 ! [X2: produc8923325533196201883nteger,Y2: produc8923325533196201883nteger] :
% 5.52/5.90 ( ( if_Pro6119634080678213985nteger @ $true @ X2 @ Y2 )
% 5.52/5.90 = X2 ) ).
% 5.52/5.90
% 5.52/5.90 % Conjectures (1)
% 5.52/5.90 thf(conj_0,conjecture,
% 5.52/5.90 ord_less_eq_nat @ ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ).
% 6.75/7.06
% 6.75/7.06 %------------------------------------------------------------------------------
% 6.75/7.06 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.wngkls7QLK/cvc5---1.0.5_28657.p...
% 6.75/7.06 (declare-sort $$unsorted 0)
% 6.75/7.06 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 6.75/7.06 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 6.75/7.06 (declare-sort tptp.produc1193250871479095198on_num 0)
% 6.75/7.06 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 6.75/7.06 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 6.75/7.06 (declare-sort tptp.produc3368934014287244435at_num 0)
% 6.75/7.06 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 6.75/7.06 (declare-sort tptp.produc7036089656553540234on_num 0)
% 6.75/7.06 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 6.75/7.06 (declare-sort tptp.set_Pr8693737435421807431at_nat 0)
% 6.75/7.06 (declare-sort tptp.produc859450856879609959at_nat 0)
% 6.75/7.06 (declare-sort tptp.set_fi4554929511873752355omplex 0)
% 6.75/7.06 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.75/7.06 (declare-sort tptp.produc3447558737645232053on_num 0)
% 6.75/7.06 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 6.75/7.06 (declare-sort tptp.produc2963631642982155120at_num 0)
% 6.75/7.06 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 6.75/7.06 (declare-sort tptp.set_fi7789364187291644575l_real 0)
% 6.75/7.06 (declare-sort tptp.filter6041513312241820739omplex 0)
% 6.75/7.06 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.75/7.06 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.75/7.06 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.75/7.06 (declare-sort tptp.set_Pr5085853215250843933omplex 0)
% 6.75/7.06 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.75/7.06 (declare-sort tptp.produc7272778201969148633d_enat 0)
% 6.75/7.06 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.75/7.06 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.75/7.06 (declare-sort tptp.filter2146258269922977983l_real 0)
% 6.75/7.06 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.75/7.06 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 6.75/7.06 (declare-sort tptp.set_Pr6218003697084177305l_real 0)
% 6.75/7.06 (declare-sort tptp.list_P3744719386663036955um_num 0)
% 6.75/7.06 (declare-sort tptp.list_P1726324292696863441at_num 0)
% 6.75/7.06 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 6.75/7.06 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 6.75/7.06 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.75/7.06 (declare-sort tptp.produc8025551001238799321T_VEBT 0)
% 6.75/7.06 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.75/7.06 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.75/7.06 (declare-sort tptp.produc4411394909380815293omplex 0)
% 6.75/7.06 (declare-sort tptp.list_set_nat_rat 0)
% 6.75/7.06 (declare-sort tptp.set_set_nat_rat 0)
% 6.75/7.06 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.75/7.06 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.75/7.06 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 6.75/7.06 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.75/7.06 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 6.75/7.06 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.75/7.06 (declare-sort tptp.set_li5464603477888414924d_enat 0)
% 6.75/7.06 (declare-sort tptp.produc2422161461964618553l_real 0)
% 6.75/7.06 (declare-sort tptp.product_prod_num_num 0)
% 6.75/7.06 (declare-sort tptp.product_prod_nat_num 0)
% 6.75/7.06 (declare-sort tptp.product_prod_nat_nat 0)
% 6.75/7.06 (declare-sort tptp.product_prod_int_int 0)
% 6.75/7.06 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.75/7.06 (declare-sort tptp.set_list_complex 0)
% 6.75/7.06 (declare-sort tptp.list_option_nat 0)
% 6.75/7.06 (declare-sort tptp.sum_sum_nat_nat 0)
% 6.75/7.06 (declare-sort tptp.set_option_nat 0)
% 6.75/7.06 (declare-sort tptp.set_nat_rat 0)
% 6.75/7.06 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.75/7.06 (declare-sort tptp.set_list_nat 0)
% 6.75/7.06 (declare-sort tptp.set_list_int 0)
% 6.75/7.06 (declare-sort tptp.product_prod_o_nat 0)
% 6.75/7.06 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.75/7.06 (declare-sort tptp.set_set_nat 0)
% 6.75/7.06 (declare-sort tptp.set_Code_integer 0)
% 6.75/7.06 (declare-sort tptp.list_Extended_enat 0)
% 6.75/7.06 (declare-sort tptp.set_Product_unit 0)
% 6.75/7.06 (declare-sort tptp.set_Extended_enat 0)
% 6.75/7.06 (declare-sort tptp.list_complex 0)
% 6.75/7.06 (declare-sort tptp.set_list_o 0)
% 6.75/7.06 (declare-sort tptp.product_prod_o_o 0)
% 6.75/7.06 (declare-sort tptp.set_complex 0)
% 6.75/7.06 (declare-sort tptp.filter_real 0)
% 6.75/7.06 (declare-sort tptp.option_num 0)
% 6.75/7.06 (declare-sort tptp.option_nat 0)
% 6.75/7.06 (declare-sort tptp.filter_nat 0)
% 6.75/7.06 (declare-sort tptp.set_char 0)
% 6.75/7.06 (declare-sort tptp.list_real 0)
% 6.75/7.06 (declare-sort tptp.set_real 0)
% 6.75/7.06 (declare-sort tptp.list_num 0)
% 6.75/7.06 (declare-sort tptp.list_nat 0)
% 6.75/7.06 (declare-sort tptp.list_int 0)
% 6.75/7.06 (declare-sort tptp.vEBT_VEBT 0)
% 6.75/7.06 (declare-sort tptp.set_rat 0)
% 6.75/7.06 (declare-sort tptp.set_num 0)
% 6.75/7.06 (declare-sort tptp.set_nat 0)
% 6.75/7.06 (declare-sort tptp.set_int 0)
% 6.75/7.06 (declare-sort tptp.code_integer 0)
% 6.75/7.06 (declare-sort tptp.product_unit 0)
% 6.75/7.06 (declare-sort tptp.extended_enat 0)
% 6.75/7.06 (declare-sort tptp.list_o 0)
% 6.75/7.06 (declare-sort tptp.complex 0)
% 6.75/7.06 (declare-sort tptp.literal 0)
% 6.75/7.06 (declare-sort tptp.set_o 0)
% 6.75/7.06 (declare-sort tptp.char 0)
% 6.75/7.06 (declare-sort tptp.real 0)
% 6.75/7.06 (declare-sort tptp.rat 0)
% 6.75/7.06 (declare-sort tptp.num 0)
% 6.75/7.06 (declare-sort tptp.nat 0)
% 6.75/7.06 (declare-sort tptp.int 0)
% 6.75/7.06 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 6.75/7.06 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.75/7.06 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.75/7.06 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.75/7.06 (declare-fun tptp.archimedean_frac_rat (tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.75/7.06 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.75/7.06 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.06 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.06 (declare-fun tptp.bNF_re1962705104956426057at_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re895249473297799549at_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re728719798268516973at_o_o ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> Bool Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re4695409256820837752l_real ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> tptp.real tptp.real) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> tptp.real tptp.real tptp.real)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re4521903465945308077real_o ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> (-> tptp.nat tptp.rat) Bool) (-> tptp.real Bool) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> tptp.real tptp.real Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re3023117138289059399t_real ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> tptp.real tptp.real)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re4297313714947099218al_o_o ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> Bool Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) (-> tptp.real Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re3403563459893282935_int_o ((-> tptp.int tptp.int Bool) (-> (-> tptp.int Bool) (-> tptp.int Bool) Bool) (-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re711492959462206631nt_int ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.int) (-> tptp.int tptp.int) Bool) (-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int tptp.int)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re5089333283451836215nt_o_o ((-> tptp.int tptp.int Bool) (-> Bool Bool Bool) (-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re4712519889275205905nt_int ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool) (-> tptp.int tptp.int) (-> tptp.int tptp.int)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re578469030762574527_nat_o ((-> tptp.nat tptp.nat Bool) (-> (-> tptp.nat Bool) (-> tptp.nat Bool) Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re1345281282404953727at_nat ((-> tptp.nat tptp.nat Bool) (-> (-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) Bool) (-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat tptp.nat)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re5653821019739307937at_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re6830278522597306478at_int ((-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.nat tptp.product_prod_nat_nat) (-> tptp.nat tptp.int)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re4702136315717946289at_rat ((-> tptp.nat tptp.nat Bool) (-> tptp.rat tptp.rat Bool) (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re8402795839162346335um_int ((-> tptp.num tptp.num Bool) (-> (-> tptp.num tptp.int) (-> tptp.num tptp.int) Bool) (-> tptp.num tptp.num tptp.int) (-> tptp.num tptp.num tptp.int)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re1822329894187522285nt_int ((-> tptp.num tptp.num Bool) (-> tptp.int tptp.int Bool) (-> tptp.num tptp.int) (-> tptp.num tptp.int)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re8699439704749558557nt_o_o ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> Bool Bool Bool) (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re1494630372529172596at_o_o ((-> tptp.product_prod_int_int tptp.rat Bool) (-> Bool Bool Bool) (-> tptp.product_prod_int_int Bool) (-> tptp.rat Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re717283939379294677_int_o ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.int Bool) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re7408651293131936558nt_int ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int tptp.int)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re6644619430987730960nt_o_o ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> Bool Bool Bool) (-> tptp.product_prod_nat_nat Bool) (-> tptp.int Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re7400052026677387805at_int ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re4202695980764964119_nat_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re3099431351363272937at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool) (-> 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 tptp.product_prod_nat_nat)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re3666534408544137501at_o_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> Bool Bool Bool) (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_re2241393799969408733at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) Bool)
% 6.75/7.06 (declare-fun tptp.bNF_We3818239936649020644el_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.75/7.06 (declare-fun tptp.basic_208271146493774413at_rat ((-> tptp.nat Bool) (-> tptp.rat Bool) (-> tptp.nat tptp.rat)) Bool)
% 6.75/7.06 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.75/7.06 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.75/7.06 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.75/7.06 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.75/7.06 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.75/7.06 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.bit_se9216721137139052372nteger (tptp.code_integer tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.bit_un1837492267222099188nd_num (tptp.num tptp.num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.bit_un5425074673868309765um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.75/7.06 (declare-fun tptp.bit_un6178654185764691216or_num (tptp.num tptp.num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.bit_un3595099601533988841um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.75/7.06 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.75/7.06 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.bit_un2901131394128224187um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.75/7.06 (declare-fun tptp.code_Neg (tptp.num) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.code_Pos (tptp.num) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.75/7.06 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.75/7.06 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.75/7.06 (declare-fun tptp.code_dup (tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.75/7.06 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.75/7.06 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.75/7.06 (declare-fun tptp.code_sub (tptp.num tptp.num) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 6.75/7.06 (declare-fun tptp.code_Target_positive (tptp.num) tptp.int)
% 6.75/7.06 (declare-fun tptp.comple2295165028678016749d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.comple8358262395181532106omplex (tptp.set_fi4554929511873752355omplex) tptp.filter6041513312241820739omplex)
% 6.75/7.06 (declare-fun tptp.comple2936214249959783750l_real (tptp.set_fi7789364187291644575l_real) tptp.filter2146258269922977983l_real)
% 6.75/7.06 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.75/7.06 (declare-fun tptp.comple4398354569131411667d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.75/7.06 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.75/7.06 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.75/7.06 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.75/7.06 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.75/7.06 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.75/7.06 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.75/7.06 (declare-fun tptp.rcis (tptp.real tptp.real) tptp.complex)
% 6.75/7.06 (declare-fun tptp.nth_item_rel (tptp.nat tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.75/7.06 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.75/7.06 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.75/7.06 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.75/7.06 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.75/7.06 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.75/7.06 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.75/7.06 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.75/7.06 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.75/7.06 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.75/7.06 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.75/7.06 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.75/7.06 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.75/7.06 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.75/7.06 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.75/7.06 (declare-fun tptp.euclid4774559944035922753ze_int (tptp.int) tptp.nat)
% 6.75/7.06 (declare-fun tptp.euclid4777050414544973029ze_nat (tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.euclid3395696857347342551nt_int (tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.euclid3398187327856392827nt_nat (tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.extended_eSuc (tptp.extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.extended_enat2 (tptp.nat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.extended_Abs_enat (tptp.option_nat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.extended_Rep_enat (tptp.extended_enat) tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.extended_case_enat_o ((-> tptp.nat Bool) Bool tptp.extended_enat) Bool)
% 6.75/7.06 (declare-fun tptp.extend3600170679010898289d_enat ((-> tptp.nat tptp.extended_enat) tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.extend5688581933313929465d_enat () tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.extended_the_enat (tptp.extended_enat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.75/7.06 (declare-fun tptp.comm_s3181272606743183617d_enat (tptp.extended_enat tptp.nat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.75/7.06 (declare-fun tptp.semiri4449623510593786356d_enat (tptp.nat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.75/7.06 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.75/7.06 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.75/7.06 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.75/7.06 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 6.75/7.06 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.75/7.06 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.75/7.06 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.75/7.06 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.75/7.06 (declare-fun tptp.princi3496590319149328850omplex (tptp.set_Pr5085853215250843933omplex) tptp.filter6041513312241820739omplex)
% 6.75/7.06 (declare-fun tptp.princi6114159922880469582l_real (tptp.set_Pr6218003697084177305l_real) tptp.filter2146258269922977983l_real)
% 6.75/7.06 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 6.75/7.06 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.75/7.06 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.75/7.06 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 6.75/7.06 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.75/7.06 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 6.75/7.06 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.75/7.06 (declare-fun tptp.finite4001608067531595151d_enat (tptp.set_Extended_enat) Bool)
% 6.75/7.06 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.75/7.06 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 6.75/7.06 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 6.75/7.06 (declare-fun tptp.finite1862508098717546133d_enat (tptp.set_li5464603477888414924d_enat) Bool)
% 6.75/7.06 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 6.75/7.06 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 6.75/7.06 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.75/7.06 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 6.75/7.06 (declare-fun tptp.finite5523153139673422903on_nat (tptp.set_option_nat) Bool)
% 6.75/7.06 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 6.75/7.06 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 6.75/7.06 (declare-fun tptp.finite6430367030675640852at_rat (tptp.set_set_nat_rat) Bool)
% 6.75/7.06 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 6.75/7.06 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.75/7.06 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.75/7.06 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.75/7.06 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 6.75/7.06 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 6.75/7.06 (declare-fun tptp.id_o (Bool) Bool)
% 6.75/7.06 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.75/7.06 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.75/7.06 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.75/7.06 (declare-fun tptp.map_fu434086159418415080_int_o ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat Bool) tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.int tptp.int) Bool)
% 6.75/7.06 (declare-fun tptp.map_fu4960017516451851995nt_int ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.map_fu4826362097070443709at_o_o ((-> tptp.int tptp.product_prod_nat_nat) (-> Bool Bool) (-> tptp.product_prod_nat_nat Bool) tptp.int) Bool)
% 6.75/7.06 (declare-fun tptp.map_fu3667384564859982768at_int ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.map_fu898904425404107465nt_o_o ((-> tptp.rat tptp.product_prod_int_int) (-> Bool Bool) (-> tptp.product_prod_int_int Bool) tptp.rat) Bool)
% 6.75/7.06 (declare-fun tptp.map_fu1532550112467129777l_real ((-> tptp.real tptp.nat tptp.rat) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real tptp.real) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.map_fu7146612038024189824t_real ((-> tptp.real tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.real) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.map_fu1856342031159181835at_o_o ((-> tptp.real tptp.nat tptp.rat) (-> Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) tptp.real) Bool)
% 6.75/7.06 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.75/7.06 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.fun_pair_leq () tptp.set_Pr8693737435421807431at_nat)
% 6.75/7.06 (declare-fun tptp.fun_pair_less () tptp.set_Pr8693737435421807431at_nat)
% 6.75/7.06 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.75/7.06 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.75/7.06 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.gcd_lcm_int (tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.gcd_lcm_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.75/7.06 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.75/7.06 (declare-fun tptp.minus_925952699566721837d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 6.75/7.06 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.75/7.06 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.minus_5999362281193037231on_nat (tptp.set_option_nat tptp.set_option_nat) tptp.set_option_nat)
% 6.75/7.06 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.minus_1626877696091177228at_rat (tptp.set_set_nat_rat tptp.set_set_nat_rat) tptp.set_set_nat_rat)
% 6.75/7.06 (declare-fun tptp.minus_5127226145743854075T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.monoid_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.75/7.06 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.one_one_int () tptp.int)
% 6.75/7.06 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.75/7.06 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.75/7.06 (declare-fun tptp.one_one_real () tptp.real)
% 6.75/7.06 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.75/7.06 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.plus_plus_literal (tptp.literal tptp.literal) tptp.literal)
% 6.75/7.06 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.75/7.06 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.75/7.06 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.75/7.06 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.75/7.06 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.75/7.06 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.75/7.06 (declare-fun tptp.zero_zero_literal () tptp.literal)
% 6.75/7.06 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.75/7.06 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.75/7.06 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups6818542070133387226omplex ((-> tptp.extended_enat tptp.complex) tptp.set_Extended_enat) tptp.complex)
% 6.75/7.06 (declare-fun tptp.groups2027974829824023292at_nat ((-> tptp.extended_enat tptp.nat) tptp.set_Extended_enat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups1392844769737527556at_rat ((-> tptp.extended_enat tptp.rat) tptp.set_Extended_enat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.groups4148127829035722712t_real ((-> tptp.extended_enat tptp.real) tptp.set_Extended_enat) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.75/7.06 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.75/7.06 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.75/7.06 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.75/7.06 (declare-fun tptp.groups7108830773950497114d_enat ((-> tptp.nat tptp.extended_enat) tptp.set_nat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups1921984841883549356at_nat ((-> tptp.option_nat tptp.nat) tptp.set_option_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups4518532050878116744t_real ((-> tptp.option_nat tptp.real) tptp.set_option_nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups4567486121110086003t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.75/7.06 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.75/7.06 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups207172935752626313at_nat ((-> tptp.set_nat_rat tptp.nat) tptp.set_set_nat_rat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups4357547368389691109t_real ((-> tptp.set_nat_rat tptp.real) tptp.set_set_nat_rat) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups1794756597179926696omplex ((-> tptp.vEBT_VEBT tptp.complex) tptp.set_VEBT_VEBT) tptp.complex)
% 6.75/7.06 (declare-fun tptp.groups769130701875090982BT_int ((-> tptp.vEBT_VEBT tptp.int) tptp.set_VEBT_VEBT) tptp.int)
% 6.75/7.06 (declare-fun tptp.groups771621172384141258BT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups136491112297645522BT_rat ((-> tptp.vEBT_VEBT tptp.rat) tptp.set_VEBT_VEBT) tptp.rat)
% 6.75/7.06 (declare-fun tptp.groups2240296850493347238T_real ((-> tptp.vEBT_VEBT tptp.real) tptp.set_VEBT_VEBT) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups8682486955453173170nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.75/7.06 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.75/7.06 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups845124408420398302nteger ((-> tptp.extended_enat tptp.code_integer) tptp.set_Extended_enat) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.groups4622424608036095791omplex ((-> tptp.extended_enat tptp.complex) tptp.set_Extended_enat) tptp.complex)
% 6.75/7.06 (declare-fun tptp.groups2878480467620962989at_int ((-> tptp.extended_enat tptp.int) tptp.set_Extended_enat) tptp.int)
% 6.75/7.06 (declare-fun tptp.groups2880970938130013265at_nat ((-> tptp.extended_enat tptp.nat) tptp.set_Extended_enat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups2245840878043517529at_rat ((-> tptp.extended_enat tptp.rat) tptp.set_Extended_enat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.groups97031904164794029t_real ((-> tptp.extended_enat tptp.real) tptp.set_Extended_enat) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups3827104343326376752nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.75/7.06 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.75/7.06 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.75/7.06 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups3455450783089532116nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.75/7.06 (declare-fun tptp.groups7961826882256487087d_enat ((-> tptp.nat tptp.extended_enat) tptp.set_nat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups6579596140936342515t_real ((-> tptp.option_nat tptp.real) tptp.set_option_nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups4075276357253098568at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.groups4077766827762148844at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.75/7.06 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.75/7.06 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.75/7.06 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.75/7.06 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups2125999189389939536t_real ((-> tptp.set_nat_rat tptp.real) tptp.set_set_nat_rat) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups127312072573709053omplex ((-> tptp.vEBT_VEBT tptp.complex) tptp.set_VEBT_VEBT) tptp.complex)
% 6.75/7.06 (declare-fun tptp.groups5726676334696518183BT_rat ((-> tptp.vEBT_VEBT tptp.rat) tptp.set_VEBT_VEBT) tptp.rat)
% 6.75/7.06 (declare-fun tptp.groups2703838992350267259T_real ((-> tptp.vEBT_VEBT tptp.real) tptp.set_VEBT_VEBT) tptp.real)
% 6.75/7.06 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.75/7.06 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.75/7.06 (declare-fun tptp.the_Pr4378521158711661632nt_int ((-> tptp.product_prod_int_int Bool)) tptp.product_prod_int_int)
% 6.75/7.06 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.75/7.06 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.if_nat_int_int (Bool (-> tptp.nat tptp.int tptp.int) (-> tptp.nat tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.if_nat_nat_nat (Bool (-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.if_nat_rat (Bool (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.75/7.06 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.75/7.06 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.75/7.06 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.75/7.06 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.75/7.06 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.75/7.06 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.75/7.06 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 6.75/7.06 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.if_Sum_sum_nat_nat (Bool tptp.sum_sum_nat_nat tptp.sum_sum_nat_nat) tptp.sum_sum_nat_nat)
% 6.75/7.06 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.75/7.06 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.75/7.06 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.75/7.06 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.75/7.06 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.75/7.06 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 6.75/7.06 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 6.75/7.06 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.75/7.06 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.75/7.06 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.75/7.06 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.75/7.06 (declare-fun tptp.inf_inf_nat_rat_o ((-> (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) Bool) (-> tptp.nat tptp.rat)) Bool)
% 6.75/7.06 (declare-fun tptp.inf_in1870772243966228564d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.06 (declare-fun tptp.semila9081495762789891438tr_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.lattic921264341876707157d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.quotie3684837364556693515t_real ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) tptp.real) (-> tptp.real tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.real Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.75/7.06 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.75/7.06 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.75/7.06 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.75/7.06 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.75/7.06 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.75/7.06 (declare-fun tptp.nil_int () tptp.list_int)
% 6.75/7.06 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.75/7.06 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.75/7.06 (declare-fun tptp.map_VE8901447254227204932T_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.75/7.06 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.75/7.06 (declare-fun tptp.set_Extended_enat2 (tptp.list_Extended_enat) tptp.set_Extended_enat)
% 6.75/7.06 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.75/7.06 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.set_option_nat2 (tptp.list_option_nat) tptp.set_option_nat)
% 6.75/7.06 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.set_set_nat_rat2 (tptp.list_set_nat_rat) tptp.set_set_nat_rat)
% 6.75/7.06 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.75/7.06 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 6.75/7.06 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 6.75/7.06 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 6.75/7.06 (declare-fun tptp.list_u3411377215356412978on_nat (tptp.list_option_nat tptp.nat tptp.option_nat) tptp.list_option_nat)
% 6.75/7.06 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 6.75/7.06 (declare-fun tptp.list_u886106648575569423at_rat (tptp.list_set_nat_rat tptp.nat tptp.set_nat_rat) tptp.list_set_nat_rat)
% 6.75/7.06 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 6.75/7.06 (declare-fun tptp.nth_option_nat (tptp.list_option_nat tptp.nat) tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.75/7.06 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.75/7.06 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 6.75/7.06 (declare-fun tptp.nth_Pr4439495888332055232nt_int (tptp.list_P5707943133018811711nt_int tptp.nat) tptp.product_prod_int_int)
% 6.75/7.06 (declare-fun tptp.nth_Pr8326237132889035090at_num (tptp.list_P1726324292696863441at_num tptp.nat) tptp.product_prod_nat_num)
% 6.75/7.06 (declare-fun tptp.nth_Pr744662078594809490T_VEBT (tptp.list_P5647936690300460905T_VEBT tptp.nat) tptp.produc8025551001238799321T_VEBT)
% 6.75/7.06 (declare-fun tptp.nth_Pr6456567536196504476um_num (tptp.list_P3744719386663036955um_num tptp.nat) tptp.product_prod_num_num)
% 6.75/7.06 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.75/7.06 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.75/7.06 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.75/7.06 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.nth_set_nat_rat (tptp.list_set_nat_rat tptp.nat) tptp.set_nat_rat)
% 6.75/7.06 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.75/7.06 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.75/7.06 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.75/7.06 (declare-fun tptp.product_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 6.75/7.06 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.75/7.06 (declare-fun tptp.product_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 6.75/7.06 (declare-fun tptp.product_nat_num (tptp.list_nat tptp.list_num) tptp.list_P1726324292696863441at_num)
% 6.75/7.06 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.75/7.06 (declare-fun tptp.product_num_num (tptp.list_num tptp.list_num) tptp.list_P3744719386663036955um_num)
% 6.75/7.06 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.75/7.06 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.75/7.06 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.75/7.06 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.75/7.06 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.75/7.06 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.75/7.06 (declare-fun tptp.replicate_option_nat (tptp.nat tptp.option_nat) tptp.list_option_nat)
% 6.75/7.06 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.75/7.06 (declare-fun tptp.replic5516892415368941373at_rat (tptp.nat tptp.set_nat_rat) tptp.list_set_nat_rat)
% 6.75/7.06 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 6.75/7.06 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.75/7.06 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.75/7.06 (declare-fun tptp.take_VEBT_VEBT (tptp.nat tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.75/7.06 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.75/7.06 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.75/7.06 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.75/7.06 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.semiri8563196900006977889d_enat ((-> tptp.extended_enat tptp.extended_enat) tptp.nat tptp.extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s3941691890525107288d_enat (tptp.list_Extended_enat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s6086282163384603972on_nat (tptp.list_option_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s3959913991096427681at_rat (tptp.list_set_nat_rat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.75/7.06 (declare-fun tptp.nat_list_decode_rel (tptp.nat tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.75/7.06 (declare-fun tptp.nat_prod_decode (tptp.nat) tptp.product_prod_nat_nat)
% 6.75/7.06 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.75/7.06 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.75/7.06 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.nat_sum_decode (tptp.nat) tptp.sum_sum_nat_nat)
% 6.75/7.06 (declare-fun tptp.nat_sum_encode (tptp.sum_sum_nat_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.75/7.06 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.75/7.06 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.75/7.06 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.75/7.06 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.75/7.06 (declare-fun tptp.one () tptp.num)
% 6.75/7.06 (declare-fun tptp.case_num_option_num (tptp.option_num (-> tptp.num tptp.option_num) (-> tptp.num tptp.option_num) tptp.num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.75/7.06 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.75/7.06 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.75/7.06 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.75/7.06 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.75/7.06 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.75/7.06 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.75/7.06 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.75/7.06 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.75/7.06 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.75/7.06 (declare-fun tptp.none_nat () tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.none_num () tptp.option_num)
% 6.75/7.06 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.75/7.06 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.75/7.06 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.75/7.06 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.75/7.06 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.75/7.06 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.size_option_nat ((-> tptp.nat tptp.nat) tptp.option_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.75/7.06 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.the_num (tptp.option_num) tptp.num)
% 6.75/7.06 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 6.75/7.06 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.order_2888998067076097458on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.75/7.06 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.75/7.06 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 6.75/7.06 (declare-fun tptp.bot_bo7653980558646680370d_enat () tptp.set_Extended_enat)
% 6.75/7.06 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.75/7.06 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.75/7.06 (declare-fun tptp.bot_bo5009843511495006442on_nat () tptp.set_option_nat)
% 6.75/7.06 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.75/7.06 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.75/7.06 (declare-fun tptp.bot_bo6797373522285170759at_rat () tptp.set_set_nat_rat)
% 6.75/7.06 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 6.75/7.06 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.ord_Le1955565732374568822d_enat ((-> tptp.extended_enat Bool)) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.75/7.06 (declare-fun tptp.ord_Least_real ((-> tptp.real Bool)) tptp.real)
% 6.75/7.06 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_nat_rat ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le1154456971122042459_nat_o ((-> tptp.option_nat Bool) (-> tptp.option_nat Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le6823063569548456766_rat_o ((-> tptp.set_nat_rat Bool) (-> tptp.set_nat_rat Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_set_nat_rat (tptp.set_nat_rat tptp.set_nat_rat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le2529575680413868914d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le1792839605950587050on_nat (tptp.set_option_nat tptp.set_option_nat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le1311537459589289991at_rat (tptp.set_set_nat_rat tptp.set_set_nat_rat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le3480810397992357184T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_eq_nat_rat ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le2679597024174929757at_rat (tptp.set_nat_rat tptp.set_nat_rat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le7203529160286727270d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le6937355464348597430on_nat (tptp.set_option_nat tptp.set_option_nat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le4375437777232675859at_rat (tptp.set_set_nat_rat tptp.set_set_nat_rat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.75/7.06 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 6.75/7.06 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.75/7.06 (declare-fun tptp.order_4130057895858720880d_enat ((-> tptp.extended_enat tptp.extended_enat)) Bool)
% 6.75/7.06 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.75/7.06 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.75/7.06 (declare-fun tptp.order_7092887310737990675l_real ((-> tptp.real tptp.real)) Bool)
% 6.75/7.06 (declare-fun tptp.ordering_top_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.top_to3028658606643905974d_enat () tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.75/7.06 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.top_to8920198386146353926on_nat () tptp.set_option_nat)
% 6.75/7.06 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.75/7.06 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.75/7.06 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.75/7.06 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.75/7.06 (declare-fun tptp.power_8040749407984259932d_enat (tptp.extended_enat tptp.nat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 6.75/7.06 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 6.75/7.06 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 6.75/7.06 (declare-fun tptp.produc851828971589881931at_num ((-> tptp.nat tptp.num tptp.num) tptp.produc2963631642982155120at_num) tptp.produc3368934014287244435at_num)
% 6.75/7.06 (declare-fun tptp.produc3576312749637752826on_num ((-> tptp.num tptp.num Bool) tptp.produc3447558737645232053on_num) tptp.produc7036089656553540234on_num)
% 6.75/7.06 (declare-fun tptp.produc5778274026573060048on_num ((-> tptp.num tptp.num tptp.num) tptp.produc3447558737645232053on_num) tptp.produc1193250871479095198on_num)
% 6.75/7.06 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 6.75/7.06 (declare-fun tptp.produc2899441246263362727at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc6121120109295599847at_nat) tptp.produc5542196010084753463at_nat)
% 6.75/7.06 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.75/7.06 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.75/7.06 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 6.75/7.06 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.75/7.06 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.75/7.06 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.75/7.06 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.75/7.06 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.75/7.06 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 6.75/7.06 (declare-fun tptp.produc1195630363706982562at_num (tptp.nat tptp.product_prod_nat_num) tptp.produc2963631642982155120at_num)
% 6.75/7.06 (declare-fun tptp.produc599794634098209291T_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.produc8025551001238799321T_VEBT)
% 6.75/7.06 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.75/7.06 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 6.75/7.06 (declare-fun tptp.produc8585076106096196333on_num (tptp.option_num tptp.option_num) tptp.produc3447558737645232053on_num)
% 6.75/7.06 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 6.75/7.06 (declare-fun tptp.produc6161850002892822231at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc859450856879609959at_nat)
% 6.75/7.06 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.75/7.06 (declare-fun tptp.produc581526299967858633d_enat (tptp.vEBT_VEBT tptp.extended_enat) tptp.produc7272778201969148633d_enat)
% 6.75/7.06 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.75/7.06 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.75/7.06 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.06 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.75/7.06 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.75/7.06 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.75/7.06 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.75/7.06 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.75/7.06 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.75/7.06 (declare-fun tptp.produc6771430404735790350plex_o ((-> tptp.complex tptp.complex Bool) tptp.produc4411394909380815293omplex) Bool)
% 6.75/7.06 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.75/7.06 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.75/7.06 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.75/7.06 (declare-fun tptp.produc6452406959799940328t_real ((-> tptp.int tptp.int tptp.set_real) tptp.product_prod_int_int) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.produc8739625826339149834_nat_o ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.75/7.06 (declare-fun tptp.produc27273713700761075at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.75/7.06 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.75/7.06 (declare-fun tptp.produc1917071388513777916omplex ((-> tptp.nat tptp.nat tptp.complex) tptp.product_prod_nat_nat) tptp.complex)
% 6.75/7.06 (declare-fun tptp.produc2676513652042109336d_enat ((-> tptp.nat tptp.nat tptp.extended_enat) tptp.product_prod_nat_nat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.75/7.06 (declare-fun tptp.produc6207742614233964070at_rat ((-> tptp.nat tptp.nat tptp.rat) tptp.product_prod_nat_nat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.produc1703576794950452218t_real ((-> tptp.nat tptp.nat tptp.real) tptp.product_prod_nat_nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.produc2011625207790711856et_int ((-> tptp.nat tptp.nat tptp.set_int) tptp.product_prod_nat_nat) tptp.set_int)
% 6.75/7.06 (declare-fun tptp.produc6189476227299908564et_nat ((-> tptp.nat tptp.nat tptp.set_nat) tptp.product_prod_nat_nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.produc3668448655016342576t_real ((-> tptp.nat tptp.nat tptp.set_real) tptp.product_prod_nat_nat) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.produc4927758841916487424_num_o ((-> tptp.nat tptp.num Bool) tptp.product_prod_nat_num) Bool)
% 6.75/7.06 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.produc9175805072616146554et_int ((-> tptp.nat tptp.num tptp.set_int) tptp.product_prod_nat_num) tptp.set_int)
% 6.75/7.06 (declare-fun tptp.produc4130284055270567454et_nat ((-> tptp.nat tptp.num tptp.set_nat) tptp.product_prod_nat_num) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.produc1435849484188172666t_real ((-> tptp.nat tptp.num tptp.set_real) tptp.product_prod_nat_num) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.produc5703948589228662326_num_o ((-> tptp.num tptp.num Bool) tptp.product_prod_num_num) Bool)
% 6.75/7.06 (declare-fun tptp.produc6406642877701697732et_int ((-> tptp.num tptp.num tptp.set_int) tptp.product_prod_num_num) tptp.set_int)
% 6.75/7.06 (declare-fun tptp.produc1361121860356118632et_nat ((-> tptp.num tptp.num tptp.set_nat) tptp.product_prod_num_num) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.produc8296048397933160132t_real ((-> tptp.num tptp.num tptp.set_real) tptp.product_prod_num_num) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.produc6590410687421337004_nat_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc859450856879609959at_nat) Bool)
% 6.75/7.06 (declare-fun tptp.produc5414030515140494994real_o ((-> tptp.real tptp.real Bool) tptp.produc2422161461964618553l_real) Bool)
% 6.75/7.06 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.75/7.06 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.75/7.06 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.quot_a3129823074075660125t_real ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> tptp.set_nat_rat tptp.real) (-> tptp.nat tptp.rat)) tptp.real)
% 6.75/7.06 (declare-fun tptp.quot_r1730120044975580712at_rat ((-> tptp.real tptp.set_nat_rat) tptp.real tptp.nat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 6.75/7.06 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.75/7.06 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.75/7.06 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 6.75/7.06 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 6.75/7.06 (declare-fun tptp.field_7254667332652039916t_real (tptp.rat) tptp.real)
% 6.75/7.06 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.75/7.06 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 6.75/7.06 (declare-fun tptp.positive (tptp.rat) Bool)
% 6.75/7.06 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.75/7.06 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.75/7.06 (declare-fun tptp.real2 ((-> tptp.nat tptp.rat)) tptp.real)
% 6.75/7.06 (declare-fun tptp.cauchy ((-> tptp.nat tptp.rat)) Bool)
% 6.75/7.06 (declare-fun tptp.cr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.75/7.06 (declare-fun tptp.pcr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.75/7.06 (declare-fun tptp.positive2 (tptp.real) Bool)
% 6.75/7.06 (declare-fun tptp.abs_real (tptp.set_nat_rat) tptp.real)
% 6.75/7.06 (declare-fun tptp.rep_real (tptp.real) tptp.set_nat_rat)
% 6.75/7.06 (declare-fun tptp.realrel ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 6.75/7.06 (declare-fun tptp.rep_real2 (tptp.real tptp.nat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.vanishes ((-> tptp.nat tptp.rat)) Bool)
% 6.75/7.06 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.75/7.06 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 6.75/7.06 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.75/7.06 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.75/7.06 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.domainp_nat_rat_real ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> tptp.nat tptp.rat)) Bool)
% 6.75/7.06 (declare-fun tptp.domainp_nat_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.domainp_rat_rat ((-> tptp.rat tptp.rat Bool) tptp.rat) Bool)
% 6.75/7.06 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.relcom2856161143838007533t_real ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.75/7.06 (declare-fun tptp.transp_nat_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 6.75/7.06 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.75/7.06 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.75/7.06 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.75/7.06 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.75/7.06 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.75/7.06 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.75/7.06 (declare-fun tptp.zero_n1046097342994218471d_enat (Bool) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.75/7.06 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.75/7.06 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.75/7.06 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.75/7.06 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.75/7.06 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 6.75/7.06 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 6.75/7.06 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.75/7.06 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 6.75/7.06 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 6.75/7.06 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.75/7.06 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.75/7.06 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 6.75/7.06 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 6.75/7.06 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.75/7.06 (declare-fun tptp.collect_nat_rat ((-> (-> tptp.nat tptp.rat) Bool)) tptp.set_nat_rat)
% 6.75/7.06 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.75/7.06 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.75/7.06 (declare-fun tptp.collec4429806609662206161d_enat ((-> tptp.extended_enat Bool)) tptp.set_Extended_enat)
% 6.75/7.06 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.75/7.06 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 6.75/7.06 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 6.75/7.06 (declare-fun tptp.collec8433460942617342167d_enat ((-> tptp.list_Extended_enat Bool)) tptp.set_li5464603477888414924d_enat)
% 6.75/7.06 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 6.75/7.06 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.75/7.06 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.75/7.06 (declare-fun tptp.collect_option_nat ((-> tptp.option_nat Bool)) tptp.set_option_nat)
% 6.75/7.06 (declare-fun tptp.collec8663557070575231912omplex ((-> tptp.produc4411394909380815293omplex Bool)) tptp.set_Pr5085853215250843933omplex)
% 6.75/7.06 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.75/7.06 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.06 (declare-fun tptp.collec3799799289383736868l_real ((-> tptp.produc2422161461964618553l_real Bool)) tptp.set_Pr6218003697084177305l_real)
% 6.75/7.06 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 6.75/7.06 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.collect_set_nat_rat ((-> tptp.set_nat_rat Bool)) tptp.set_set_nat_rat)
% 6.75/7.06 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.75/7.06 (declare-fun tptp.image_80655429650038917d_enat ((-> tptp.extended_enat tptp.extended_enat) tptp.set_Extended_enat) tptp.set_Extended_enat)
% 6.75/7.06 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.75/7.06 (declare-fun tptp.image_5971271580939081552omplex ((-> tptp.real tptp.filter6041513312241820739omplex) tptp.set_real) tptp.set_fi4554929511873752355omplex)
% 6.75/7.06 (declare-fun tptp.image_2178119161166701260l_real ((-> tptp.real tptp.filter2146258269922977983l_real) tptp.set_real) tptp.set_fi7789364187291644575l_real)
% 6.75/7.06 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.image_VEBT_VEBT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 6.75/7.06 (declare-fun tptp.insert_Extended_enat (tptp.extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 6.75/7.06 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.75/7.06 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.insert_num (tptp.num tptp.set_num) tptp.set_num)
% 6.75/7.06 (declare-fun tptp.insert_option_nat (tptp.option_nat tptp.set_option_nat) tptp.set_option_nat)
% 6.75/7.06 (declare-fun tptp.insert_rat (tptp.rat tptp.set_rat) tptp.set_rat)
% 6.75/7.06 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.insert_set_nat_rat (tptp.set_nat_rat tptp.set_set_nat_rat) tptp.set_set_nat_rat)
% 6.75/7.06 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.set_fo2538466533108834004d_enat ((-> tptp.nat tptp.extended_enat tptp.extended_enat) tptp.nat tptp.nat tptp.extended_enat) tptp.extended_enat)
% 6.75/7.06 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.75/7.06 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.set_or5403411693681687835d_enat (tptp.extended_enat tptp.extended_enat) tptp.set_Extended_enat)
% 6.75/7.06 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.75/7.06 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.75/7.06 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.75/7.06 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.set_or5795412311047298440at_rat (tptp.set_nat_rat tptp.set_nat_rat) tptp.set_set_nat_rat)
% 6.75/7.06 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.75/7.06 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.set_or5632376147039224640at_rat ((-> tptp.nat tptp.rat)) tptp.set_nat_rat)
% 6.75/7.06 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.75/7.06 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 6.75/7.06 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 6.75/7.06 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.set_or3094126398206284534at_rat (tptp.set_nat_rat) tptp.set_set_nat_rat)
% 6.75/7.06 (declare-fun tptp.set_or4236626031148496127et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.75/7.06 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.set_or6855495488841395556at_rat ((-> tptp.nat tptp.rat)) tptp.set_nat_rat)
% 6.75/7.06 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.75/7.06 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.75/7.06 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 6.75/7.06 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.75/7.06 (declare-fun tptp.set_or6234697943151750426at_rat (tptp.set_nat_rat) tptp.set_set_nat_rat)
% 6.75/7.06 (declare-fun tptp.abort_real (tptp.literal (-> tptp.product_unit tptp.real)) tptp.real)
% 6.75/7.06 (declare-fun tptp.literal2 (Bool Bool Bool Bool Bool Bool Bool tptp.literal) tptp.literal)
% 6.75/7.06 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.75/7.06 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.75/7.06 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.75/7.06 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.75/7.06 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.75/7.06 (declare-fun tptp.sum_Inl_nat_nat (tptp.nat) tptp.sum_sum_nat_nat)
% 6.75/7.06 (declare-fun tptp.sum_Inr_nat_nat (tptp.nat) tptp.sum_sum_nat_nat)
% 6.75/7.06 (declare-fun tptp.sum_ca6763686470577984908at_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.sum_sum_nat_nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.75/7.06 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.75/7.06 (declare-fun tptp.topolo4899668324122417113eq_int ((-> tptp.nat tptp.int)) Bool)
% 6.75/7.06 (declare-fun tptp.topolo4902158794631467389eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.75/7.06 (declare-fun tptp.topolo1459490580787246023eq_num ((-> tptp.nat tptp.num)) Bool)
% 6.75/7.06 (declare-fun tptp.topolo4267028734544971653eq_rat ((-> tptp.nat tptp.rat)) Bool)
% 6.75/7.06 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.75/7.06 (declare-fun tptp.topolo7278393974255667507et_nat ((-> tptp.nat tptp.set_nat)) Bool)
% 6.75/7.06 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.75/7.06 (declare-fun tptp.topolo7531315842566124627t_real ((-> tptp.nat tptp.real)) Bool)
% 6.75/7.06 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.75/7.06 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.75/7.06 (declare-fun tptp.topolo896644834953643431omplex () tptp.filter6041513312241820739omplex)
% 6.75/7.06 (declare-fun tptp.topolo1511823702728130853y_real () tptp.filter2146258269922977983l_real)
% 6.75/7.06 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 6.75/7.06 (declare-fun tptp.diffs_int ((-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 6.75/7.06 (declare-fun tptp.diffs_rat ((-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.75/7.06 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.pi () tptp.real)
% 6.75/7.06 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.powr_real2 (tptp.real tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.75/7.06 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.75/7.06 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.75/7.06 (declare-fun tptp.left_t2768085380646472630at_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.left_unique_nat_nat ((-> tptp.nat tptp.nat Bool)) Bool)
% 6.75/7.06 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.06 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.06 (declare-fun tptp.type_d7649664348572268762on_nat ((-> tptp.extended_enat tptp.option_nat) (-> tptp.option_nat tptp.extended_enat) tptp.set_option_nat) Bool)
% 6.75/7.06 (declare-fun tptp.type_d8072115097938612567at_rat ((-> tptp.real tptp.set_nat_rat) (-> tptp.set_nat_rat tptp.real) tptp.set_set_nat_rat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_T_i_n_s_e_r_t (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_T_i_n_s_e_r_t2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_T5076183648494686801_t_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_T9217963907923527482_t_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_T_m_a_x_t (tptp.vEBT_VEBT) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_T_m_a_x_t_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_T_m_e_m_b_e_r (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_T_m_e_m_b_e_r2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_T8099345112685741742_r_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_T5837161174952499735_r_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_T_m_i_n_N_u_l_l (tptp.vEBT_VEBT) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_T5462971552011256508_l_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_T_m_i_n_t (tptp.vEBT_VEBT) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_T_m_i_n_t_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_T_s_u_c_c (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_T_s_u_c_c2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_T_s_u_c_c_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_T_s_u_c_c_rel2 (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_elim_dead (tptp.vEBT_VEBT tptp.extended_enat) tptp.vEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.vEBT_V312737461966249ad_rel (tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_height (tptp.vEBT_VEBT) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_height_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.vEBT_V819420779217536731ft_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 6.75/7.06 (declare-fun tptp.vEBT_V1502963449132264192at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.option4927543243414619207at_nat)
% 6.75/7.06 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.75/7.06 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.75/7.06 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.75/7.06 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.75/7.06 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.75/7.06 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 6.75/7.06 (declare-fun tptp.accp_P6183159247885693666d_enat ((-> tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat Bool) tptp.produc7272778201969148633d_enat) Bool)
% 6.75/7.06 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.75/7.06 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.less_than () tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.06 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.06 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.75/7.06 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 6.75/7.06 (declare-fun tptp.member_nat_rat ((-> tptp.nat tptp.rat) tptp.set_nat_rat) Bool)
% 6.75/7.06 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.75/7.06 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.75/7.06 (declare-fun tptp.member_Extended_enat (tptp.extended_enat tptp.set_Extended_enat) Bool)
% 6.75/7.06 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.75/7.06 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 6.75/7.06 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.75/7.06 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.75/7.06 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.75/7.06 (declare-fun tptp.member_option_nat (tptp.option_nat tptp.set_option_nat) Bool)
% 6.75/7.06 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.75/7.06 (declare-fun tptp.member8206827879206165904at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 6.75/7.06 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.75/7.06 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.75/7.06 (declare-fun tptp.member_set_nat_rat (tptp.set_nat_rat tptp.set_set_nat_rat) Bool)
% 6.75/7.06 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.75/7.06 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.75/7.06 (declare-fun tptp.deg () tptp.nat)
% 6.75/7.06 (declare-fun tptp.m () tptp.nat)
% 6.75/7.06 (declare-fun tptp.ma () tptp.nat)
% 6.75/7.06 (declare-fun tptp.mi () tptp.nat)
% 6.75/7.06 (declare-fun tptp.na () tptp.nat)
% 6.75/7.06 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.75/7.06 (declare-fun tptp.xa () tptp.nat)
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.75/7.06 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat)) (and (@ (@ tptp.member_nat X) Xs) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_eq_nat Y) X)))))))
% 6.75/7.06 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat)) (and (@ (@ tptp.member_nat X) Xs) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_eq_nat X) Y)))))))
% 6.75/7.06 (assert (forall ((Summary tptp.vEBT_VEBT) (Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height Summary))) (@ tptp.vEBT_VEBT_height (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)))))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))
% 6.75/7.06 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_s_u_c_c tptp.summary) X2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height tptp.summary))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.one)))))))))
% 6.75/7.06 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat _let_1))))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_succ tptp.summary) _let_2))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_5 (@ tptp.bit0 _let_1))) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_5)))) (@ tptp.vEBT_T_m_a_x_t (@ _let_4 _let_2)))) (@ (@ tptp.vEBT_T_s_u_c_c tptp.summary) _let_2))) (@ (@ (@ tptp.if_nat (= _let_3 tptp.none_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat _let_5)) (@ tptp.vEBT_T_m_i_n_t (@ _let_4 (@ tptp.the_nat _let_3)))))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (or (= X2 Mi) (= X2 Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))))
% 6.75/7.06 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.75/7.06 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.75/7.06 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.75/7.06 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.75/7.06 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_a_x_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_T_m_a_x_t T)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_T_m_i_n_t T)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 6.75/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Z))))
% 6.75/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Z))))
% 6.75/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.75/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.75/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Z))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 6.75/7.06 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((V tptp.num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.75/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.75/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.75/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.75/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 6.75/7.06 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num X2) tptp.one) (= X2 tptp.one))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ (@ tptp.plus_plus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.75/7.06 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X2))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 6.75/7.06 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 6.75/7.06 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.75/7.06 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.75/7.06 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.75/7.06 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.75/7.06 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.75/7.06 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.75/7.06 (assert (forall ((Y2 tptp.num)) (=> (not (= Y2 tptp.one)) (=> (forall ((X22 tptp.num)) (not (= Y2 (@ tptp.bit0 X22)))) (not (forall ((X3 tptp.num)) (not (= Y2 (@ tptp.bit1 X3)))))))))
% 6.75/7.06 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.option_nat) (P (-> tptp.option_nat Bool))) (= (@ (@ tptp.member_option_nat A) (@ tptp.collect_option_nat P)) (@ P A))))
% 6.75/7.06 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.75/7.06 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 6.75/7.06 (assert (forall ((A tptp.set_nat_rat) (P (-> tptp.set_nat_rat Bool))) (= (@ (@ tptp.member_set_nat_rat A) (@ tptp.collect_set_nat_rat P)) (@ P A))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.75/7.06 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.75/7.06 (assert (forall ((A (-> tptp.nat tptp.rat)) (P (-> (-> tptp.nat tptp.rat) Bool))) (= (@ (@ tptp.member_nat_rat A) (@ tptp.collect_nat_rat P)) (@ P A))))
% 6.75/7.06 (assert (forall ((A2 tptp.set_option_nat)) (= (@ tptp.collect_option_nat (lambda ((X tptp.option_nat)) (@ (@ tptp.member_option_nat X) A2))) A2)))
% 6.75/7.06 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A2))) A2)))
% 6.75/7.06 (assert (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A2))) A2)))
% 6.75/7.06 (assert (forall ((A2 tptp.set_set_nat_rat)) (= (@ tptp.collect_set_nat_rat (lambda ((X tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X) A2))) A2)))
% 6.75/7.06 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A2))) A2)))
% 6.75/7.06 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A2))) A2)))
% 6.75/7.06 (assert (forall ((A2 tptp.set_nat_rat)) (= (@ tptp.collect_nat_rat (lambda ((X (-> tptp.nat tptp.rat))) (@ (@ tptp.member_nat_rat X) A2))) A2)))
% 6.75/7.06 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X4 tptp.list_nat)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_list_nat P) (@ tptp.collect_list_nat Q)))))
% 6.75/7.06 (assert (forall ((P (-> tptp.set_nat_rat Bool)) (Q (-> tptp.set_nat_rat Bool))) (=> (forall ((X4 tptp.set_nat_rat)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_set_nat_rat P) (@ tptp.collect_set_nat_rat Q)))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 6.75/7.06 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 6.75/7.06 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool)) (Q (-> (-> tptp.nat tptp.rat) Bool))) (=> (forall ((X4 (-> tptp.nat tptp.rat))) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_nat_rat P) (@ tptp.collect_nat_rat Q)))))
% 6.75/7.06 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.75/7.06 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.75/7.06 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.75/7.06 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.75/7.06 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.75/7.06 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.75/7.06 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.75/7.06 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.75/7.06 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.75/7.06 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.75/7.06 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.75/7.06 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.75/7.06 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.75/7.06 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) tptp.one)))))
% 6.75/7.06 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X2) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) tptp.none_nat)))))))
% 6.75/7.06 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.75/7.06 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.75/7.06 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 6.75/7.06 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 6.75/7.06 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 6.75/7.06 (assert (forall ((X23 tptp.product_prod_nat_nat) (Y22 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X23) (@ tptp.some_P7363390416028606310at_nat Y22)) (= X23 Y22))))
% 6.75/7.06 (assert (forall ((X23 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.some_nat X23) (@ tptp.some_nat Y22)) (= X23 Y22))))
% 6.75/7.06 (assert (forall ((X23 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.some_num X23) (@ tptp.some_num Y22)) (= X23 Y22))))
% 6.75/7.06 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 6.75/7.06 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 6.75/7.06 (assert (forall ((X2 tptp.option4927543243414619207at_nat)) (= (not (= X2 tptp.none_P5556105721700978146at_nat)) (exists ((Y tptp.product_prod_nat_nat)) (= X2 (@ tptp.some_P7363390416028606310at_nat Y))))))
% 6.75/7.06 (assert (forall ((X2 tptp.option_nat)) (= (not (= X2 tptp.none_nat)) (exists ((Y tptp.nat)) (= X2 (@ tptp.some_nat Y))))))
% 6.75/7.06 (assert (forall ((X2 tptp.option_num)) (= (not (= X2 tptp.none_num)) (exists ((Y tptp.num)) (= X2 (@ tptp.some_num Y))))))
% 6.75/7.06 (assert (forall ((X2 tptp.option4927543243414619207at_nat)) (= (forall ((Y tptp.product_prod_nat_nat)) (not (= X2 (@ tptp.some_P7363390416028606310at_nat Y)))) (= X2 tptp.none_P5556105721700978146at_nat))))
% 6.75/7.06 (assert (forall ((X2 tptp.option_nat)) (= (forall ((Y tptp.nat)) (not (= X2 (@ tptp.some_nat Y)))) (= X2 tptp.none_nat))))
% 6.75/7.06 (assert (forall ((X2 tptp.option_num)) (= (forall ((Y tptp.num)) (not (= X2 (@ tptp.some_num Y)))) (= X2 tptp.none_num))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N))))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 6.75/7.06 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.75/7.06 (assert (= tptp.ord_less_eq_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 6.75/7.06 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N)) (@ tptp.bit0 (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N)))))))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)))
% 6.75/7.06 (assert (forall ((A tptp.nat) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat L)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num K) L)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int L)) (@ _let_1 (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num K) L)))))))
% 6.75/7.06 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_a_x_t (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_t (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((X23 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X23)))))
% 6.75/7.06 (assert (forall ((X23 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X23)))))
% 6.75/7.06 (assert (forall ((X23 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X23)))))
% 6.75/7.06 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X23 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X23)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 6.75/7.06 (assert (forall ((Option tptp.option_nat) (X23 tptp.nat)) (=> (= Option (@ tptp.some_nat X23)) (not (= Option tptp.none_nat)))))
% 6.75/7.06 (assert (forall ((Option tptp.option_num) (X23 tptp.num)) (=> (= Option (@ tptp.some_num X23)) (not (= Option tptp.none_num)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.option4927543243414619207at_nat)) (=> (not (= Y2 tptp.none_P5556105721700978146at_nat)) (not (forall ((X22 tptp.product_prod_nat_nat)) (not (= Y2 (@ tptp.some_P7363390416028606310at_nat X22))))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.option_nat)) (=> (not (= Y2 tptp.none_nat)) (not (forall ((X22 tptp.nat)) (not (= Y2 (@ tptp.some_nat X22))))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.option_num)) (=> (not (= Y2 tptp.none_num)) (not (forall ((X22 tptp.num)) (not (= Y2 (@ tptp.some_num X22))))))))
% 6.75/7.06 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X5 tptp.option4927543243414619207at_nat)) (@ P2 X5))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P3 tptp.none_P5556105721700978146at_nat) (exists ((X tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X)))))))
% 6.75/7.06 (assert (= (lambda ((P2 (-> tptp.option_nat Bool))) (exists ((X5 tptp.option_nat)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_nat Bool))) (or (@ P3 tptp.none_nat) (exists ((X tptp.nat)) (@ P3 (@ tptp.some_nat X)))))))
% 6.75/7.06 (assert (= (lambda ((P2 (-> tptp.option_num Bool))) (exists ((X5 tptp.option_num)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_num Bool))) (or (@ P3 tptp.none_num) (exists ((X tptp.num)) (@ P3 (@ tptp.some_num X)))))))
% 6.75/7.06 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X5 tptp.option4927543243414619207at_nat)) (@ P2 X5))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P3 tptp.none_P5556105721700978146at_nat) (forall ((X tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X)))))))
% 6.75/7.06 (assert (= (lambda ((P2 (-> tptp.option_nat Bool))) (forall ((X5 tptp.option_nat)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_nat Bool))) (and (@ P3 tptp.none_nat) (forall ((X tptp.nat)) (@ P3 (@ tptp.some_nat X)))))))
% 6.75/7.06 (assert (= (lambda ((P2 (-> tptp.option_num Bool))) (forall ((X5 tptp.option_num)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_num Bool))) (and (@ P3 tptp.none_num) (forall ((X tptp.num)) (@ P3 (@ tptp.some_num X)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y2 (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y2 tptp.option_nat)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y2 tptp.none_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.nat)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y2 (@ tptp.some_nat B2)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y2 tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y2 tptp.none_num) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.num)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y2 (@ tptp.some_num B2)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.option_nat) (P (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_nat) _let_1) (=> (=> (= Y2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_nat A3)) (=> (= Y2 (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.option_nat) (P (-> tptp.option_nat tptp.option_nat Bool)) (Y2 tptp.option_nat)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_nat) _let_1) (=> (=> (= Y2 tptp.none_nat) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= X2 (@ tptp.some_nat A3)) (=> (= Y2 (@ tptp.some_nat B2)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.option_nat) (P (-> tptp.option_nat tptp.option_num Bool)) (Y2 tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_nat) _let_1) (=> (=> (= Y2 tptp.none_num) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= X2 (@ tptp.some_nat A3)) (=> (= Y2 (@ tptp.some_num B2)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_num A3)) (=> (= Y2 (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option_nat Bool)) (Y2 tptp.option_nat)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y2 tptp.none_nat) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.nat)) (=> (= X2 (@ tptp.some_num A3)) (=> (= Y2 (@ tptp.some_nat B2)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y2 tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y2 tptp.none_num) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= X2 (@ tptp.some_num A3)) (=> (= Y2 (@ tptp.some_num B2)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N) K)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 6.75/7.06 (assert (forall ((I tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I) J)) U)) K))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N) Q2)) (@ (@ tptp.divide_divide_nat (@ _let_1 N)) Q2)))))
% 6.75/7.06 (assert (forall ((X23 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X23)) X23)))
% 6.75/7.06 (assert (forall ((X23 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X23)) X23)))
% 6.75/7.06 (assert (forall ((X23 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X23)) X23)))
% 6.75/7.06 (assert (forall ((Option tptp.option_nat) (Option2 tptp.option_nat)) (let ((_let_1 (= Option2 tptp.none_nat))) (let ((_let_2 (= Option tptp.none_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_nat Option) (@ tptp.the_nat Option2)))) (= Option Option2)))))))
% 6.75/7.06 (assert (forall ((Option tptp.option4927543243414619207at_nat) (Option2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (= Option2 tptp.none_P5556105721700978146at_nat))) (let ((_let_2 (= Option tptp.none_P5556105721700978146at_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_Pr8591224930841456533at_nat Option) (@ tptp.the_Pr8591224930841456533at_nat Option2)))) (= Option Option2)))))))
% 6.75/7.06 (assert (forall ((Option tptp.option_num) (Option2 tptp.option_num)) (let ((_let_1 (= Option2 tptp.none_num))) (let ((_let_2 (= Option tptp.none_num))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_num Option) (@ tptp.the_num Option2)))) (= Option Option2)))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N)) M)))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N))) M)))
% 6.75/7.06 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 6.75/7.06 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 6.75/7.06 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 6.75/7.06 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X2) Ma) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X2) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) tptp.none_nat)))))))
% 6.75/7.06 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat X2) Mi) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ tptp.some_nat Mi))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 6.75/7.06 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.75/7.06 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B) A)) C))))
% 6.75/7.06 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B) A)) C))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B) A)) C))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) B))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) B))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num M) N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num M) N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num M) N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num M) N))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ _let_1 B)) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C)))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.75/7.06 (assert (forall ((Deg tptp.nat) (Ma tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat Ma) X2) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ tptp.some_nat Ma))))))
% 6.75/7.06 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.75/7.06 (assert (forall ((X6 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X6))))
% 6.75/7.06 (assert (forall ((X6 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X6))))
% 6.75/7.06 (assert (forall ((X6 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X6) X_1))))
% 6.75/7.06 (assert (forall ((X6 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X6) X_1))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_real X2) Y2)) (@ (@ tptp.ord_less_real Y2) X2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_rat X2) Y2)) (@ (@ tptp.ord_less_rat Y2) X2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_int X2) Y2)) (@ (@ tptp.ord_less_int Y2) X2)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 6.75/7.06 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ P M2))) (@ P N2))) (@ P N))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2)))))) (@ P N))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ F I2)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.06 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (or (@ (@ tptp.ord_less_nat M3) N3) (= M3 N3)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.06 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N3) (not (= M3 N3))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.75/7.06 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K) (@ (@ tptp.ord_less_nat I) K))))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.75/7.06 (assert (forall ((M tptp.real) (N tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_real M) N)))))))
% 6.75/7.06 (assert (forall ((M tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M) N)))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 6.75/7.06 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B) tptp.one_one_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B) tptp.one_one_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B) tptp.one_one_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B) tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N2) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 6.75/7.06 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) __flatten_var_0))))
% 6.75/7.06 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A4) tptp.one_one_int)) __flatten_var_0))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) I))))
% 6.75/7.06 (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 ((X4 tptp.nat)) (and (@ P X4) (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) X4)))))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 6.75/7.06 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Y2 tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X2) (@ tptp.size_s6755466524823107622T_VEBT Y2))) (not (= X2 Y2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (=> (not (= (@ tptp.size_size_num X2) (@ tptp.size_size_num Y2))) (not (= X2 Y2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.list_o) (Y2 tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X2) (@ tptp.size_size_list_o Y2))) (not (= X2 Y2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.list_nat) (Y2 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X2) (@ tptp.size_size_list_nat Y2))) (not (= X2 Y2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.vEBT_VEBT)) (=> (not (= (@ tptp.size_size_VEBT_VEBT X2) (@ tptp.size_size_VEBT_VEBT Y2))) (not (= X2 Y2)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (E tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) C)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) E)) C))))
% 6.75/7.06 (assert (forall ((A tptp.real) (E tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E)) C))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E)) C))))
% 6.75/7.06 (assert (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E)) C))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex C) B))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real C) B))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat C) B))))))
% 6.75/7.06 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X2) W)) (@ (@ tptp.times_times_complex Y2) Z)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X2) W)) (@ (@ tptp.times_times_real Y2) Z)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X2) W)) (@ (@ tptp.times_times_rat Y2) Z)))))
% 6.75/7.06 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex Y2) W)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y2) W)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y2) W)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))))
% 6.75/7.06 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (exists ((K2 tptp.nat)) (= N3 (@ (@ tptp.plus_plus_nat M3) K2))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N2 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N2))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) L))))))
% 6.75/7.06 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.75/7.06 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 6.75/7.06 (assert (= tptp.ord_less_nat (lambda ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) Y2)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y2) _let_1)) X2)) N) Y2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X2))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X2))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.times_times_nat X2) Y2) Z) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X2)) (@ tptp.some_nat Y2)) (@ tptp.some_nat Z)))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X2) Y2) Z) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X2)) (@ tptp.some_nat Y2)) (@ tptp.some_nat Z)))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.power_power_nat X2) Y2) Z) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X2)) (@ tptp.some_nat Y2)) (@ tptp.some_nat Z)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) (@ (@ tptp.plus_plus_complex C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (@ _let_1 A)) (@ _let_1 B)))))
% 6.75/7.06 (assert (= tptp.vEBT_VEBT_high (lambda ((X tptp.nat) (N3 tptp.nat)) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.75/7.06 (assert (forall ((Ma tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N)) (@ _let_1 M))))))
% 6.75/7.06 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.75/7.06 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.75/7.06 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L2 tptp.nat) (D tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D))) L2))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.75/7.06 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.75/7.06 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 6.75/7.06 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.75/7.06 (assert (= tptp.times_times_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real B3) A4))))
% 6.75/7.06 (assert (= tptp.times_times_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat B3) A4))))
% 6.75/7.06 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.times_times_nat B3) A4))))
% 6.75/7.06 (assert (= tptp.times_times_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.times_times_int B3) A4))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.complex)) (= (= tptp.one_one_complex X2) (= X2 tptp.one_one_complex))))
% 6.75/7.06 (assert (forall ((X2 tptp.real)) (= (= tptp.one_one_real X2) (= X2 tptp.one_one_real))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat)) (= (= tptp.one_one_rat X2) (= X2 tptp.one_one_rat))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat)) (= (= tptp.one_one_nat X2) (= X2 tptp.one_one_nat))))
% 6.75/7.06 (assert (forall ((X2 tptp.int)) (= (= tptp.one_one_int X2) (= X2 tptp.one_one_int))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ (@ tptp.plus_plus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 6.75/7.06 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_real I) K) (@ (@ tptp.plus_plus_real J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_rat I) K) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_int I) K) (@ (@ tptp.plus_plus_int J) L)))))
% 6.75/7.06 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A2) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.75/7.06 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.75/7.06 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.75/7.06 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A2) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.75/7.06 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_complex A2) B) (@ _let_1 (@ (@ tptp.plus_plus_complex A) B)))))))
% 6.75/7.06 (assert (forall ((B4 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 6.75/7.06 (assert (forall ((B4 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 6.75/7.06 (assert (forall ((B4 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 6.75/7.06 (assert (forall ((B4 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 6.75/7.06 (assert (forall ((B4 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (let ((_let_2 (@ tptp.plus_plus_complex K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ (@ tptp.plus_plus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) (@ (@ tptp.plus_plus_complex C) A)) (= B C))))
% 6.75/7.06 (assert (= tptp.plus_plus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real B3) A4))))
% 6.75/7.06 (assert (= tptp.plus_plus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat B3) A4))))
% 6.75/7.06 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.plus_plus_nat B3) A4))))
% 6.75/7.06 (assert (= tptp.plus_plus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int B3) A4))))
% 6.75/7.06 (assert (= tptp.plus_plus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex B3) A4))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.06 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex B))) (let ((_let_2 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex B) A) (@ (@ tptp.plus_plus_complex C) A)) (= B C))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.75/7.06 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (= K L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (= K L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (= K L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C2))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 6.75/7.06 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (exists ((C3 tptp.nat)) (= B3 (@ (@ tptp.plus_plus_nat A4) C3))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.75/7.06 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (= K L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (= K L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (= K L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.75/7.06 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.75/7.06 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_nat X2) Y2))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_nat X2) Y2))))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_nat X2) Y2))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_nat X2) Y2))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num) (B tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num) (B tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num) (B tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X2) Y2))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X2) Y2))))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X2) Y2))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X2) Y2))))))
% 6.75/7.06 (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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))
% 6.75/7.06 (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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))))))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y2) _let_2)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.75/7.06 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X2) Y2)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X2) _let_2)) (@ (@ tptp.power_power_complex Y2) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) Y2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) Y2)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X2) Y2)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y2) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X2) Y2)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y2) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X2)) Y2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X2) Y2)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_2)) (@ (@ tptp.power_power_int Y2) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X2)) Y2)))))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 6.75/7.06 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) N) (= Deg N))))
% 6.75/7.06 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 6.75/7.06 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 6.75/7.06 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_eq_nat Ma) X2) (= (@ (@ tptp.vEBT_vebt_succ _let_1) X2) tptp.none_nat))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat _let_1) (@ tptp.vEBT_VEBT_height T))) (@ (@ tptp.times_times_nat _let_1) N))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ tptp.vEBT_vebt_succ T) X2) (@ tptp.some_nat Y2)) (@ (@ tptp.ord_less_nat Y2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ tptp.vEBT_vebt_pred T) X2) (@ tptp.some_nat Y2)) (@ (@ tptp.ord_less_nat Y2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.06 (assert (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I3)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I3)))))
% 6.75/7.06 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N2 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N2) (@ P M2))) (@ P N2))) (@ P N))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ (@ tptp.times_times_real A) C))) (@ (@ tptp.times_times_real B) D2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) _let_2)) (@ (@ tptp.power_power_real D2) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real B) _let_2)) (@ (@ tptp.power_power_real C) _let_2))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) _let_2))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X2) N))) (let ((_let_2 (@ tptp.times_times_complex Y2))) (=> (= (@ (@ tptp.times_times_complex X2) Y2) (@ _let_2 X2)) (= (@ (@ tptp.times_times_complex _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X2) N))) (let ((_let_2 (@ tptp.times_times_real Y2))) (=> (= (@ (@ tptp.times_times_real X2) Y2) (@ _let_2 X2)) (= (@ (@ tptp.times_times_real _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X2) N))) (let ((_let_2 (@ tptp.times_times_rat Y2))) (=> (= (@ (@ tptp.times_times_rat X2) Y2) (@ _let_2 X2)) (= (@ (@ tptp.times_times_rat _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X2) N))) (let ((_let_2 (@ tptp.times_times_nat Y2))) (=> (= (@ (@ tptp.times_times_nat X2) Y2) (@ _let_2 X2)) (= (@ (@ tptp.times_times_nat _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X2) N))) (let ((_let_2 (@ tptp.times_times_int Y2))) (=> (= (@ (@ tptp.times_times_int X2) Y2) (@ _let_2 X2)) (= (@ (@ tptp.times_times_int _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A) B)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (= (@ (@ tptp.times_times_complex _let_1) A) (@ (@ tptp.times_times_complex A) _let_1)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (= (@ (@ tptp.times_times_real _let_1) A) (@ (@ tptp.times_times_real A) _let_1)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (= (@ (@ tptp.times_times_rat _let_1) A) (@ (@ tptp.times_times_rat A) _let_1)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) B)) N) (@ (@ tptp.divide_divide_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_real (@ _let_1 M)) N)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_int (@ _let_1 M)) N)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 6.75/7.06 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X2) Y2) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y2) N)) tptp.one_one_complex))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X2) Y2) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y2) N)) tptp.one_one_real))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X2) Y2) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_rat Y2) N)) tptp.one_one_rat))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X2) Y2) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y2) N)) tptp.one_one_nat))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X2) Y2) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y2) N)) tptp.one_one_int))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_complex A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real A) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat A) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.75/7.06 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X2) X2)) X2)) X2))))
% 6.75/7.06 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X2) X2)) X2)) X2))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X2) X2)) X2)) X2))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.power_power_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X2) X2)) X2)) X2))))
% 6.75/7.06 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X2) X2)) X2)) X2))))
% 6.75/7.06 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.75/7.06 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.75/7.06 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.75/7.06 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.75/7.06 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex A) A)) A))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real A) A)) A))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat A) A)) A))))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat A) A)) A))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) A)) A))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) _let_1)) (@ (@ tptp.power_power_nat N) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat K) M)))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (not (= Mi Ma)) (= (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt Summary)) (@ (@ tptp.vEBT_VEBT_high Ma) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.some_nat M) (@ tptp.vEBT_vebt_mint T)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (=> (@ (@ tptp.ord_less_nat Y2) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X2)) Y2) (or (@ (@ tptp.vEBT_vebt_member T) Y2) (= X2 Y2)))))))))
% 6.75/7.06 (assert (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X6) tptp.na) (forall ((Xa tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_s_u_c_c X6) Xa)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height X6))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))))))))))
% 6.75/7.06 (assert (forall ((Tree tptp.vEBT_VEBT) (X2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X2) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.06 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_nat A) B)) (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va)) Vb) tptp.none_nat)))
% 6.75/7.06 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va) tptp.none_nat)))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (=> (@ (@ tptp.ord_less_nat Y2) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y2)) X2))))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X2)) X2)))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2) (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2) (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_option_nat) (P (-> tptp.option_nat Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.option_nat)) (=> (@ (@ tptp.member_option_nat X4) (@ tptp.set_option_nat2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6086282163384603972on_nat Xs2)) (@ P (@ (@ tptp.nth_option_nat Xs2) N))))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) N))))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_set_nat_rat) (P (-> tptp.set_nat_rat Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X4) (@ tptp.set_set_nat_rat2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3959913991096427681at_rat Xs2)) (@ P (@ (@ tptp.nth_set_nat_rat Xs2) N))))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) N))))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) N))))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) N))))))
% 6.75/7.06 (assert (=> (= tptp.mi tptp.ma) (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X6) X_12)))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.75/7.06 (assert (forall ((R tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R)) (@ (@ tptp.divide_divide_real A) R)))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X2) (@ (@ tptp.ord_less_eq_nat X2) Maxi))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X2) (@ (@ tptp.ord_less_eq_nat Mini) X2))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT T) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.vEBT_VEBT_height (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X6) X_12))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) B) A)))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) B) A)))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.75/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex C))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_complex A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_real A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_int A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) A) B)))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.75/7.06 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.minus_minus_complex A) B))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real A) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat A) B))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.minus_minus_nat A) B))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int A) B))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) B) A)))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.75/7.06 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member T) X2) (@ (@ tptp.member_nat X2) (@ tptp.vEBT_set_vebt T))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B)) B) A))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 6.75/7.06 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K)))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) J)))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (=> (not (= Mi Ma)) (and (@ (@ tptp.ord_less_nat Mi) Ma) (exists ((M4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M4) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))))
% 6.75/7.06 (assert (= tptp.m (@ tptp.suc tptp.na)))
% 6.75/7.06 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I3)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((X6 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X6) tptp.na) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I3)) (@ (@ tptp.vEBT_VEBT_low X6) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X6) (@ (@ tptp.ord_less_eq_nat X6) tptp.ma)))))))))
% 6.75/7.06 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.power_power_real X2) N2))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D2 tptp.complex)) (=> (= (@ (@ tptp.minus_minus_complex A) B) (@ (@ tptp.minus_minus_complex C) D2)) (= (= A B) (= C D2)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D2)) (= (= A B) (= C D2)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (= A B) (= C D2)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (= A B) (= C D2)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 C)) B) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (D2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real D2) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D2) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D2))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D2)) (= (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real C) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D2)) (= (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real C) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (D2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real D2) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D2) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D2))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) C)) A) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex B) A)) (@ (@ tptp.times_times_complex C) A)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) C)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B) A)) (@ (@ tptp.times_times_real C) A)))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) C)) A) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B) A)) (@ (@ tptp.times_times_rat C) A)))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)))))
% 6.75/7.06 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.75/7.06 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_complex A2) B) (@ _let_1 (@ (@ tptp.minus_minus_complex A) B)))))))
% 6.75/7.06 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A2) B) (@ _let_1 (@ (@ tptp.minus_minus_real A) B)))))))
% 6.75/7.06 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A2) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))))
% 6.75/7.06 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A2) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.minus_minus_complex A) B) C) (= A (@ (@ tptp.plus_plus_complex C) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B) C) (= A (@ (@ tptp.plus_plus_real C) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B) C) (= A (@ (@ tptp.plus_plus_rat C) B)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B) C) (= A (@ (@ tptp.plus_plus_int C) B)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.minus_minus_complex C) B)) (= (@ (@ tptp.plus_plus_complex A) B) C))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C) B)) (= (@ (@ tptp.plus_plus_real A) B) C))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C) B)) (= (@ (@ tptp.plus_plus_rat A) B) C))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C) B)) (= (@ (@ tptp.plus_plus_int A) B) C))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) B))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) B))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 C)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 C)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B)))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex C) B) A) (= C (@ (@ tptp.minus_minus_complex A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B) A) (= C (@ (@ tptp.minus_minus_real A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B) A) (= C (@ (@ tptp.minus_minus_rat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B) A) (= C (@ (@ tptp.minus_minus_nat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B) A) (= C (@ (@ tptp.minus_minus_int A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex) (D2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) (@ (@ tptp.plus_plus_complex B) D2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex C) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real C) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat C) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int C) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))))
% 6.75/7.06 (assert (forall ((J tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 6.75/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) A) B))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B) A)) B))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C) (= B (@ (@ tptp.plus_plus_nat C) A))))))))
% 6.75/7.06 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N) (@ (@ tptp.ord_less_eq_real I) (@ (@ tptp.minus_minus_real N) K)))))
% 6.75/7.06 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N) (@ (@ tptp.ord_less_eq_rat I) (@ (@ tptp.minus_minus_rat N) K)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat N) K)))))
% 6.75/7.06 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N) (@ (@ tptp.ord_less_eq_int I) (@ (@ tptp.minus_minus_int N) K)))))
% 6.75/7.06 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real) (J tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N) (@ (@ tptp.plus_plus_real J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N) K)) J)))))))))
% 6.75/7.06 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K)) J)))))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K)) J)))))))))
% 6.75/7.06 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K)) J)))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.ord_less_real A) B)) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A) B)) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A) B)) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.ord_less_int A) B)) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 6.75/7.06 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X2))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 Y2)) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_complex Y2) B))) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) A)) B))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y2)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y2) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) A)) B))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y2)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y2) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) A)) B))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y2)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y2) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) A)) B))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B tptp.complex) (D2 tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) D2)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) E)) C) D2))))
% 6.75/7.06 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C) D2))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C) D2))))
% 6.75/7.06 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C) D2))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B tptp.complex) (D2 tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) D2)) (= C (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) A)) E)) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) X2)) (@ (@ tptp.times_times_complex Y2) Y2)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X2) Y2)) (@ (@ tptp.minus_minus_complex X2) Y2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.minus_minus_real X2) Y2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y2) Y2)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X2) Y2)) (@ (@ tptp.minus_minus_rat X2) Y2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y2) Y2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X2) Y2)) (@ (@ tptp.minus_minus_int X2) Y2)))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) J))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))))
% 6.75/7.06 (assert (forall ((J tptp.nat) (K tptp.nat) (I tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I) K)))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) J)))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.minus_minus_nat J) I) K) (= J (@ (@ tptp.plus_plus_nat K) I))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D2))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D2))))
% 6.75/7.06 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D2))))
% 6.75/7.06 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D2))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D2))))
% 6.75/7.06 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D2))))
% 6.75/7.06 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) X2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X2) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) X2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) X2)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X2) X2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X2) tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I) K))))))
% 6.75/7.06 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M) N)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.75/7.06 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.75/7.06 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.75/7.06 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X2) Y2)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y2) X2)) _let_1)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) Y2)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y2) X2)) _let_1)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X2) Y2)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y2) X2)) _let_1)))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X2) Y2)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y2) X2)) _let_1)))))
% 6.75/7.06 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X2) Y2)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X2) _let_2)) (@ (@ tptp.power_power_complex Y2) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) Y2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) Y2)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X2) Y2)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y2) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X2) Y2)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_2)) (@ (@ tptp.power_power_int Y2) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X2)) Y2)))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X2))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2)))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2)))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (=> (= N (@ tptp.suc (@ tptp.suc Va))) (=> (not (@ (@ tptp.ord_less_nat Ma) Mi)) (=> (not (= Ma Mi)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_3) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))))) (@ tptp.suc _let_2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))))))))))
% 6.75/7.06 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.75/7.06 (assert (forall ((L tptp.num) (R tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q2) R)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R))))))))))
% 6.75/7.06 (assert (forall ((L tptp.num) (R tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q2) R)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R))))))))))
% 6.75/7.06 (assert (forall ((L tptp.num) (R tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L) (@ (@ tptp.produc1086072967326762835nteger Q2) R)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2))))))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X2 Mi) (= X2 Ma) (and (@ (@ tptp.ord_less_nat X2) Ma) (@ (@ tptp.ord_less_nat Mi) X2) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2)))))))))))
% 6.75/7.06 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_nat tptp.deg) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ tptp.summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_7 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))) (@ tptp.vEBT_T_m_a_x_t _let_9))) (@ (@ (@ tptp.if_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ _let_7 (@ (@ tptp.vEBT_T_s_u_c_c _let_9) _let_8))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_2) (@ (@ tptp.vEBT_T_s_u_c_c tptp.summary) _let_4))) (@ (@ (@ tptp.if_nat (= _let_5 tptp.none_nat)) tptp.one_one_nat) (@ _let_7 (@ tptp.vEBT_T_m_i_n_t (@ _let_6 (@ tptp.the_nat _let_5))))))))))))))))))))
% 6.75/7.06 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (= X2 Mi) (= X2 Ma)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat)) (=> (forall ((N2 tptp.nat)) (not (= X2 (@ (@ tptp.plus_plus_nat N2) N2)))) (not (forall ((N2 tptp.nat)) (not (= X2 (@ (@ tptp.plus_plus_nat N2) (@ tptp.suc N2)))))))))
% 6.75/7.06 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N))) TreeList2) S2))))))
% 6.75/7.06 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (D2 tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X2) D2)) (@ (@ tptp.vEBT_VEBT_low X2) D2)) D2) X2)))
% 6.75/7.06 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.75/7.06 (assert (forall ((X23 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.suc X23) (@ tptp.suc Y22)) (= X23 Y22))))
% 6.75/7.06 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (Y11 tptp.option4927543243414619207at_nat) (Y12 tptp.nat) (Y13 tptp.list_VEBT_VEBT) (Y14 tptp.vEBT_VEBT)) (= (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ (@ (@ tptp.vEBT_Node Y11) Y12) Y13) Y14)) (and (= X11 Y11) (= X12 Y12) (= X13 Y13) (= X14 Y14)))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y2) _let_1)) X2)) N) X2)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 6.75/7.06 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_1))))) (not (and (not (= _let_2 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_1))) _let_2))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 6.75/7.06 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (@ (@ tptp.vEBT_VEBT_low X2) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X2)))))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) (@ tptp.suc J))))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 6.75/7.06 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.75/7.06 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat M) _let_1))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Y2) (and (@ (@ tptp.vEBT_vebt_member T) Y2) (@ (@ tptp.ord_less_nat X2) Y2) (forall ((Z2 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z2) (@ (@ tptp.ord_less_nat X2) Z2)) (@ (@ tptp.ord_less_eq_nat Y2) Z2)))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Y2) (and (@ (@ tptp.vEBT_vebt_member T) Y2) (@ (@ tptp.ord_less_nat Y2) X2) (forall ((Z2 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z2) (@ (@ tptp.ord_less_nat Z2) X2)) (@ (@ tptp.ord_less_eq_nat Z2) Y2)))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X2) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Sx)))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Px tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X2) (@ tptp.some_nat Px)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Px)))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X2) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_set_vebt T)) X2) Sx)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X2) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_set_vebt T)) X2) Sx)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2))))))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2)))))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P N) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M5 tptp.nat)) (and (= M (@ tptp.suc M5)) (@ (@ tptp.ord_less_nat N) M5))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (@ (@ P I2) (@ tptp.suc I2))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ P I2))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K3) (=> (@ _let_1 J2) (=> (@ (@ P J2) K3) (@ _let_1 K3))))))) (@ (@ P I) J))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (=> (= J (@ tptp.suc I2)) (@ P I2))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ P (@ tptp.suc I2)) (@ P I2)))) (@ P I))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat) (R2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X4 tptp.nat)) (@ (@ R2 X4) X4)) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ R2 X4))) (=> (@ _let_1 Y3) (=> (@ (@ R2 Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((N2 tptp.nat)) (@ (@ R2 N2) (@ tptp.suc N2))) (@ (@ R2 M) N)))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P N2) (@ P (@ tptp.suc N2))))) (@ P N))))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2) (@ P M2))) (@ P N2))) (@ P N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M6) (exists ((M4 tptp.nat)) (= M6 (@ tptp.suc M4))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 6.75/7.06 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ tptp.suc A2) (@ _let_1 (@ tptp.suc A)))))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))))
% 6.75/7.06 (assert (forall ((Z tptp.extended_enat) (Y2 tptp.extended_enat) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X2))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y2) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y2) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y2)) Z))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_real (@ F N)) (@ F N5))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N5))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_num (@ F N)) (@ F N5))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N5))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_int (@ F N)) (@ F N5))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) A)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) A)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) A)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) A)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) A)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N5)) (@ F N))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N5)) (@ F N))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N)) (@ F N5))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N5))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N5))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N5))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N5))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 6.75/7.06 (assert (= tptp.ord_less_nat (lambda ((N3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N3)) __flatten_var_0))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J) (=> (@ P (@ tptp.suc N2)) (@ P N2))))) (@ P I))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J) (=> (@ P N2) (@ P (@ tptp.suc N2)))))) (@ P J))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K3 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K3)))))))
% 6.75/7.06 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (exists ((K2 tptp.nat)) (= N3 (@ tptp.suc (@ (@ tptp.plus_plus_nat M3) K2)))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q3 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q3)))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.75/7.06 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.75/7.06 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.75/7.06 (assert (= tptp.suc (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 6.75/7.06 (assert (forall ((X2 tptp.product_prod_num_num)) (=> (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N2 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N2))))) (=> (forall ((N2 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N2))))) (=> (forall ((M4 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N2 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit0 N2))))) (=> (forall ((M4 tptp.num) (N2 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit1 N2))))) (=> (forall ((M4 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N2 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit0 N2))))) (not (forall ((M4 tptp.num) (N2 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit1 N2))))))))))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc N)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc N)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N)))))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (Q2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q2)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q2))) (= (@ (@ tptp.divide_divide_nat M) N) Q2))))))
% 6.75/7.06 (assert (forall ((V tptp.num) (N tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_complex A) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_rat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat (@ _let_2 N)) _let_1)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1)))))))
% 6.75/7.06 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 6.75/7.06 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.75/7.06 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 6.75/7.06 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (X tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) (@ (@ tptp.vEBT_VEBT_high X) N3))) (@ (@ tptp.vEBT_VEBT_low X) N3)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real B) A)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 6.75/7.06 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X2) X2))) _let_1) TreeList) Summary)))))
% 6.75/7.06 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ tptp.summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_6 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (let ((_let_10 (@ tptp.bit1 tptp.one))) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 _let_10)))) (@ tptp.vEBT_T_m_a_x_t _let_8))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat _let_10)) (@ (@ (@ tptp.if_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ _let_6 (@ (@ tptp.vEBT_T_s_u_c_c _let_8) _let_7))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.vEBT_T_s_u_c_c tptp.summary) _let_3))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_4 tptp.none_nat)) tptp.one_one_nat) (@ _let_6 (@ tptp.vEBT_T_m_i_n_t (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Mi))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Ma))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M) (@ tptp.suc (@ _let_1 N)))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X2) Ma) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X2)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 6.75/7.06 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X2) Ma) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X2)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.75/7.06 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 6.75/7.06 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X2) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 6.75/7.06 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X2) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.75/7.06 (assert (forall ((C tptp.real)) (= (lambda ((X tptp.real)) (@ (@ tptp.times_times_real X) C)) (@ tptp.times_times_real C))))
% 6.75/7.06 (assert (forall ((C tptp.rat)) (= (lambda ((X tptp.rat)) (@ (@ tptp.times_times_rat X) C)) (@ tptp.times_times_rat C))))
% 6.75/7.06 (assert (forall ((C tptp.nat)) (= (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat X) C)) (@ tptp.times_times_nat C))))
% 6.75/7.06 (assert (forall ((C tptp.int)) (= (lambda ((X tptp.int)) (@ (@ tptp.times_times_int X) C)) (@ tptp.times_times_int C))))
% 6.75/7.06 (assert (= (lambda ((X tptp.complex)) X) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.75/7.06 (assert (= (lambda ((X tptp.real)) X) (@ tptp.times_times_real tptp.one_one_real)))
% 6.75/7.06 (assert (= (lambda ((X tptp.rat)) X) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.75/7.06 (assert (= (lambda ((X tptp.nat)) X) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.75/7.06 (assert (= (lambda ((X tptp.int)) X) (@ tptp.times_times_int tptp.one_one_int)))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_complex _let_2) _let_2))))))
% 6.75/7.06 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_real _let_2) _let_2))))))
% 6.75/7.06 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_rat _let_2) _let_2))))))
% 6.75/7.06 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_nat _let_2) _let_2))))))
% 6.75/7.06 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_int _let_2) _let_2))))))
% 6.75/7.06 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex Z) _let_2)) _let_2))))))
% 6.75/7.06 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real Z) _let_2)) _let_2))))))
% 6.75/7.06 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z) _let_2)) _let_2))))))
% 6.75/7.06 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z) _let_2)) _let_2))))))
% 6.75/7.06 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z) _let_2)) _let_2))))))
% 6.75/7.06 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_nat Y) X) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member_nat Z2) Xs) (=> (@ (@ tptp.ord_less_nat Z2) X) (@ (@ tptp.ord_less_eq_nat Z2) Y))))))))
% 6.75/7.06 (assert (= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_nat X) Y) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member_nat Z2) Xs) (=> (@ (@ tptp.ord_less_nat X) Z2) (@ (@ tptp.ord_less_eq_nat Y) Z2))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc5491161045314408544at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (V2 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X4 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X4)) (@ tptp.some_P7363390416028606310at_nat Y3)))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc2233624965454879586on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat Bool)) (Uv2 tptp.option_nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat Bool)) (V2 tptp.nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat Bool)) (X4 tptp.nat) (Y3 tptp.nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X4)) (@ tptp.some_nat Y3)))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc7036089656553540234on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num Bool)) (Uv2 tptp.option_num)) (not (= X2 (@ (@ tptp.produc3576312749637752826on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num Bool)) (V2 tptp.num)) (not (= X2 (@ (@ tptp.produc3576312749637752826on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num Bool)) (X4 tptp.num) (Y3 tptp.num)) (not (= X2 (@ (@ tptp.produc3576312749637752826on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X4)) (@ tptp.some_num Y3)))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc5542196010084753463at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V2 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A3 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A3)) (@ tptp.some_P7363390416028606310at_nat B2)))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc8306885398267862888on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat tptp.nat)) (Uv2 tptp.option_nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat tptp.nat)) (V2 tptp.nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B2 tptp.nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A3)) (@ tptp.some_nat B2)))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc1193250871479095198on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num tptp.num)) (Uv2 tptp.option_num)) (not (= X2 (@ (@ tptp.produc5778274026573060048on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num tptp.num)) (V2 tptp.num)) (not (= X2 (@ (@ tptp.produc5778274026573060048on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num tptp.num)) (A3 tptp.num) (B2 tptp.num)) (not (= X2 (@ (@ tptp.produc5778274026573060048on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A3)) (@ tptp.some_num B2)))))))))))
% 6.75/7.06 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat F) (@ tptp.some_P7363390416028606310at_nat A)) (@ tptp.some_P7363390416028606310at_nat B)) (@ tptp.some_P7363390416028606310at_nat (@ (@ F A) B)))))
% 6.75/7.06 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (A tptp.num) (B tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num F) (@ tptp.some_num A)) (@ tptp.some_num B)) (@ tptp.some_num (@ (@ F A) B)))))
% 6.75/7.06 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat F) (@ tptp.some_nat A)) (@ tptp.some_nat B)) (@ tptp.some_nat (@ (@ F A) B)))))
% 6.75/7.06 (assert (forall ((Uu (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv tptp.option4927543243414619207at_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uu) tptp.none_P5556105721700978146at_nat) Uv) tptp.none_P5556105721700978146at_nat)))
% 6.75/7.06 (assert (forall ((Uu (-> tptp.num tptp.num tptp.num)) (Uv tptp.option_num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uu) tptp.none_num) Uv) tptp.none_num)))
% 6.75/7.06 (assert (forall ((Uu (-> tptp.nat tptp.nat tptp.nat)) (Uv tptp.option_nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uu) tptp.none_nat) Uv) tptp.none_nat)))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X2))) (let ((_let_12 (@ (@ tptp.ord_less_nat X2) Mi))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Mi))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 6.75/7.06 (assert (forall ((Ma tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X2))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma) X2))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Ma))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X2)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (let ((_let_8 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low X2) _let_3))) (let ((_let_10 (@ _let_6 _let_4))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X2) (@ _let_8 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ tptp.plus_plus_nat (@ _let_8 (@ tptp.vEBT_T_m_a_x_t _let_10))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ (@ tptp.if_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ _let_7 (@ (@ tptp.vEBT_T_s_u_c_c _let_10) _let_9))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_8 (@ (@ tptp.vEBT_T_s_u_c_c Summary) _let_4))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_5 tptp.none_nat)) tptp.one_one_nat) (@ _let_7 (@ tptp.vEBT_T_m_i_n_t (@ _let_6 (@ tptp.the_nat _let_5)))))))))) tptp.one_one_nat))))))))))))))))))
% 6.75/7.06 (assert (forall ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uw) (@ tptp.some_P7363390416028606310at_nat V)) tptp.none_P5556105721700978146at_nat) tptp.none_P5556105721700978146at_nat)))
% 6.75/7.06 (assert (forall ((Uw (-> tptp.num tptp.num tptp.num)) (V tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uw) (@ tptp.some_num V)) tptp.none_num) tptp.none_num)))
% 6.75/7.06 (assert (forall ((Uw (-> tptp.nat tptp.nat tptp.nat)) (V tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uw) (@ tptp.some_nat V)) tptp.none_nat) tptp.none_nat)))
% 6.75/7.06 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y2 tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X2) Xa2) Xb) Y2) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat)) (= Xa2 (@ tptp.some_P7363390416028606310at_nat V2))) (=> (= Xb tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A3)) (forall ((B2 tptp.product_prod_nat_nat)) (=> (= Xb (@ tptp.some_P7363390416028606310at_nat B2)) (not (= Y2 (@ tptp.some_P7363390416028606310at_nat (@ (@ X2 A3) B2)))))))))))))))
% 6.75/7.06 (assert (forall ((X2 (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y2 tptp.option_num)) (let ((_let_1 (not (= Y2 tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X2) Xa2) Xb) Y2) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V2 tptp.num)) (= Xa2 (@ tptp.some_num V2))) (=> (= Xb tptp.none_num) _let_1)) (not (forall ((A3 tptp.num)) (=> (= Xa2 (@ tptp.some_num A3)) (forall ((B2 tptp.num)) (=> (= Xb (@ tptp.some_num B2)) (not (= Y2 (@ tptp.some_num (@ (@ X2 A3) B2)))))))))))))))
% 6.75/7.06 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y2 tptp.option_nat)) (let ((_let_1 (not (= Y2 tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X2) Xa2) Xb) Y2) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa2 (@ tptp.some_nat V2))) (=> (= Xb tptp.none_nat) _let_1)) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A3)) (forall ((B2 tptp.nat)) (=> (= Xb (@ tptp.some_nat B2)) (not (= Y2 (@ tptp.some_nat (@ (@ X2 A3) B2)))))))))))))))
% 6.75/7.06 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)))
% 6.75/7.06 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X2) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2) (=> (not (= X2 Mi)) (=> (not (= X2 Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_6 (@ tptp.vEBT_vebt_maxt _let_5))) (let ((_let_7 (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2))) (let ((_let_8 (@ (@ tptp.ord_less_nat X2) Mi))) (and (=> _let_8 (= _let_7 tptp.one_one_nat)) (=> (not _let_8) (= _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_nat (and (not (= _let_6 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_4)) _let_6))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.vEBT_T_s_u_c_c2 _let_5) _let_4))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_s_u_c_c2 Summary) _let_3)) tptp.one_one_nat))) tptp.one_one_nat))))))))))))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high X2) _let_4))) (let ((_let_6 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_3) TreeList) Summary)) X2) (@ (@ tptp.plus_plus_nat _let_2) (@ (@ (@ tptp.if_nat (= X2 Mi)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (= X2 Ma)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma) X2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ _let_6 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_5)) (@ (@ tptp.vEBT_VEBT_low X2) _let_4)))) tptp.one_one_nat)))))))))))))))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X2) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat Y) X2)))) tptp.bot_bot_set_nat)))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X2) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat X2) Y)))) tptp.bot_bot_set_nat)))))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Vc)) X2) (or (= X2 Mi) (= X2 Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4)))))))))
% 6.75/7.06 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 6.75/7.06 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_m_e_m_b_e_r T) X2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.75/7.06 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X) (@ (@ tptp.vEBT_VEBT_membermima T2) X)))))
% 6.75/7.06 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X2) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X2) (@ (@ tptp.vEBT_VEBT_membermima Tree) X2))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.75/7.06 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.75/7.06 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X2))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) X2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_s_u_c_c X2) Xa2) Y2) (=> (=> (exists ((Uu2 Bool) (B2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) B2))) (=> (= Xa2 tptp.zero_zero_nat) (not (= Y2 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N2 tptp.nat)) (= Xa2 (@ tptp.suc N2))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (let ((_let_8 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_10 (@ _let_6 _let_4))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (= Y2 (@ _let_8 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.plus_plus_nat (@ _let_8 (@ tptp.vEBT_T_m_a_x_t _let_10))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ (@ tptp.if_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ _let_7 (@ (@ tptp.vEBT_T_s_u_c_c _let_10) _let_9))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_8 (@ (@ tptp.vEBT_T_s_u_c_c Summary2) _let_4))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_5 tptp.none_nat)) tptp.one_one_nat) (@ _let_7 (@ tptp.vEBT_T_m_i_n_t (@ _let_6 (@ tptp.the_nat _let_5)))))))))) tptp.one_one_nat)))))))))))))))))))))))))))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I4)))))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool))) (= (forall ((X Bool)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P X))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I4)))))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ P X))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I4)))))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_option_nat) (P (-> tptp.option_nat Bool)) (X2 tptp.option_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6086282163384603972on_nat Xs2)) (@ P (@ (@ tptp.nth_option_nat Xs2) I2)))) (=> (@ (@ tptp.member_option_nat X2) (@ tptp.set_option_nat2 Xs2)) (@ P X2)))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (X2 tptp.real)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) I2)))) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs2)) (@ P X2)))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_set_nat_rat) (P (-> tptp.set_nat_rat Bool)) (X2 tptp.set_nat_rat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3959913991096427681at_rat Xs2)) (@ P (@ (@ tptp.nth_set_nat_rat Xs2) I2)))) (=> (@ (@ tptp.member_set_nat_rat X2) (@ tptp.set_set_nat_rat2 Xs2)) (@ P X2)))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (X2 tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I2)))) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (@ P X2)))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X2 tptp.vEBT_VEBT)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)))) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X2)))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (X2 Bool)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I2)))) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (@ P X2)))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I2)))) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (@ P X2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.option_nat) (Xs2 tptp.list_option_nat)) (= (@ (@ tptp.member_option_nat X2) (@ tptp.set_option_nat2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6086282163384603972on_nat Xs2)) (= (@ (@ tptp.nth_option_nat Xs2) I4) X2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I4) X2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.set_nat_rat) (Xs2 tptp.list_set_nat_rat)) (= (@ (@ tptp.member_set_nat_rat X2) (@ tptp.set_set_nat_rat2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3959913991096427681at_rat Xs2)) (= (@ (@ tptp.nth_set_nat_rat Xs2) I4) X2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I4) X2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I4) X2))))))
% 6.75/7.06 (assert (forall ((X2 Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I4) X2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I4) X2))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X4))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs2)) (@ P X4))) (@ P (@ (@ tptp.nth_o Xs2) N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs2)) (@ P X4))) (@ P (@ (@ tptp.nth_nat Xs2) N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_option_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6086282163384603972on_nat Xs2)) (@ (@ tptp.member_option_nat (@ (@ tptp.nth_option_nat Xs2) N)) (@ tptp.set_option_nat2 Xs2)))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs2) N)) (@ tptp.set_real2 Xs2)))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_set_nat_rat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3959913991096427681at_rat Xs2)) (@ (@ tptp.member_set_nat_rat (@ (@ tptp.nth_set_nat_rat Xs2) N)) (@ tptp.set_set_nat_rat2 Xs2)))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs2) N)) (@ tptp.set_int2 Xs2)))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N)) (@ tptp.set_VEBT_VEBT2 Xs2)))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs2) N)) (@ tptp.set_o2 Xs2)))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs2) N)) (@ tptp.set_nat2 Xs2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.option_nat)) (let ((_let_1 (not (= Y2 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X2) Xa2) Y2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A3 Bool)) (=> (exists ((Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y2 tptp.none_nat))))))) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (=> (exists ((Va3 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va3)))) (not (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y2 tptp.none_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_11 (= Y2 (@ tptp.some_nat Ma2))) (=> (not _let_11) (= Y2 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat)))))))))))))))))))))))))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X2))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X2))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.75/7.06 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A4 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A4) B3))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B2 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B2))))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A3 Bool) (B2 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B2)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (= A B))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.75/7.06 (assert (forall ((A tptp.literal)) (= (@ (@ tptp.plus_plus_literal A) tptp.zero_zero_literal) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X2) Y2) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y2 tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X2) Y2)) (and (= X2 tptp.zero_zero_nat) (= Y2 tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.literal)) (= (@ (@ tptp.plus_plus_literal tptp.zero_zero_literal) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_real B) A))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_rat B) A))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_int B) A))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex C) B)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real C) B)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.times_times_complex C) A) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real)) (= (= (@ (@ tptp.times_times_real C) A) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int)) (= (= (@ (@ tptp.times_times_int C) A) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2)) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y2) Y2)) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y2) Y2)) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y2 tptp.zero_zero_int)))))
% 6.75/7.06 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.75/7.06 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.75/7.06 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.75/7.06 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B)))))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B)))))))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A) B)))))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A) B)))))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A) B)))))))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_real A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) A) B))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) A) B))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) A) B))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) A) B))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C) A)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C) A)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C) A)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.75/7.06 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) B) A))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) B) A))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) B) A))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) B) A))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex C) B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real C) B)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat C) B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A) B)) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A) B)) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ (@ tptp.divide1717551699836669952omplex A) A))) (let ((_let_2 (= A tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 tptp.one_one_complex)))))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real A) A))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat A) A))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.divide_divide_real B) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B) A)) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B) A)) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 6.75/7.06 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.75/7.06 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.75/7.06 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (@ _let_1 M) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N)) (and (= M _let_1) (= N _let_1))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X2) M) _let_1) (or (= M tptp.zero_zero_nat) (= X2 _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X2) N)) (or (@ _let_1 X2) (= N tptp.zero_zero_nat))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (= K tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M) N)))))))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real B) A)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat B) A)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_real B) A)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B) A)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B)))))
% 6.75/7.06 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M)) N) M))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N)) N) M))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (@ (@ tptp.ord_less_eq_real A) B))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (@ (@ tptp.ord_less_eq_rat A) B))))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 6.75/7.06 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.75/7.06 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.75/7.06 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.75/7.06 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.75/7.06 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (= (@ (@ tptp.power_power_real X2) _let_1) (@ (@ tptp.power_power_real Y2) _let_1)) (= X2 Y2))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (= (@ (@ tptp.power_power_rat X2) _let_1) (@ (@ tptp.power_power_rat Y2) _let_1)) (= X2 Y2))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (= (@ (@ tptp.power_power_nat X2) _let_1) (@ (@ tptp.power_power_nat Y2) _let_1)) (= X2 Y2))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (= (@ (@ tptp.power_power_int X2) _let_1) (@ (@ tptp.power_power_int Y2) _let_1)) (= X2 Y2))))))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1)) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.zero_zero_real))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1)) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y2 tptp.zero_zero_int))))))
% 6.75/7.06 (assert (forall ((X2 tptp.literal)) (= (= tptp.zero_zero_literal X2) (= X2 tptp.zero_zero_literal))))
% 6.75/7.06 (assert (forall ((X2 tptp.real)) (= (= tptp.zero_zero_real X2) (= X2 tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat)) (= (= tptp.zero_zero_rat X2) (= X2 tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((X2 tptp.int)) (= (= tptp.zero_zero_int X2) (= X2 tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ tptp.vEBT_Leaf A) B)) X2) (@ _let_1 (@ (@ (@ tptp.if_nat (= X2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B2 Bool) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) X4)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S2)) X4)))))))))
% 6.75/7.06 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N) tptp.zero_zero_complex))))
% 6.75/7.06 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (let ((_let_1 (= X2 tptp.one_one_nat))) (let ((_let_2 (= X2 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X2) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.75/7.06 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X222 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X222)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y2 (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y2 (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) Deg3))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X2))) (let ((_let_4 (= X2 tptp.one_one_nat))) (let ((_let_5 (= X2 tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.75/7.06 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (let ((_let_1 (= X2 tptp.one_one_nat))) (let ((_let_2 (= X2 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X2) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.75/7.06 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)))
% 6.75/7.06 (assert (forall ((Uu Bool) (B Bool)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ tptp.vEBT_Leaf Uu) B)) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2)))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.75/7.06 (assert (forall ((D1 tptp.real) (D22 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E2))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.75/7.06 (assert (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E2))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B tptp.zero_zero_real))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (= A B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (= A B)))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (= A B)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (= A B)))))
% 6.75/7.06 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.75/7.06 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.75/7.06 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.75/7.06 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.75/7.06 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.75/7.06 (assert (= (lambda ((Y5 tptp.complex) (Z4 tptp.complex)) (= Y5 Z4)) (lambda ((A4 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A4) B3) tptp.zero_zero_complex))))
% 6.75/7.06 (assert (= (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4)) (lambda ((A4 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.minus_minus_real A4) B3) tptp.zero_zero_real))))
% 6.75/7.06 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((A4 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A4) B3) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A4 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int A4) B3) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (N tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex)))))
% 6.75/7.06 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.75/7.06 (assert (forall ((X23 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X23)))))
% 6.75/7.06 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.75/7.06 (assert (forall ((Nat tptp.nat) (X23 tptp.nat)) (=> (= Nat (@ tptp.suc X23)) (not (= Nat tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.nat)) (=> (not (= Y2 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y2 (@ tptp.suc Nat3))))))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc N2)))) (@ P N)))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (@ (@ P X4) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X4) Y3) (@ (@ P (@ tptp.suc X4)) (@ tptp.suc Y3)))) (@ (@ P M) N))))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.75/7.06 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2))))))) (@ P N)))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S)) X2) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (= A B))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (= A B))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (= A B))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (= A B))))))))
% 6.75/7.06 (assert (forall ((Uu Bool) (B Bool)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ tptp.vEBT_Leaf Uu) B)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))
% 6.75/7.06 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.75/7.06 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.75/7.06 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.75/7.06 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ tptp.vEBT_T_m_i_n_t (@ (@ tptp.vEBT_Leaf A) B)) (@ _let_1 (@ (@ (@ tptp.if_nat A) tptp.zero_zero_nat) (@ _let_1 tptp.one_one_nat)))))))
% 6.75/7.06 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S)) X2) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))))
% 6.75/7.06 (assert (forall ((B Bool) (Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uu) B)) tptp.zero_zero_nat))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))
% 6.75/7.06 (assert (forall ((B Bool) (A Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.75/7.06 (assert (forall ((A Bool) (Uw Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) Uw)) (@ tptp.suc tptp.zero_zero_nat)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))
% 6.75/7.06 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2)))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2)))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A) B))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.75/7.06 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (= (@ (@ tptp.plus_plus_real X2) Y2) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.zero_zero_real))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (= (@ (@ tptp.plus_plus_rat X2) Y2) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (= (@ (@ tptp.plus_plus_nat X2) Y2) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y2 tptp.zero_zero_nat))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (= (@ (@ tptp.plus_plus_int X2) Y2) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y2 tptp.zero_zero_int))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X2) Y2) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.zero_zero_real)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X2) Y2) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y2) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X2) Y2) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y2 tptp.zero_zero_nat)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y2) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X2) Y2) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y2 tptp.zero_zero_int)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real B) A))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C2 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C2)) (= C2 tptp.zero_zero_nat)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X2) Y2)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X2) Y2)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X2) Y2)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y2) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A4) B3)) tptp.zero_zero_real))))
% 6.75/7.06 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A4) B3)) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A4) B3)) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y2)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y2)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y2)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y2)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y2))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real A) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat A) C))))))
% 6.75/7.06 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A4) B3)) tptp.zero_zero_real))))
% 6.75/7.06 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A4) B3)) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A4) B3)) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)) (not (= C tptp.zero_zero_real))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)) (not (= C tptp.zero_zero_rat))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y2)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y2)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y2)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y2)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y2))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X2) Y2) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X2) Z) (@ (@ tptp.times_times_complex W) Y2)))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X2) Y2) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X2) Z) (@ (@ tptp.times_times_real W) Y2)))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X2) Y2) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X2) Z) (@ (@ tptp.times_times_rat W) Y2)))))))
% 6.75/7.06 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) B)) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) B)) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B (@ (@ tptp.times_times_complex A) C)) (= (@ (@ tptp.divide1717551699836669952omplex B) C) A)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B (@ (@ tptp.times_times_real A) C)) (= (@ (@ tptp.divide_divide_real B) C) A)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B (@ (@ tptp.times_times_rat A) C)) (= (@ (@ tptp.divide_divide_rat B) C) A)))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A) C) B) (= A (@ (@ tptp.divide1717551699836669952omplex B) C))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C) B) (= A (@ (@ tptp.divide_divide_real B) C))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C) B) (= A (@ (@ tptp.divide_divide_rat B) C))))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (= B (@ (@ tptp.times_times_complex A) C))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B) C) A) (= B (@ (@ tptp.times_times_real A) C))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (= B (@ (@ tptp.times_times_rat A) C))))))
% 6.75/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (= (@ (@ tptp.times_times_complex A) C) B)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B) C)) (= (@ (@ tptp.times_times_real A) C) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (= (@ (@ tptp.times_times_rat A) C) B)))))
% 6.75/7.06 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (= A B)))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (= A B)))))
% 6.75/7.06 (assert (forall ((X2 tptp.option_nat) (Xs2 tptp.list_option_nat)) (=> (@ (@ tptp.member_option_nat X2) (@ tptp.set_option_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6086282163384603972on_nat Xs2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Xs2 tptp.list_real)) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.set_nat_rat) (Xs2 tptp.list_set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X2) (@ tptp.set_set_nat_rat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3959913991096427681at_rat Xs2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Xs2 tptp.list_int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))))
% 6.75/7.06 (assert (forall ((X2 Bool) (Xs2 tptp.list_o)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs2)))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.75/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.75/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.75/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M3 tptp.nat)) (= N (@ tptp.suc M3))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P tptp.zero_zero_nat) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 6.75/7.06 (assert (forall ((X23 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((X23 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K3) N) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K3) (not (@ P I3)))) (@ P K3)))))))
% 6.75/7.06 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.plus_plus_nat I) K3) J))))))
% 6.75/7.06 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.75/7.06 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.75/7.06 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K))))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N) (= N tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (Uw2 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) Uw2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B2 Bool) (Va3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) (@ tptp.suc (@ tptp.suc Va3)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2)) Vb2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve)) Vf)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X4)))))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B2 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B2)) tptp.zero_zero_nat)))) (=> (forall ((Uv2 Bool) (Uw2 Bool) (N2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (@ tptp.suc N2))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2)) Va2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2)) Ve)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh)) Vi)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X4))))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B2 Bool) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) X4)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2)) X4)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2)) X4)))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2)) X4)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X4)))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B2 Bool) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) X4)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X4)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X4)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X4)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X4)))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2)) X4)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2)) X4)))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2)) X4)))))))))))
% 6.75/7.06 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))
% 6.75/7.06 (assert (forall ((B Bool) (A Bool) (Va tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va))))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.75/7.06 (assert (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (= X2 (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2)))))))))))
% 6.75/7.06 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.vEBT_Leaf A) B)) X2) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ (@ tptp.if_nat (= X2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))))
% 6.75/7.06 (assert (forall ((Uv Bool) (Uw Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N)) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((Uv Bool) (Uw Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N)) tptp.none_nat)))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2)))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_real B) (@ (@ tptp.plus_plus_real A) C))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A) C))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real Y2) E2)))) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat Y2) E2)))) (@ (@ tptp.ord_less_eq_rat X2) Y2))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y2) X2)) X2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y2) X2)) X2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y2) X2)) X2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X2) Y2)) X2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X2) Y2)) X2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X2) Y2)) X2)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.one_one_real))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.one_one_rat))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) A)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) A)))))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) A)))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) A)))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (@ _let_1 (@ (@ tptp.divide_divide_nat A) B)))))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y2)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y2)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y2)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y2)) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y2)) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y2) W)))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_rat X2) Y2) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y2) W)))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y2) W))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat X2) Y2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y2) W))))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.real) (X2 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y2) W))))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_eq_rat X2) Y2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y2) W))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y2) Y2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y2) Y2)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2))) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y2) Y2))) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y2) Y2))) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y2 tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((Uv Bool) (Uw Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N)) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2))) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y2) Y2))) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y2) Y2))) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2))) (or (not (= X2 tptp.zero_zero_real)) (not (= Y2 tptp.zero_zero_real))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y2) Y2))) (or (not (= X2 tptp.zero_zero_rat)) (not (= Y2 tptp.zero_zero_rat))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y2) Y2))) (or (not (= X2 tptp.zero_zero_int)) (not (= Y2 tptp.zero_zero_int))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.75/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y2)) X2) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X2) Y2))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y2)) X2) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X2) Y2))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real Z) Y2)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y2)) Z)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.times_times_rat Z) Y2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y2)) Z)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B)) (= A tptp.zero_zero_real))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B)) (= A tptp.zero_zero_rat))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.one_one_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.one_one_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.75/7.06 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.75/7.06 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.75/7.06 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.75/7.06 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.75/7.06 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.75/7.06 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.75/7.06 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 6.75/7.06 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 6.75/7.06 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W) Y2))) (@ (@ tptp.times_times_complex Y2) Z)))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y2))) (@ (@ tptp.times_times_real Y2) Z)))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y2))) (@ (@ tptp.times_times_rat Y2) Z)))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.complex) (X2 tptp.complex) (Z tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Z) Y2))) Y2)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Y2)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Z) Y2))) Y2)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Y2)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Z) Y2))) Y2)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.complex) (Z tptp.complex) (X2 tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Z) Y2))) Y2)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Z) Y2))) Y2)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Z) Y2))) Y2)))))
% 6.75/7.06 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.divide1717551699836669952omplex Y2) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) Y2)) Z)))))
% 6.75/7.06 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real Y2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) Y2)) Z)))))
% 6.75/7.06 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat Y2) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) Y2)) Z)))))
% 6.75/7.06 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Z)) Y2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Y2) Z))) Z)))))
% 6.75/7.06 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Z)) Y2) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Y2) Z))) Z)))))
% 6.75/7.06 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Z)) Y2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Y2) Z))) Z)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 6.75/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Z)) Y2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex Y2) Z))) Z)))))
% 6.75/7.06 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X2) Z)) Y2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real Y2) Z))) Z)))))
% 6.75/7.06 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X2) Z)) Y2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.times_times_rat Y2) Z))) Z)))))
% 6.75/7.06 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.divide1717551699836669952omplex Y2) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) Y2)) Z)))))
% 6.75/7.06 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real Y2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) Y2)) Z)))))
% 6.75/7.06 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat Y2) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) Y2)) Z)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W) Y2))) (@ (@ tptp.times_times_complex Y2) Z)))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y2))) (@ (@ tptp.times_times_real Y2) Z)))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y2))) (@ (@ tptp.times_times_rat Y2) Z)))))))
% 6.75/7.06 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 6.75/7.06 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 6.75/7.06 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 6.75/7.06 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ tptp.vEBT_T_m_a_x_t (@ (@ tptp.vEBT_Leaf A) B)) (@ _let_1 (@ (@ (@ tptp.if_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))
% 6.75/7.06 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.75/7.06 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X23)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs2 Ys)))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys))) (not (= Xs2 Ys)))))
% 6.75/7.06 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys))) (not (= Xs2 Ys)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) K3) (not (@ P I3)))) (@ P (@ tptp.suc K3))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ P N2) (@ P (@ tptp.suc N2))))) (@ P N))))))
% 6.75/7.06 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))) N))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M) N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P tptp.zero_zero_nat)) (forall ((D tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D)) (@ P D)))))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P tptp.zero_zero_nat))) (exists ((D tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D)) (not (@ P D)))))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N)) (and (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N) K)))))
% 6.75/7.06 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I) (@ _let_1 (@ (@ tptp.power_power_nat I) N))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N) M) (= N tptp.one_one_nat)))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) M)))))
% 6.75/7.06 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q2)) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N) Q2))))))
% 6.75/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M) N))))))
% 6.75/7.06 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))
% 6.75/7.06 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (=> (= (@ tptp.vEBT_T_m_i_n_t X2) Y2) (=> (forall ((A3 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (exists ((B2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B2))) (not (= Y2 (@ _let_1 (@ (@ (@ tptp.if_nat A3) tptp.zero_zero_nat) (@ _let_1 tptp.one_one_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (not (=> (exists ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) _let_1))))))))
% 6.75/7.06 (assert (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)) Uz))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (forall ((A3 Bool) (B2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2)))))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 6.75/7.06 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (=> (@ (@ tptp.ord_less_real Z3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z3) X2)) Y2)))) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (forall ((Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (=> (@ (@ tptp.ord_less_rat Z3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z3) X2)) Y2)))) (@ (@ tptp.ord_less_eq_rat X2) Y2))))
% 6.75/7.06 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A) C))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))))))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.75/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.75/7.06 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.times_times_real Z) Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y2)) Z)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.times_times_rat Z) Y2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y2)) Z)))))
% 6.75/7.06 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y2)) X2) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X2) Y2))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y2)) X2) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X2) Y2))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)) (= A tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)) (= A tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (A tptp.real) (Y2 tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X2) A) (=> (@ (@ tptp.ord_less_eq_real Y2) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X2)) (@ (@ tptp.times_times_real V) Y2))) A)))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (A tptp.rat) (Y2 tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X2) A) (=> (@ (@ tptp.ord_less_eq_rat Y2) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X2)) (@ (@ tptp.times_times_rat V) Y2))) A)))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (A tptp.int) (Y2 tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X2) A) (=> (@ (@ tptp.ord_less_eq_int Y2) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X2)) (@ (@ tptp.times_times_int V) Y2))) A)))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X2) Y2) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y2 tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y2 tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y2 (@ tptp.some_nat Ma2)))))))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.75/7.06 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.75/7.06 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y2))) (@ (@ tptp.times_times_real Y2) Z))) tptp.zero_zero_real))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y2))) (@ (@ tptp.times_times_rat Y2) Z))) tptp.zero_zero_rat))))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X2) Y2) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y2 tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y2 tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y2 (@ tptp.some_nat Mi2)))))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y2))) (@ (@ tptp.times_times_real Y2) Z))) tptp.zero_zero_real))))))
% 6.75/7.06 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y2))) (@ (@ tptp.times_times_rat Y2) Z))) tptp.zero_zero_rat))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) A)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) A)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) A)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) A)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) tptp.one_one_real)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) tptp.one_one_rat)))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) tptp.one_one_nat)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) tptp.one_one_int)))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.75/7.06 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.75/7.06 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.75/7.06 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.75/7.06 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_real A) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_nat A) N)))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_int A) N)))))))
% 6.75/7.06 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.75/7.06 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.75/7.06 (assert (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_rat (@ _let_1 M)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N))))))))
% 6.75/7.06 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.75/7.06 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M3) N3) (= N3 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M3) N3)) N3))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 6.75/7.06 (assert (= tptp.plus_plus_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N3) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N3))))))
% 6.75/7.06 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q2)) N)))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P I4))))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N)))))))
% 6.75/7.06 (assert (= tptp.times_times_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N3) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N3))))))
% 6.75/7.06 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2))))
% 6.75/7.06 (assert (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve2 tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc) Vd)) Ve2) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc) Vd)) Ve2) tptp.none_nat)))
% 6.75/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va) Vb)) X2) (or (= X2 Mi) (= X2 Ma)))))
% 6.75/7.06 (assert (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve2)) Vf2) tptp.none_nat)))
% 6.75/7.06 (assert (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve2 tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc) Vd)) Ve2) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (A tptp.real) (Y2 tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X2) A) (=> (@ (@ tptp.ord_less_real Y2) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X2)) (@ (@ tptp.times_times_real V) Y2))) A)))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (A tptp.rat) (Y2 tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X2) A) (=> (@ (@ tptp.ord_less_rat Y2) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X2)) (@ (@ tptp.times_times_rat V) Y2))) A)))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (A tptp.int) (Y2 tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X2) A) (=> (@ (@ tptp.ord_less_int Y2) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X2)) (@ (@ tptp.times_times_int V) Y2))) A)))))))))
% 6.75/7.06 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 6.75/7.06 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.75/7.06 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.75/7.06 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((U tptp.real) (V tptp.real) (R tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R) (=> (@ (@ tptp.ord_less_eq_real R) S) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R) (@ (@ tptp.minus_minus_real V) U))) S))) V))))))
% 6.75/7.06 (assert (forall ((U tptp.rat) (V tptp.rat) (R tptp.rat) (S tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R) (=> (@ (@ tptp.ord_less_eq_rat R) S) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R) (@ (@ tptp.minus_minus_rat V) U))) S))) V))))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X2) _let_2) (@ (@ tptp.power_power_real Y2) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= X2 Y2))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_rat X2) _let_2) (@ (@ tptp.power_power_rat Y2) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= X2 Y2))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X2) _let_2) (@ (@ tptp.power_power_nat Y2) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= X2 Y2))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X2) _let_2) (@ (@ tptp.power_power_int Y2) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= X2 Y2))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real X2) Y2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_eq_rat X2) Y2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y2) (@ (@ tptp.ord_less_eq_nat X2) Y2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (@ (@ tptp.ord_less_eq_int X2) Y2))))))
% 6.75/7.06 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 N) tptp.zero_zero_nat))))))
% 6.75/7.06 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 N) tptp.zero_zero_int))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_nat))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_int))))))
% 6.75/7.06 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 6.75/7.06 (assert (= tptp.power_power_complex (lambda ((P4 tptp.complex) (M3 tptp.nat)) (@ (@ (@ tptp.if_complex (= M3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P4) (@ (@ tptp.power_power_complex P4) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.75/7.06 (assert (= tptp.power_power_real (lambda ((P4 tptp.real) (M3 tptp.nat)) (@ (@ (@ tptp.if_real (= M3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P4) (@ (@ tptp.power_power_real P4) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.75/7.06 (assert (= tptp.power_power_rat (lambda ((P4 tptp.rat) (M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P4) (@ (@ tptp.power_power_rat P4) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.75/7.06 (assert (= tptp.power_power_nat (lambda ((P4 tptp.nat) (M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P4) (@ (@ tptp.power_power_nat P4) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.75/7.06 (assert (= tptp.power_power_int (lambda ((P4 tptp.int) (M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P4) (@ (@ tptp.power_power_int P4) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q4))) (@ P Q4))))))))
% 6.75/7.06 (assert (forall ((V tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((V tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2) tptp.none_nat)))
% 6.75/7.06 (assert (forall ((V tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2) tptp.none_nat)))
% 6.75/7.06 (assert (forall ((V tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2) tptp.one_one_nat)))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_real X2) Y2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_rat X2) Y2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y2) (@ (@ tptp.ord_less_nat X2) Y2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (@ (@ tptp.ord_less_int X2) Y2))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.zero_zero_real))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1))) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1))) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y2 tptp.zero_zero_int))))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) tptp.zero_zero_real)))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1))) tptp.zero_zero_rat)))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1))) tptp.zero_zero_int)))))
% 6.75/7.06 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) (or (not (= X2 tptp.zero_zero_real)) (not (= Y2 tptp.zero_zero_real)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1))) (or (not (= X2 tptp.zero_zero_rat)) (not (= Y2 tptp.zero_zero_rat)))))))
% 6.75/7.06 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1))) (or (not (= X2 tptp.zero_zero_int)) (not (= Y2 tptp.zero_zero_int)))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.75/7.06 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ P N))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.75/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.06 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.75/7.06 (assert (forall ((P (-> tptp.list_o Bool)) (Xs2 tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.75/7.06 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs2 tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) Y2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (= Y2 (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y2) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S2))) (= Y2 (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S2))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.75/7.06 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (=> (= (@ tptp.vEBT_T_m_a_x_t X2) Y2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (not (= Y2 (@ _let_1 (@ (@ (@ tptp.if_nat B2) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (not (=> (exists ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) _let_1))))))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 6.75/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_real))))
% 6.75/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_rat))))
% 6.75/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_int))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X2) N)) (@ _let_1 M)))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X2) N)) (@ _let_1 N)))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X2) Xa2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) Y2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y2) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (= Y2 (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (= Y2 (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (= Y2 (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.75/7.06 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X2) Xa2) Y2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (= Y2 (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y2) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (= Y2 (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 6.75/7.06 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V))) TreeList) Summary)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.75/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) Y2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))))
% 6.75/7.06 (assert (forall ((U tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X2) Y2)) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.75/7.06 (assert (forall ((U tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X2) Y2)) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) Y2)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.75/7.06 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (not (= Y2 _let_1)))) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r X2) Xa2) Y2) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B2))) (not (= Y2 (@ (@ tptp.plus_plus_nat _let_1) (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) _let_2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) _let_2) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (not (= Y2 (@ (@ tptp.plus_plus_nat _let_2) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ _let_5 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3)))) tptp.one_one_nat)))))))))))))))))))))))))))))
% 6.75/7.06 (assert (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A1) A22) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A3) B2))) (not (= A22 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X6) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 N2) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M4)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X6) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X6) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 (@ tptp.suc N2)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M4)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X6) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X6) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M4)) (=> (= M4 N2) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M4)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3)))) (=> (=> _let_1 (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X6) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma2) N2))) (forall ((X6 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X6) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X6) N2))) (and (@ (@ tptp.ord_less_nat Mi2) X6) (@ (@ tptp.ord_less_eq_nat X6) Ma2))))))))))))))))))))))) (not (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X6) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M4)) (=> (= M4 (@ tptp.suc N2)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M4)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3)))) (=> (=> _let_1 (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X6) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma2) N2))) (forall ((X6 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X6) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X6) N2))) (and (@ (@ tptp.ord_less_nat Mi2) X6) (@ (@ tptp.ord_less_eq_nat X6) Ma2)))))))))))))))))))))))))))))))
% 6.75/7.07 (assert (= tptp.vEBT_invar_vebt (lambda ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (or (and (exists ((A4 Bool) (B3 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A4) B3))) (= A23 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) N3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) (= A23 (@ (@ tptp.plus_plus_nat N3) N3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X7))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N3))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A23 (@ (@ tptp.plus_plus_nat N3) _let_1)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X7))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N3 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) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) N3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 N3)) (= A23 (@ (@ tptp.plus_plus_nat N3) N3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7)))))) (@ (@ 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))) N3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N3) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N3) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X) N3))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N3 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 N3))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 _let_3)) (= A23 (@ (@ tptp.plus_plus_nat N3) _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 N3))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7)))))) (@ (@ 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 N3))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N3) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N3) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X) N3))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I2) (@ (@ tptp.nth_VEBT_VEBT Ys) I2)))) (= Xs2 Ys)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I2) (@ (@ tptp.nth_o Ys) I2)))) (= Xs2 Ys)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I2) (@ (@ tptp.nth_nat Ys) I2)))) (= Xs2 Ys)))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X7 tptp.vEBT_VEBT)) (@ (@ P I4) X7)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_VEBT_VEBT Xs) I4)))))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X7 Bool)) (@ (@ P I4) X7)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_o Xs) I4)))))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X7 tptp.nat)) (@ (@ P I4) X7)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_nat Xs) I4)))))))))
% 6.75/7.07 (assert (= (lambda ((Y5 tptp.list_VEBT_VEBT) (Z4 tptp.list_VEBT_VEBT)) (= Y5 Z4)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I4) (@ (@ tptp.nth_VEBT_VEBT Ys3) I4))))))))
% 6.75/7.07 (assert (= (lambda ((Y5 tptp.list_o) (Z4 tptp.list_o)) (= Y5 Z4)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I4) (@ (@ tptp.nth_o Ys3) I4))))))))
% 6.75/7.07 (assert (= (lambda ((Y5 tptp.list_nat) (Z4 tptp.list_nat)) (= Y5 Z4)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) (@ (@ tptp.nth_nat Ys3) I4))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_s_u_c_c2 X2) Xa2) Y2) (=> (=> (exists ((Uu2 Bool) (B2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) B2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N2 tptp.nat)) (= Xa2 (@ tptp.suc N2))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (let ((_let_6 (@ tptp.vEBT_vebt_maxt _let_5))) (let ((_let_7 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2)) (not (and (=> _let_7 (= Y2 tptp.one_one_nat)) (=> (not _let_7) (= Y2 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_nat (and (not (= _let_6 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_4)) _let_6))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.vEBT_T_s_u_c_c2 _let_5) _let_4))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_s_u_c_c2 Summary2) _let_3)) tptp.one_one_nat))) tptp.one_one_nat))))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.option_nat)) (let ((_let_1 (not (= Y2 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X2) Xa2) Y2) (=> (forall ((Uu2 Bool) (B2 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uu2) B2)) (=> (= Xa2 tptp.zero_zero_nat) (not (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y2 tptp.none_nat))))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N2 tptp.nat)) (= Xa2 (@ tptp.suc N2))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_11 (= Y2 (@ tptp.some_nat Mi2))) (=> (not _let_11) (= Y2 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X2) Xa2) Y2) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B2))) _let_1) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ tptp.ord_less_nat Xa2))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (not (= Y2 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_3 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi2) Xa2) (@ _let_3 Ma2))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) tptp.zero_zero_nat)) tptp.zero_zero_nat))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ tptp.ord_less_nat X2))) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= X2 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X2 Ma)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_4 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma) X2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi) X2) (@ _let_4 Ma))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) tptp.zero_zero_nat)) tptp.zero_zero_nat)))))))))))))
% 6.75/7.07 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_s_u_c_c X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B2))) (=> (= X2 _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y2 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (= Xa2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat _let_3)))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_8 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_3))))) (let ((_let_9 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_10 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_11 (@ _let_7 _let_5))) (let ((_let_12 (@ tptp.vEBT_vebt_maxt _let_11))) (=> (= X2 _let_2) (=> (= Y2 (@ _let_9 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_3)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.plus_plus_nat (@ _let_9 (@ tptp.vEBT_T_m_a_x_t _let_11))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ (@ tptp.if_nat (and (not (= _let_12 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_10)) _let_12))) (@ _let_8 (@ (@ tptp.vEBT_T_s_u_c_c _let_11) _let_10))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_9 (@ (@ tptp.vEBT_T_s_u_c_c Summary2) _let_5))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_6 tptp.none_nat)) tptp.one_one_nat) (@ _let_8 (@ tptp.vEBT_T_m_i_n_t (@ _let_7 (@ tptp.the_nat _let_6)))))))))) tptp.one_one_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B2))) (=> (= X2 _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y2 tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (= Xa2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X2 _let_2) (=> (and (=> _let_12 (= Y2 (@ tptp.some_nat Mi2))) (=> (not _let_12) (= Y2 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_succ _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_mint (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= X2 _let_2) (=> (= Xa2 _let_1) (=> (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y2 tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (=> (= Xa2 _let_1) (=> (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y2 tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_mint _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X2 _let_2) (=> (and (=> _let_12 (= Y2 (@ tptp.some_nat Ma2))) (=> (not _let_12) (= Y2 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_maxt (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_s_u_c_c2 X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B2))) (=> (= X2 _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (= Xa2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4))) (let ((_let_7 (@ tptp.vEBT_vebt_maxt _let_6))) (let ((_let_8 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X2 _let_2) (=> (and (=> _let_8 (= Y2 tptp.one_one_nat)) (=> (not _let_8) (= Y2 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_nat (and (not (= _let_7 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_5)) _let_7))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.vEBT_T_s_u_c_c2 _let_6) _let_5))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_s_u_c_c2 Summary2) _let_4)) tptp.one_one_nat))) tptp.one_one_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 6.75/7.07 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 6.75/7.07 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 6.75/7.07 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.divide_divide_int K) L) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.divide_divide_int K) L) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.75/7.07 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 6.75/7.07 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X2) X2))) (= X2 tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ _let_1 K)))))
% 6.75/7.07 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K) L)) L)) tptp.one_one_int))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (A5 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A5) B))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B5 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) B5) (=> (@ (@ tptp.ord_less_eq_int B5) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B5))))))))
% 6.75/7.07 (assert (forall ((I tptp.int) (K tptp.int)) (= (= (@ (@ tptp.divide_divide_int I) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I) (@ (@ tptp.ord_less_int I) K)) (and (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int R) B) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (A5 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A5) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A5) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B5 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) B5) (=> (@ (@ tptp.ord_less_eq_int B5) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B5)) (@ _let_1 B))))))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) L)) (or (= K tptp.zero_zero_int) (= L tptp.zero_zero_int) (and (@ _let_1 K) (@ _let_1 L)) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))))
% 6.75/7.07 (assert (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L) K) (=> (@ _let_1 L) (@ _let_1 (@ (@ tptp.divide_divide_int K) L)))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X2) K)) X2)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((K tptp.int) (I tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K) (= (@ _let_1 (@ (@ tptp.divide_divide_int I) K)) (@ (@ tptp.ord_less_eq_int K) I))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 6.75/7.07 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 6.75/7.07 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.75/7.07 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 6.75/7.07 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 6.75/7.07 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ P M3))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N) (@ P M3))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 6.75/7.07 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)))))
% 6.75/7.07 (assert (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) (@ tptp.suc N)) A))))))
% 6.75/7.07 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) N2)) Y2))))))
% 6.75/7.07 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.vEBT_Leaf A) B)) X2) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X2)) (=> (forall ((Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X2) (=> (not (= X2 (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) N) A)))))))
% 6.75/7.07 (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 ((X4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real X4) N) A) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.power_power_real Y4) N) A)) (= Y4 X4)))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int B) A))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 Bool)) (let ((_let_1 (not Y2))) (=> (= (@ tptp.vEBT_VEBT_minNull X2) Y2) (=> (=> (= X2 (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2))) Y2) (=> (=> (exists ((Uu2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true))) Y2) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) Y2))))))))))
% 6.75/7.07 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X2) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((M tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ tptp.divide_divide_int (@ _let_1 M)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat M) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.75/7.07 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ tptp.vEBT_VEBT_minNull T) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) L)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))))
% 6.75/7.07 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 T) X2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_1) (=> (= Y2 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ tptp.numeral_numeral_nat _let_3))) (let ((_let_5 (@ (@ tptp.divide_divide_nat _let_1) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_5))) (let ((_let_7 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_2) (=> (= Y2 (@ (@ tptp.plus_plus_nat _let_4) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_3)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ _let_7 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_5)))) tptp.one_one_nat))))))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ tptp.ord_less_nat Xa2))) (=> (= X2 _let_2) (=> (= Y2 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_5 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi2) Xa2) (@ _let_5 Ma2))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) tptp.zero_zero_nat)) tptp.zero_zero_nat))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t X2) Xa2) Y2) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B2))) (not (= Y2 (@ _let_2 (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))))) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) _let_1) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) _let_1) (=> (=> (exists ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2))) (not (= Y2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) Mi2) Xa2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_5))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (= Y2 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_1))))) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_6) (@ (@ tptp.vEBT_VEBT_low _let_4) _let_3))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_6))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_6)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t Summary2) _let_5)) tptp.one_one_nat))) tptp.one_one_nat))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)) Mi) X2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_5))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X2) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_1))))) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X2 Mi) (= X2 Ma))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_6) (@ (@ tptp.vEBT_VEBT_low _let_4) _let_3))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_6))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_6)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t Summary) _let_5)) tptp.one_one_nat))) tptp.one_one_nat)))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X2 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_1) (=> (= Y2 (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B2) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X2 _let_2) (=> (= Y2 (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (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 TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 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 TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N) K)) (@ _let_1 K)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))))
% 6.75/7.07 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (and (= M tptp.one_one_int) (= N tptp.one_one_int))))))
% 6.75/7.07 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.75/7.07 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.75/7.07 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_2 Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ _let_1 R) (=> (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_1 Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ (@ tptp.ord_less_int R) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (Q2 tptp.int) (R tptp.int) (B5 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B5) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (@ (@ tptp.ord_less_eq_int B5) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (Q2 tptp.int) (R tptp.int) (B5 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 B5) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B5) (=> (@ _let_1 R) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (@ (@ tptp.ord_less_eq_int B5) B) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))))
% 6.75/7.07 (assert (forall ((B5 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 B5) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (@ _let_1 Q5)))))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))))
% 6.75/7.07 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_int I2) K) (=> (@ P I2) (@ P (@ (@ tptp.minus_minus_int I2) tptp.one_one_int))))) (@ P I))))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))))
% 6.75/7.07 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I2) (=> (@ P I2) (@ P (@ (@ tptp.plus_plus_int I2) tptp.one_one_int))))) (@ P I))))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))))
% 6.75/7.07 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 6.75/7.07 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_T_m_i_n_N_u_l_l T)) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((Uu Bool)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf Uu) true)) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((Uv Bool)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf true) Uv)) tptp.one_one_nat)))
% 6.75/7.07 (assert (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf false) false)) tptp.one_one_nat))
% 6.75/7.07 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy)) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (=> (= (@ tptp.vEBT_T_m_i_n_N_u_l_l X2) Y2) (=> (=> (= X2 (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2))) _let_1) (=> (=> (exists ((Uu2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true))) _let_1) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) _let_1))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X2 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_1) (=> (= Y2 (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B2) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) 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 TreeList2)))) (=> (= X2 _let_2) (=> (= Y2 (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_1) (=> (= Y2 (@ _let_2 (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat _let_3)))) (let ((_let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_4))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (=> (= Y2 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_3))))) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_4))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_7))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t Summary2) _let_6)) tptp.one_one_nat))) tptp.one_one_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (=> (= X2 _let_1) (=> (= Y2 (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y2 (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y2 (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 X2) Xa2) Y2) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B2))) _let_1) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) _let_1) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) _let_1) (=> (=> (exists ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) Mi2) Xa2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2)) (not (= Y2 (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 _let_5) (@ (@ tptp.vEBT_VEBT_low _let_3) _let_2))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_5)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 Summary2) _let_4)) tptp.one_one_nat))) tptp.one_one_nat)))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 6.75/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.set_or5403411693681687835d_enat A) B) tptp.bot_bo7653980558646680370d_enat))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat))))
% 6.75/7.07 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real))))
% 6.75/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D2 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C) D2)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ (@ tptp.ord_less_eq_set_nat C) A) (@ (@ tptp.ord_less_eq_set_nat B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D2)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D2)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D2)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D2)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D2)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (= (= (@ (@ tptp.set_or5403411693681687835d_enat A) B) tptp.bot_bo7653980558646680370d_enat) (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat A) B) tptp.bot_bot_set_set_nat) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.75/7.07 (assert (forall ((I tptp.set_nat_rat) (L tptp.set_nat_rat) (U tptp.set_nat_rat)) (= (@ (@ tptp.member_set_nat_rat I) (@ (@ tptp.set_or5795412311047298440at_rat L) U)) (and (@ (@ tptp.ord_le2679597024174929757at_rat L) I) (@ (@ tptp.ord_le2679597024174929757at_rat I) U)))))
% 6.75/7.07 (assert (forall ((I tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ (@ tptp.set_or4548717258645045905et_nat L) U)) (and (@ (@ tptp.ord_less_eq_set_nat L) I) (@ (@ tptp.ord_less_eq_set_nat I) U)))))
% 6.75/7.07 (assert (forall ((I tptp.rat) (L tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I) (@ (@ tptp.set_or633870826150836451st_rat L) U)) (and (@ (@ tptp.ord_less_eq_rat L) I) (@ (@ tptp.ord_less_eq_rat I) U)))))
% 6.75/7.07 (assert (forall ((I tptp.num) (L tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I) (@ (@ tptp.set_or7049704709247886629st_num L) U)) (and (@ (@ tptp.ord_less_eq_num L) I) (@ (@ tptp.ord_less_eq_num I) U)))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I) (@ (@ tptp.ord_less_eq_nat I) U)))))
% 6.75/7.07 (assert (forall ((I tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I) (@ (@ tptp.ord_less_eq_int I) U)))))
% 6.75/7.07 (assert (forall ((I tptp.real) (L tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (and (@ (@ tptp.ord_less_eq_real L) I) (@ (@ tptp.ord_less_eq_real I) U)))))
% 6.75/7.07 (assert (forall ((L tptp.set_nat) (H2 tptp.set_nat) (L3 tptp.set_nat) (H3 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat L) H2) (@ (@ tptp.set_or4548717258645045905et_nat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_nat L) H2)) (not (@ (@ tptp.ord_less_eq_set_nat L3) H3)))))))
% 6.75/7.07 (assert (forall ((L tptp.rat) (H2 tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L) H2) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_rat L) H2)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))))
% 6.75/7.07 (assert (forall ((L tptp.num) (H2 tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L) H2) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_num L) H2)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))))
% 6.75/7.07 (assert (forall ((L tptp.nat) (H2 tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H2) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_nat L) H2)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))))
% 6.75/7.07 (assert (forall ((L tptp.int) (H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H2) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_int L) H2)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))))
% 6.75/7.07 (assert (forall ((L tptp.real) (H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L) H2) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_real L) H2)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))))
% 6.75/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (= (= tptp.bot_bo7653980558646680370d_enat (@ (@ tptp.set_or5403411693681687835d_enat A) B)) (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.75/7.07 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ tptp.vEBT_Leaf A) B)) X2) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat Bool)) (X2 tptp.nat) (M7 tptp.nat)) (=> (@ P X2) (=> (forall ((X4 tptp.nat)) (=> (@ P X4) (@ (@ tptp.ord_less_eq_nat X4) M7))) (not (forall ((M4 tptp.nat)) (=> (@ P M4) (not (forall ((X6 tptp.nat)) (=> (@ P X6) (@ (@ tptp.ord_less_eq_nat X6) M4)))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.produc3368934014287244435at_num)) (not (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A3 tptp.nat) (B2 tptp.nat) (Acc tptp.num)) (not (= X2 (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A3) (@ (@ tptp.product_Pair_nat_num B2) Acc)))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B2 tptp.nat) (Acc tptp.nat)) (not (= X2 (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A3) (@ (@ tptp.product_Pair_nat_nat B2) Acc)))))))))
% 6.75/7.07 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S)) X2) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S)) X2) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V))) TreeList) Summary)) X2) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 T) Y2)) tptp.one_one_nat)))))
% 6.75/7.07 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ tptp.vEBT_VEBT_minNull T) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 T) L)) tptp.one_one_nat)))))
% 6.75/7.07 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 T) X2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 6.75/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (= (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_nat B) D2) (or (@ (@ tptp.ord_less_set_nat C) A) (@ (@ tptp.ord_less_set_nat B) D2)))) (@ _let_1 D2))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) D2) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B) D2)))) (@ _let_1 D2))))))
% 6.75/7.07 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_num B) D2) (or (@ (@ tptp.ord_less_num C) A) (@ (@ tptp.ord_less_num B) D2)))) (@ _let_1 D2))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) D2) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B) D2)))) (@ _let_1 D2))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) D2) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B) D2)))) (@ _let_1 D2))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) D2) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B) D2)))) (@ _let_1 D2))))))
% 6.75/7.07 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)) Mi) X2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_4))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X2 Mi) (= X2 Ma))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 _let_5) (@ (@ tptp.vEBT_VEBT_low _let_3) _let_2))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_5)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 Summary) _let_4)) tptp.one_one_nat))) tptp.one_one_nat)))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) Mi2) Xa2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_5))) (=> (= X2 _let_2) (=> (= Y2 (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 _let_6) (@ (@ tptp.vEBT_VEBT_low _let_4) _let_3))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_6)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 Summary2) _let_5)) tptp.one_one_nat))) tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa))))))) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D4))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P5 X4) (@ P5 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (= (exists ((X7 tptp.int)) (@ P X7)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P5 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) B4) (@ P (@ (@ tptp.plus_plus_int Y) X))))))))))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa))))))) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D4))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P5 X4) (@ P5 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (= (exists ((X7 tptp.int)) (@ P X7)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P5 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) A2) (@ P (@ (@ tptp.minus_minus_int Y) X))))))))))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X6 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X6) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X6) D4)) T)))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B4) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X6) (@ _let_1 (@ (@ tptp.minus_minus_int X6) D4))))))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X6 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X6) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X6) D4)) T))))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X6) (@ _let_1 (@ (@ tptp.plus_plus_int X6) D4)))))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B4) (forall ((X6 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X6 T) (= (@ (@ tptp.minus_minus_int X6) D4) T))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X6) (= (and (@ P X6) (@ Q X6)) (and (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X6) (= (and (@ P X6) (@ Q X6)) (and (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X6) (= (and (@ P X6) (@ Q X6)) (and (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (= (and (@ P X6) (@ Q X6)) (and (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X6) (= (and (@ P X6) (@ Q X6)) (and (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X6) (= (or (@ P X6) (@ Q X6)) (or (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X6) (= (or (@ P X6) (@ Q X6)) (or (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X6) (= (or (@ P X6) (@ Q X6)) (or (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (= (or (@ P X6) (@ Q X6)) (or (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X6) (= (or (@ P X6) (@ Q X6)) (or (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X6) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X6) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X6) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X6) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X6) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X6) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X6) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X6) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X6) (not (@ (@ tptp.ord_less_real X6) T)))))))
% 6.75/7.07 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X6) (not (@ (@ tptp.ord_less_rat X6) T)))))))
% 6.75/7.07 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X6) (not (@ (@ tptp.ord_less_num X6) T)))))))
% 6.75/7.07 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (not (@ (@ tptp.ord_less_nat X6) T)))))))
% 6.75/7.07 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X6) (not (@ (@ tptp.ord_less_int X6) T)))))))
% 6.75/7.07 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X6) (@ (@ tptp.ord_less_real T) X6))))))
% 6.75/7.07 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X6) (@ (@ tptp.ord_less_rat T) X6))))))
% 6.75/7.07 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X6) (@ (@ tptp.ord_less_num T) X6))))))
% 6.75/7.07 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (@ (@ tptp.ord_less_nat T) X6))))))
% 6.75/7.07 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X6) (@ (@ tptp.ord_less_int T) X6))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Z3) (= (and (@ P X6) (@ Q X6)) (and (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z3) (= (and (@ P X6) (@ Q X6)) (and (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z3) (= (and (@ P X6) (@ Q X6)) (and (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (= (and (@ P X6) (@ Q X6)) (and (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z3) (= (and (@ P X6) (@ Q X6)) (and (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Z3) (= (or (@ P X6) (@ Q X6)) (or (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z3) (= (or (@ P X6) (@ Q X6)) (or (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z3) (= (or (@ P X6) (@ Q X6)) (or (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (= (or (@ P X6) (@ Q X6)) (or (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z3) (= (or (@ P X6) (@ Q X6)) (or (@ P5 X6) (@ Q6 X6))))))))))
% 6.75/7.07 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Z3) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z3) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z3) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z3) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Z3) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z3) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z3) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z3) (not (= X6 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X6))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X6))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X6))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X6))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X6))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.75/7.07 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Z3) (not (@ (@ tptp.ord_less_real T) X6)))))))
% 6.75/7.07 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z3) (not (@ (@ tptp.ord_less_rat T) X6)))))))
% 6.75/7.07 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z3) (not (@ (@ tptp.ord_less_num T) X6)))))))
% 6.75/7.07 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (not (@ (@ tptp.ord_less_nat T) X6)))))))
% 6.75/7.07 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z3) (not (@ (@ tptp.ord_less_int T) X6)))))))
% 6.75/7.07 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Z3) (not (@ (@ tptp.ord_less_eq_real T) X6)))))))
% 6.75/7.07 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z3) (not (@ (@ tptp.ord_less_eq_rat T) X6)))))))
% 6.75/7.07 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z3) (not (@ (@ tptp.ord_less_eq_num T) X6)))))))
% 6.75/7.07 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (not (@ (@ tptp.ord_less_eq_nat T) X6)))))))
% 6.75/7.07 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z3) (not (@ (@ tptp.ord_less_eq_int T) X6)))))))
% 6.75/7.07 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Z3) (@ (@ tptp.ord_less_eq_real X6) T))))))
% 6.75/7.07 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z3) (@ (@ tptp.ord_less_eq_rat X6) T))))))
% 6.75/7.07 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z3) (@ (@ tptp.ord_less_eq_num X6) T))))))
% 6.75/7.07 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (@ (@ tptp.ord_less_eq_nat X6) T))))))
% 6.75/7.07 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z3) (@ (@ tptp.ord_less_eq_int X6) T))))))
% 6.75/7.07 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X6) (@ (@ tptp.ord_less_eq_real T) X6))))))
% 6.75/7.07 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X6) (@ (@ tptp.ord_less_eq_rat T) X6))))))
% 6.75/7.07 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X6) (@ (@ tptp.ord_less_eq_num T) X6))))))
% 6.75/7.07 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (@ (@ tptp.ord_less_eq_nat T) X6))))))
% 6.75/7.07 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X6) (@ (@ tptp.ord_less_eq_int T) X6))))))
% 6.75/7.07 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X6) (not (@ (@ tptp.ord_less_eq_real X6) T)))))))
% 6.75/7.07 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X6) (not (@ (@ tptp.ord_less_eq_rat X6) T)))))))
% 6.75/7.07 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X6) (not (@ (@ tptp.ord_less_eq_num X6) T)))))))
% 6.75/7.07 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (not (@ (@ tptp.ord_less_eq_nat X6) T)))))))
% 6.75/7.07 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X6) (not (@ (@ tptp.ord_less_eq_int X6) T)))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.complex Bool)) (D4 tptp.complex) (Q (-> tptp.complex Bool))) (=> (forall ((X4 tptp.complex) (K3 tptp.complex)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.times_times_complex K3) D4))))) (=> (forall ((X4 tptp.complex) (K3 tptp.complex)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.times_times_complex K3) D4))))) (forall ((X6 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex X6) (@ (@ tptp.times_times_complex K4) D4)))) (= (or (@ P X6) (@ Q X6)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K3) D4))))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K3) D4))))) (forall ((X6 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X6) (@ (@ tptp.times_times_real K4) D4)))) (= (or (@ P X6) (@ Q X6)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D4))))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D4))))) (forall ((X6 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K4) D4)))) (= (or (@ P X6) (@ Q X6)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (forall ((X6 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K4) D4)))) (= (or (@ P X6) (@ Q X6)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.complex Bool)) (D4 tptp.complex) (Q (-> tptp.complex Bool))) (=> (forall ((X4 tptp.complex) (K3 tptp.complex)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.times_times_complex K3) D4))))) (=> (forall ((X4 tptp.complex) (K3 tptp.complex)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.times_times_complex K3) D4))))) (forall ((X6 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex X6) (@ (@ tptp.times_times_complex K4) D4)))) (= (and (@ P X6) (@ Q X6)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K3) D4))))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K3) D4))))) (forall ((X6 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X6) (@ (@ tptp.times_times_real K4) D4)))) (= (and (@ P X6) (@ Q X6)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D4))))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D4))))) (forall ((X6 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K4) D4)))) (= (and (@ P X6) (@ Q X6)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (forall ((X6 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K4) D4)))) (= (and (@ P X6) (@ Q X6)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (P5 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P5 X4) (@ P5 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D2))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((X_12 tptp.int)) (@ P5 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P1 X4) (@ P1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D2))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P1 X4))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X6 tptp.int)) (=> (@ P X6) (@ P (@ (@ tptp.plus_plus_int X6) (@ (@ tptp.times_times_int K) D2))))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X6 tptp.int)) (=> (@ P X6) (@ P (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K) D2))))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D2))))) (= (exists ((X7 tptp.int)) (@ P X7)) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D2)) (@ P X))))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X6) (@ _let_1 (@ (@ tptp.plus_plus_int X6) D4)))))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X6 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X6) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X6) D4)) T))))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X6 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X6 T)) (not (= (@ (@ tptp.plus_plus_int X6) D4) T)))))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X6 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X6 T) (= (@ (@ tptp.plus_plus_int X6) D4) T))))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B4) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X6) (@ _let_1 (@ (@ tptp.minus_minus_int X6) D4))))))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X6 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X6) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X6) D4)) T)))))))
% 6.75/7.07 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B4) (forall ((X6 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X6 T)) (not (= (@ (@ tptp.minus_minus_int X6) D4) T)))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (not (= A2 B4)) (@ (@ tptp.ord_less_set_nat A2) B4)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int tptp.zero_zero_nat) A) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat tptp.zero_zero_nat) A) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A3 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B2) (=> (@ (@ P B2) C2) (=> (@ (@ tptp.ord_less_eq_real A3) B2) (=> (@ (@ tptp.ord_less_eq_real B2) C2) (@ _let_1 C2))))))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((A3 tptp.real) (B2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A3) X4) (@ (@ tptp.ord_less_eq_real X4) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B2) A3)) D5)) (@ (@ P A3) B2)))))))) (@ (@ P A) B))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y2) Z)) (@ (@ tptp.ord_less_eq_real X2) Y2)))))
% 6.75/7.07 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y2) Z)) (@ (@ tptp.ord_less_eq_rat X2) Y2)))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X2) Z)) (@ (@ tptp.times_times_int Y2) Z)) (@ (@ tptp.ord_less_eq_int X2) Y2)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N) K)) (@ _let_1 K)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M)) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 6.75/7.07 (assert (forall ((A2 tptp.set_option_nat) (B4 tptp.set_option_nat) (C tptp.option_nat)) (let ((_let_1 (@ tptp.member_option_nat C))) (=> (@ (@ tptp.ord_le1792839605950587050on_nat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (B4 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_set_real A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_set_nat_rat) (B4 tptp.set_set_nat_rat) (C tptp.set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat C))) (=> (@ (@ tptp.ord_le1311537459589289991at_rat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_option_nat) (B4 tptp.set_option_nat)) (=> (@ (@ tptp.ord_le1792839605950587050on_nat A2) B4) (exists ((B2 tptp.option_nat)) (@ (@ tptp.member_option_nat B2) (@ (@ tptp.minus_5999362281193037231on_nat B4) A2))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (B4 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B4) (exists ((B2 tptp.real)) (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_set_nat_rat) (B4 tptp.set_set_nat_rat)) (=> (@ (@ tptp.ord_le1311537459589289991at_rat A2) B4) (exists ((B2 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat B2) (@ (@ tptp.minus_1626877696091177228at_rat B4) A2))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B4) (exists ((B2 tptp.nat)) (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B4) A2))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B4) (exists ((B2 tptp.int)) (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A2))))))
% 6.75/7.07 (assert (= tptp.ord_le1792839605950587050on_nat (lambda ((A6 tptp.set_option_nat) (B6 tptp.set_option_nat)) (@ (@ tptp.ord_le1154456971122042459_nat_o (lambda ((X tptp.option_nat)) (@ (@ tptp.member_option_nat X) A6))) (lambda ((X tptp.option_nat)) (@ (@ tptp.member_option_nat X) B6))))))
% 6.75/7.07 (assert (= tptp.ord_less_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ (@ tptp.ord_less_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B6))))))
% 6.75/7.07 (assert (= tptp.ord_le1311537459589289991at_rat (lambda ((A6 tptp.set_set_nat_rat) (B6 tptp.set_set_nat_rat)) (@ (@ tptp.ord_le6823063569548456766_rat_o (lambda ((X tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X) A6))) (lambda ((X tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X) B6))))))
% 6.75/7.07 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B6))))))
% 6.75/7.07 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B6))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A2) tptp.bot_bot_set_nat))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A2) tptp.bot_bot_set_int))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat)) (not (@ (@ tptp.ord_le2529575680413868914d_enat A2) tptp.bot_bo7653980558646680370d_enat))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B4) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (@ (@ tptp.ord_less_eq_set_nat B4) A2))))))
% 6.75/7.07 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B6) (not (= A6 B6))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B4) (@ (@ tptp.ord_less_eq_set_nat A2) B4))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A2))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C4) (@ _let_1 C4))))))
% 6.75/7.07 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B6) (not (@ (@ tptp.ord_less_eq_set_nat B6) A6))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (@ (@ tptp.ord_less_set_nat B4) C4) (@ (@ tptp.ord_less_set_nat A2) C4)))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A6) B6) (= A6 B6)))))
% 6.75/7.07 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N3 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M3) N3)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.unique5026877609467782581ep_nat N3) (@ (@ tptp.unique5055182867167087721od_nat M3) (@ tptp.bit0 N3)))))))
% 6.75/7.07 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N3 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M3) N3)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.unique5024387138958732305ep_int N3) (@ (@ tptp.unique5052692396658037445od_int M3) (@ tptp.bit0 N3)))))))
% 6.75/7.07 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N3 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M3) N3)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.unique4921790084139445826nteger N3) (@ (@ tptp.unique3479559517661332726nteger M3) (@ tptp.bit0 N3)))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y2) Z)) (@ (@ tptp.ord_less_real X2) Y2)))))
% 6.75/7.07 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y2) Z)) (@ (@ tptp.ord_less_rat X2) Y2)))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X2) Z)) (@ (@ tptp.times_times_int Y2) Z)) (@ (@ tptp.ord_less_int X2) Y2)))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))))
% 6.75/7.07 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_rat X2) Y2))))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_int X2) Y2))))))
% 6.75/7.07 (assert (forall ((Q2 tptp.nat) (R tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R)) (= R tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((Q2 tptp.int) (R tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R)) (= R tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R)) tptp.one_one_int)))))))))
% 6.75/7.07 (assert (= tptp.vEBT_VEBT_low (lambda ((X tptp.nat) (N3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.75/7.07 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A2) Z) (=> (@ tptp.finite_finite_nat A2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A2) X2) X_1)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (Z tptp.nat) (A2 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A2) Z) (=> (@ tptp.finite_finite_nat B4) (=> (= A2 B4) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A2) X2) X_1))))))))
% 6.75/7.07 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set Xs2) A) X_1))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) Xs2) (@ (@ tptp.ord_less_nat A) X6))))))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set Xs2) A) X_1))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) Xs2) (@ (@ tptp.ord_less_nat X6) A))))))))
% 6.75/7.07 (assert (forall ((X1 tptp.product_prod_nat_nat) (X23 tptp.product_prod_nat_nat) (Y1 tptp.product_prod_nat_nat) (Y22 tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.produc6161850002892822231at_nat X1) X23) (@ (@ tptp.produc6161850002892822231at_nat Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 6.75/7.07 (assert (forall ((X1 tptp.num) (X23 tptp.num) (Y1 tptp.num) (Y22 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num X1) X23) (@ (@ tptp.product_Pair_num_num Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 6.75/7.07 (assert (forall ((X1 tptp.nat) (X23 tptp.num) (Y1 tptp.nat) (Y22 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num X1) X23) (@ (@ tptp.product_Pair_nat_num Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 6.75/7.07 (assert (forall ((X1 tptp.nat) (X23 tptp.nat) (Y1 tptp.nat) (Y22 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X23) (@ (@ tptp.product_Pair_nat_nat Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 6.75/7.07 (assert (forall ((X1 tptp.int) (X23 tptp.int) (Y1 tptp.int) (Y22 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X23) (@ (@ tptp.product_Pair_int_int Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 6.75/7.07 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (A5 tptp.product_prod_nat_nat) (B5 tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.produc6161850002892822231at_nat A) B) (@ (@ tptp.produc6161850002892822231at_nat A5) B5)) (and (= A A5) (= B B5)))))
% 6.75/7.07 (assert (forall ((A tptp.num) (B tptp.num) (A5 tptp.num) (B5 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A5) B5)) (and (= A A5) (= B B5)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.num) (A5 tptp.nat) (B5 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A5) B5)) (and (= A A5) (= B B5)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (A5 tptp.nat) (B5 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A5) B5)) (and (= A A5) (= B B5)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (A5 tptp.int) (B5 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A5) B5)) (and (= A A5) (= B B5)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) B))) (= (@ (@ tptp.modulo_modulo_nat _let_1) B) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (= (@ (@ tptp.modulo_modulo_int _let_1) B) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.75/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.75/7.07 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))) (@ (@ tptp.ord_less_rat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))) (@ (@ tptp.ord_less_real A) B))))
% 6.75/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N) K)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) K)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.75/7.07 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.75/7.07 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.75/7.07 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.75/7.07 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.75/7.07 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ (@ tptp.modulo_modulo_nat M) _let_1)))))
% 6.75/7.07 (assert (forall ((K tptp.num) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 6.75/7.07 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= R R4))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= Q2 Q5))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (A5 tptp.nat) (B tptp.nat) (B5 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A5) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B5) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A5) B5)) C))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B5) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A5) B5)) C))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) B)) C))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) B)) C))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (A5 tptp.nat) (B tptp.nat) (B5 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A5) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B5) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A5) B5)) C))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B5) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A5) B5)) C))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B5) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A5) B5)) C))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N)) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N)) B))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 6.75/7.07 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N6) (@ (@ tptp.ord_less_nat X) M3)))))))
% 6.75/7.07 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N4) (@ (@ tptp.ord_less_nat X4) N))) (@ tptp.finite_finite_nat N4))))
% 6.75/7.07 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N6) (@ (@ tptp.ord_less_eq_nat X) M3)))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ P K2) (@ (@ tptp.ord_less_nat K2) I)))))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ F N2))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) U)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (= (@ tptp.size_size_list_int Xs) N))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (= (@ tptp.size_s3451745648224563538omplex Xs) N))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat) (N tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite1862508098717546133d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs tptp.list_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs)) A2) (= (@ tptp.size_s3941691890525107288d_enat Xs) N))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (= (@ tptp.size_size_list_o Xs) N))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (= (@ tptp.size_size_list_nat Xs) N))))))))
% 6.75/7.07 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R)) (= (@ (@ tptp.divide_divide_int K) L) Q2))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A) B)) A))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A) B)) A))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) B)) B))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) B)) B))))
% 6.75/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) A) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) A) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat tptp.one))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (not (forall ((D3 tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D3)))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C)))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P6 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P6) (=> (@ (@ tptp.ord_less_nat M) P6) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) P6) (=> (@ P N2) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N2)) P6))))) (@ P M)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 6.75/7.07 (assert (forall ((M tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D2) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M (@ (@ tptp.times_times_nat D2) Q3))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 6.75/7.07 (assert (= tptp.modulo_modulo_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M3) N3)) M3) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M3) N3)) N3)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X2) N) (@ (@ tptp.modulo_modulo_nat Y2) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X2) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y2) (@ _let_1 Q22))))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs)) N))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat) (N tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite1862508098717546133d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs tptp.list_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3941691890525107288d_enat Xs)) N))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.modulo_modulo_nat A) B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.modulo_modulo_int A) B) A)))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.75/7.07 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1))))))
% 6.75/7.07 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))))
% 6.75/7.07 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B)) C) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) A)))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) A)))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) A)))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) A)))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.75/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 6.75/7.07 (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))))))))))
% 6.75/7.07 (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))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X2) N) (@ (@ tptp.modulo_modulo_nat Y2) N)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (exists ((Q3 tptp.nat)) (= X2 (@ (@ tptp.plus_plus_nat Y2) (@ (@ tptp.times_times_nat N) Q3))))))))
% 6.75/7.07 (assert (forall ((L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q2) L)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N))) (= (@ _let_1 (@ _let_2 Q2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N)) Q2))) (@ _let_1 N)))))))
% 6.75/7.07 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N3))) (let ((_let_2 (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.75/7.07 (assert (= tptp.modulo_modulo_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.minus_minus_nat M3) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M3) N3)) N3)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.produc859450856879609959at_nat)) (not (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (not (= Y2 (@ (@ tptp.produc6161850002892822231at_nat A3) B2)))))))
% 6.75/7.07 (assert (forall ((Y2 tptp.product_prod_num_num)) (not (forall ((A3 tptp.num) (B2 tptp.num)) (not (= Y2 (@ (@ tptp.product_Pair_num_num A3) B2)))))))
% 6.75/7.07 (assert (forall ((Y2 tptp.product_prod_nat_num)) (not (forall ((A3 tptp.nat) (B2 tptp.num)) (not (= Y2 (@ (@ tptp.product_Pair_nat_num A3) B2)))))))
% 6.75/7.07 (assert (forall ((Y2 tptp.product_prod_nat_nat)) (not (forall ((A3 tptp.nat) (B2 tptp.nat)) (not (= Y2 (@ (@ tptp.product_Pair_nat_nat A3) B2)))))))
% 6.75/7.07 (assert (forall ((Y2 tptp.product_prod_int_int)) (not (forall ((A3 tptp.int) (B2 tptp.int)) (not (= Y2 (@ (@ tptp.product_Pair_int_int A3) B2)))))))
% 6.75/7.07 (assert (forall ((P6 tptp.produc859450856879609959at_nat)) (exists ((X4 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (= P6 (@ (@ tptp.produc6161850002892822231at_nat X4) Y3)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_num_num)) (exists ((X4 tptp.num) (Y3 tptp.num)) (= P6 (@ (@ tptp.product_Pair_num_num X4) Y3)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_nat_num)) (exists ((X4 tptp.nat) (Y3 tptp.num)) (= P6 (@ (@ tptp.product_Pair_nat_num X4) Y3)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_nat_nat)) (exists ((X4 tptp.nat) (Y3 tptp.nat)) (= P6 (@ (@ tptp.product_Pair_nat_nat X4) Y3)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_int_int)) (exists ((X4 tptp.int) (Y3 tptp.int)) (= P6 (@ (@ tptp.product_Pair_int_int X4) Y3)))))
% 6.75/7.07 (assert (forall ((P (-> tptp.produc859450856879609959at_nat Bool)) (P6 tptp.produc859450856879609959at_nat)) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (@ P (@ (@ tptp.produc6161850002892822231at_nat A3) B2))) (@ P P6))))
% 6.75/7.07 (assert (forall ((P (-> tptp.product_prod_num_num Bool)) (P6 tptp.product_prod_num_num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (@ P (@ (@ tptp.product_Pair_num_num A3) B2))) (@ P P6))))
% 6.75/7.07 (assert (forall ((P (-> tptp.product_prod_nat_num Bool)) (P6 tptp.product_prod_nat_num)) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (@ P (@ (@ tptp.product_Pair_nat_num A3) B2))) (@ P P6))))
% 6.75/7.07 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P6 tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A3) B2))) (@ P P6))))
% 6.75/7.07 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P6 tptp.product_prod_int_int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A3) B2))) (@ P P6))))
% 6.75/7.07 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (A5 tptp.product_prod_nat_nat) (B5 tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.produc6161850002892822231at_nat A) B) (@ (@ tptp.produc6161850002892822231at_nat A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 6.75/7.07 (assert (forall ((A tptp.num) (B tptp.num) (A5 tptp.num) (B5 tptp.num)) (=> (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.num) (A5 tptp.nat) (B5 tptp.num)) (=> (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (A5 tptp.nat) (B5 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (A5 tptp.int) (B5 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 6.75/7.07 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P J3))))))))))
% 6.75/7.07 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N3))) (let ((_let_2 (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.75/7.07 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N3))) (let ((_let_2 (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B)) C))) (@ _let_1 B))))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N))) M) tptp.one_one_nat))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.modulo_modulo_nat A) _let_1)) tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.modulo_modulo_int A) _let_1)) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 6.75/7.07 (assert (forall ((Y2 tptp.produc859450856879609959at_nat)) (not (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.nat) (C2 tptp.nat)) (not (= Y2 (@ (@ tptp.produc6161850002892822231at_nat A3) (@ (@ tptp.product_Pair_nat_nat B2) C2))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.produc859450856879609959at_nat Bool)) (X2 tptp.produc859450856879609959at_nat)) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.nat) (C2 tptp.nat)) (@ P (@ (@ tptp.produc6161850002892822231at_nat A3) (@ (@ tptp.product_Pair_nat_nat B2) C2)))) (@ P X2))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))) (= (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q2)) R)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (@ (@ tptp.ord_less_int R) L))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R) (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 6.75/7.07 (assert (forall ((M tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B) (@ _let_1 B)))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B) (@ _let_1 B)))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.modulo_modulo_nat A) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B))))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.modulo_modulo_int A) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B))))))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R)))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.nat) (B4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B4) (=> (@ (@ 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 B4) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B4) N))))))
% 6.75/7.07 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (or (= _let_2 tptp.zero_zero_nat) (= _let_2 tptp.one_one_nat) (= _let_2 (@ tptp.numeral_numeral_nat _let_1)) (= _let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))))))
% 6.75/7.07 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) K))))))
% 6.75/7.07 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat N3) K))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z2 tptp.real)) (= (@ (@ tptp.power_power_real Z2) N) tptp.one_one_real)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N)) N)) (@ (@ tptp.modulo_modulo_nat A2) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.nat) (B4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B4) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ tptp.divide_divide_nat B4) N))))))))
% 6.75/7.07 (assert (forall ((X23 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.bit0 X23) (@ tptp.bit0 Y22)) (= X23 Y22))))
% 6.75/7.07 (assert (forall ((X32 tptp.num) (Y32 tptp.num)) (= (= (@ tptp.bit1 X32) (@ tptp.bit1 Y32)) (= X32 Y32))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A) I4) (@ (@ tptp.ord_less_int I4) B)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N) K)) (@ _let_1 K)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A) I4) (@ (@ tptp.ord_less_eq_int I4) B)))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I4) (@ (@ tptp.ord_less_int I4) B)))))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.modulo_modulo_int K) L) K)))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) K)))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W))))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((M tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M) K)) M))))
% 6.75/7.07 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K) L)) L))))
% 6.75/7.07 (assert (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L))))))
% 6.75/7.07 (assert (forall ((M tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M) D2) tptp.zero_zero_int) (exists ((Q4 tptp.int)) (= M (@ (@ tptp.times_times_int D2) Q4))))))
% 6.75/7.07 (assert (forall ((M tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D2) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M (@ (@ tptp.times_times_int D2) Q3))))))
% 6.75/7.07 (assert (forall ((A2 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (=> (= (@ (@ tptp.modulo_modulo_int A2) N) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B4) N) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ tptp.divide_divide_int B4) N))))))))
% 6.75/7.07 (assert (forall ((M7 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M7) (exists ((N2 tptp.nat)) (forall ((X6 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X6) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X6)) N2)))))))
% 6.75/7.07 (assert (forall ((M7 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M7) (exists ((N2 tptp.nat)) (forall ((X6 tptp.list_o)) (=> (@ (@ tptp.member_list_o X6) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X6)) N2)))))))
% 6.75/7.07 (assert (forall ((M7 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M7) (exists ((N2 tptp.nat)) (forall ((X6 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X6) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X6)) N2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.int) (N tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) N)) N)) (@ (@ tptp.modulo_modulo_int A2) N)))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R)) (= (@ (@ tptp.modulo_modulo_int K) L) R))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ tptp.ord_less_int B))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B))))))
% 6.75/7.07 (assert (forall ((I tptp.int) (K tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I) K) I) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I) (@ (@ tptp.ord_less_int I) K)) (and (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I))))))
% 6.75/7.07 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K) L)))))
% 6.75/7.07 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L)) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (or (= A B) (not (@ (@ tptp.ord_less_eq_num A) B)) (not (@ (@ tptp.ord_less_eq_num B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (@ (@ tptp.ord_less_eq_int A) B)) (not (@ (@ tptp.ord_less_eq_int B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.75/7.07 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.75/7.07 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N3))) (let ((_let_2 (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.75/7.07 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K) L)) (@ (@ tptp.modulo_modulo_int K) L)))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K) L))) (=> (@ (@ 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) L) _let_1))))))
% 6.75/7.07 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L)) L))))))
% 6.75/7.07 (assert (forall ((A2 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B4) (=> (@ (@ 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 B4) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B4) N))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R) (= (@ (@ tptp.modulo_modulo_int A) B) R))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int R) B) (= (@ (@ tptp.modulo_modulo_int A) B) R))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 6.75/7.07 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 6.75/7.07 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 6.75/7.07 (assert (forall ((B5 tptp.real) (A5 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B5) A5)) (@ (@ tptp.ord_less_real A5) B5))))
% 6.75/7.07 (assert (forall ((B5 tptp.rat) (A5 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B5) A5)) (@ (@ tptp.ord_less_rat A5) B5))))
% 6.75/7.07 (assert (forall ((B5 tptp.num) (A5 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B5) A5)) (@ (@ tptp.ord_less_num A5) B5))))
% 6.75/7.07 (assert (forall ((B5 tptp.nat) (A5 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B5) A5)) (@ (@ tptp.ord_less_nat A5) B5))))
% 6.75/7.07 (assert (forall ((B5 tptp.int) (A5 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B5) A5)) (@ (@ tptp.ord_less_int A5) B5))))
% 6.75/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.75/7.07 (assert (forall ((X23 tptp.num)) (not (= tptp.one (@ tptp.bit0 X23)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_real A) X4) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_set_nat_rat) (A tptp.set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat A2) (=> (@ (@ tptp.member_set_nat_rat A) A2) (exists ((X4 tptp.set_nat_rat)) (and (@ (@ tptp.member_set_nat_rat X4) A2) (@ (@ tptp.ord_le2679597024174929757at_rat A) X4) (forall ((Xa tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat Xa) A2) (=> (@ (@ tptp.ord_le2679597024174929757at_rat X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_le2932123472753598470d_enat A) X4) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A2) (@ (@ tptp.ord_less_eq_set_nat A) X4) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A2) (=> (@ (@ tptp.member_rat A) A2) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A2) (@ (@ tptp.ord_less_eq_rat A) X4) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A2) (@ (@ tptp.ord_less_eq_num A) X4) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_nat A) X4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_int A) X4) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_real X4) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_set_nat_rat) (A tptp.set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat A2) (=> (@ (@ tptp.member_set_nat_rat A) A2) (exists ((X4 tptp.set_nat_rat)) (and (@ (@ tptp.member_set_nat_rat X4) A2) (@ (@ tptp.ord_le2679597024174929757at_rat X4) A) (forall ((Xa tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat Xa) A2) (=> (@ (@ tptp.ord_le2679597024174929757at_rat Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_le2932123472753598470d_enat X4) A) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A2) (@ (@ tptp.ord_less_eq_set_nat X4) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A2) (=> (@ (@ tptp.member_rat A) A2) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A2) (@ (@ tptp.ord_less_eq_rat X4) A) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A2) (@ (@ tptp.ord_less_eq_num X4) A) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_nat X4) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_int X4) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((X23 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X23) (@ tptp.bit1 X32)))))
% 6.75/7.07 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((B7 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B7) A7) (@ P B7))) (@ P A7)))) (@ P A2)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((B7 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B7) A7) (@ P B7))) (@ P A7)))) (@ P A2)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (forall ((B7 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex B7) A7) (@ P B7))) (@ P A7)))) (@ P A2)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((A7 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A7) (=> (forall ((B7 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat B7) A7) (@ P B7))) (@ P A7)))) (@ P A2)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.modulo_modulo_int (@ _let_2 (@ _let_1 B))) (@ _let_1 A)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B) A)))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X4) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X4) Xa) (= X4 Xa))))))))))
% 6.75/7.07 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.75/7.07 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs2) Ys)) N) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4439495888332055232nt_int (@ (@ tptp.product_int_int Xs2) Ys)) N) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr8326237132889035090at_num (@ (@ tptp.product_nat_num Xs2) Ys)) N) (@ (@ tptp.product_Pair_nat_num (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) N) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.complex)) (Y2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y2 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y2 I4)) tptp.one_one_complex))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.complex)) (Y2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y2 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y2 I4)) tptp.one_one_complex))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.complex)) (Y2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y2 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y2 I4)) tptp.one_one_complex))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.complex)) (Y2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y2 I4) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y2 I4)) tptp.one_one_complex))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_Extended_enat) (X2 (-> tptp.extended_enat tptp.complex)) (Y2 (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ Y2 I4) tptp.one_one_complex)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y2 I4)) tptp.one_one_complex))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.real)) (Y2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y2 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y2 I4)) tptp.one_one_real))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.real)) (Y2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y2 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y2 I4)) tptp.one_one_real))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.real)) (Y2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y2 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y2 I4)) tptp.one_one_real))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.real)) (Y2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y2 I4) tptp.one_one_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y2 I4)) tptp.one_one_real))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_Extended_enat) (X2 (-> tptp.extended_enat tptp.real)) (Y2 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ Y2 I4) tptp.one_one_real)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y2 I4)) tptp.one_one_real))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.complex)) (Y2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_complex))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.complex)) (Y2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_complex))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.complex)) (Y2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_complex))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.complex)) (Y2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_complex))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_Extended_enat) (X2 (-> tptp.extended_enat tptp.complex)) (Y2 (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_complex)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_complex))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.real)) (Y2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_real))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.real)) (Y2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_real))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.real)) (Y2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_real))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.real)) (Y2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_real))))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_Extended_enat) (X2 (-> tptp.extended_enat tptp.real)) (Y2 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_real)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_real))))))))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.75/7.07 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_height (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.75/7.07 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.75/7.07 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.75/7.07 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (= (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.product_nat_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 6.75/7.07 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))
% 6.75/7.07 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))
% 6.75/7.07 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))
% 6.75/7.07 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (forall ((A3 Bool) (B2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList2) Summary2))))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) tptp.one_one_int)) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X2 tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat X2) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X2 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X2) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat Mi) X2) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X2 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X2) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X2) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M4 tptp.nat)) (@ (@ P M4) tptp.zero_zero_nat)) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ P N2) (@ (@ tptp.modulo_modulo_nat M4) N2)) (@ (@ P M4) N2)))) (@ (@ P M) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N)) K) L) (@ (@ 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)) L)))))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.75/7.07 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.75/7.07 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.75/7.07 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_o) (I tptp.nat) (X2 Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs2) I) X2)) (@ tptp.size_size_list_o Xs2))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X2)) (@ tptp.size_size_list_nat Xs2))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs2) I) (@ (@ tptp.nth_nat Xs2) I)) Xs2)))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) (@ (@ tptp.nth_VEBT_VEBT Xs2) I)) Xs2)))
% 6.75/7.07 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (not (= I J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X2)) J) (@ (@ tptp.nth_nat Xs2) J)))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (not (= I J)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2)) J) (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)))
% 6.75/7.07 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.75/7.07 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.75/7.07 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (@ tptp.numera1916890842035813515d_enat V))) (let ((_let_3 (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U))) (let ((_let_2 (@ tptp.numeral_numeral_nat V))) (let ((_let_3 (@ (@ tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 6.75/7.07 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 6.75/7.07 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 6.75/7.07 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 6.75/7.07 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.75/7.07 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 6.75/7.07 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 6.75/7.07 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 6.75/7.07 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 6.75/7.07 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 6.75/7.07 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) I) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2) Xs2))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_o) (I tptp.nat) (X2 Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) I) (= (@ (@ (@ tptp.list_update_o Xs2) I) X2) Xs2))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) I) (= (@ (@ (@ tptp.list_update_nat Xs2) I) X2) Xs2))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N) K) L)) (@ _let_1 L)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N) K) L)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2)) I) X2))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I) X2)) I) X2))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X2)) I) X2))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_VEBT_VEBT2 Xs2))))))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_o2 Xs2))))))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_nat2 Xs2))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X2))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y2) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y2)) (@ _let_1 Z))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X2))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y2) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y2)) (@ _let_1 Z))))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y2) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y2)) (@ _let_1 Z))))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X2))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y2) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y2)) (@ _let_1 Z))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X2) Y2)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X2) Z)) (@ (@ tptp.plus_plus_real Y2) Z)))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X2) Y2)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X2) Z)) (@ (@ tptp.plus_plus_rat Y2) Z)))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X2) Y2)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X2) Z)) (@ (@ tptp.plus_plus_nat Y2) Z)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X2) Y2)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X2) Z)) (@ (@ tptp.plus_plus_int Y2) Z)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X2) Y2)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X2) Z)) (@ (@ tptp.minus_minus_real Y2) Z)))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X2) Y2)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X2) Z)) (@ (@ tptp.minus_minus_rat Y2) Z)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X2) Y2)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X2) Z)) (@ (@ tptp.minus_minus_int Y2) Z)))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q2)) (@ (@ tptp.plus_plus_nat N) Q2)))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 6.75/7.07 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.75/7.07 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A4 tptp.extended_enat) (B3 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A4) B3)) B3) A4))))
% 6.75/7.07 (assert (= tptp.ord_max_set_nat (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A4) B3)) B3) A4))))
% 6.75/7.07 (assert (= tptp.ord_max_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A4) B3)) B3) A4))))
% 6.75/7.07 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B3 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B3)) B3) A4))))
% 6.75/7.07 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B3)) B3) A4))))
% 6.75/7.07 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B3)) B3) A4))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L tptp.int) (R tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L) R)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 L)) R)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N) M)) M) (@ (@ tptp.ord_max_nat N) M))))
% 6.75/7.07 (assert (= tptp.neg_numeral_dbl_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real X) X))))
% 6.75/7.07 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat X) X))))
% 6.75/7.07 (assert (= tptp.neg_numeral_dbl_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) X))))
% 6.75/7.07 (assert (= tptp.neg_nu7009210354673126013omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex X) X))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_option_nat) (X2 tptp.option_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6086282163384603972on_nat Xs2)) (@ (@ tptp.member_option_nat X2) (@ tptp.set_option_nat2 (@ (@ (@ tptp.list_u3411377215356412978on_nat Xs2) N) X2))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N) X2))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_set_nat_rat) (X2 tptp.set_nat_rat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3959913991096427681at_rat Xs2)) (@ (@ tptp.member_set_nat_rat X2) (@ tptp.set_set_nat_rat2 (@ (@ (@ tptp.list_u886106648575569423at_rat Xs2) N) X2))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N) X2))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N) X2))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o X2) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N) X2))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N) X2))))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2) Xs2) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I) X2)))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (= (@ (@ (@ tptp.list_update_o Xs2) I) X2) Xs2) (= (@ (@ tptp.nth_o Xs2) I) X2)))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (= (= (@ (@ (@ tptp.list_update_nat Xs2) I) X2) Xs2) (= (@ (@ tptp.nth_nat Xs2) I) X2)))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (X2 Bool) (J tptp.nat)) (let ((_let_1 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I) X2)) J) (and (=> _let_1 X2) (=> (not _let_1) (@ (@ tptp.nth_o Xs2) J))))))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs2) J)))))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N))) tptp.one_one_complex))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N))) tptp.one_one_real))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.bitM N)) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 N))) tptp.one_one_rat))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ P A3) B2) (@ (@ P B2) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B2))))) (@ (@ P A) B))))))
% 6.75/7.07 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X2) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X2 Mi) (= X2 Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X2) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X2) Xa2) Y2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_2) (not (and (=> _let_4 (= Y2 (@ (@ tptp.vEBT_Leaf true) B2))) (=> (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))) (=> (= X2 _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))) (=> (= X2 _let_1) (not (= Y2 _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2)) (not (= Y2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList2) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (not (= Y2 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_2) (=> (and (=> _let_4 (= Y2 (@ (@ tptp.vEBT_Leaf true) B2))) (=> (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))) (=> (= X2 _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X2 _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (= X2 _let_2) (=> (= Y2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList2) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (=> (= Y2 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.75/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.75/7.07 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.75/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.75/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.75/7.07 (assert (forall ((X2 tptp.extended_enat) (Y2 tptp.extended_enat) (Z tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y2)) Z) (and (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (@ (@ tptp.ord_le72135733267957522d_enat Y2) Z)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X2) Y2)) Z) (and (@ (@ tptp.ord_less_real X2) Z) (@ (@ tptp.ord_less_real Y2) Z)))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X2) Y2)) Z) (and (@ (@ tptp.ord_less_rat X2) Z) (@ (@ tptp.ord_less_rat Y2) Z)))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (Y2 tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X2) Y2)) Z) (and (@ (@ tptp.ord_less_num X2) Z) (@ (@ tptp.ord_less_num Y2) Z)))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X2) Y2)) Z) (and (@ (@ tptp.ord_less_nat X2) Z) (@ (@ tptp.ord_less_nat Y2) Z)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X2) Y2)) Z) (and (@ (@ tptp.ord_less_int X2) Z) (@ (@ tptp.ord_less_int Y2) Z)))))
% 6.75/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.75/7.07 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.75/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.75/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.75/7.07 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (and (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C) A)))))
% 6.75/7.07 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (and (@ (@ tptp.ord_less_eq_num B) A) (@ (@ tptp.ord_less_eq_num C) A)))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C) A)))))
% 6.75/7.07 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)))
% 6.75/7.07 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)))
% 6.75/7.07 (assert (forall ((X2 tptp.product_prod_nat_nat)) (not (forall ((K3 tptp.nat) (M4 tptp.nat)) (not (= X2 (@ (@ tptp.product_Pair_nat_nat K3) M4)))))))
% 6.75/7.07 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (D2 tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat D2) B) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat C) D2)) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (A tptp.rat) (D2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C) D2)) (@ (@ tptp.ord_max_rat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.num) (A tptp.num) (D2 tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C) A) (=> (@ (@ tptp.ord_less_eq_num D2) B) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C) D2)) (@ (@ tptp.ord_max_num A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (D2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D2) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D2)) (@ (@ tptp.ord_max_nat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (D2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D2)) (@ (@ tptp.ord_max_int A) B))))))
% 6.75/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 6.75/7.07 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.75/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.75/7.07 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (not (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C) A)))))))
% 6.75/7.07 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_num B) A) (not (@ (@ tptp.ord_less_eq_num C) A)))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))))
% 6.75/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A)))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A)))))
% 6.75/7.07 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A)))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A)))))
% 6.75/7.07 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B3 tptp.extended_enat) (A4 tptp.extended_enat)) (= A4 (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3)))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (= A4 (@ (@ tptp.ord_max_rat A4) B3)))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A4 tptp.num)) (= A4 (@ (@ tptp.ord_max_num A4) B3)))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (= A4 (@ (@ tptp.ord_max_nat A4) B3)))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A4 tptp.int)) (= A4 (@ (@ tptp.ord_max_int A4) B3)))))
% 6.75/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 6.75/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat B) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 6.75/7.07 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 6.75/7.07 (assert (forall ((Z tptp.extended_enat) (X2 tptp.extended_enat) (Y2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.75/7.07 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.75/7.07 (assert (forall ((Z tptp.num) (X2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.75/7.07 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.75/7.07 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B3 tptp.extended_enat) (A4 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3) A4))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B3) A4))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B3) A4))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B3) A4))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B3) A4))))
% 6.75/7.07 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A4 tptp.extended_enat) (B3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3) B3))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B3) B3))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B3 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B3) B3))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B3) B3))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B3) B3))))
% 6.75/7.07 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.75/7.07 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B3 tptp.extended_enat) (A4 tptp.extended_enat)) (and (= A4 (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3)) (not (= A4 B3))))))
% 6.75/7.07 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A4 tptp.real)) (and (= A4 (@ (@ tptp.ord_max_real A4) B3)) (not (= A4 B3))))))
% 6.75/7.07 (assert (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (and (= A4 (@ (@ tptp.ord_max_rat A4) B3)) (not (= A4 B3))))))
% 6.75/7.07 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A4 tptp.num)) (and (= A4 (@ (@ tptp.ord_max_num A4) B3)) (not (= A4 B3))))))
% 6.75/7.07 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (and (= A4 (@ (@ tptp.ord_max_nat A4) B3)) (not (= A4 B3))))))
% 6.75/7.07 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A4 tptp.int)) (and (= A4 (@ (@ tptp.ord_max_int A4) B3)) (not (= A4 B3))))))
% 6.75/7.07 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (not (@ (@ tptp.ord_le72135733267957522d_enat C) A)))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real B) C)) A) (not (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real C) A)))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C) A)))))))
% 6.75/7.07 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num C) A)))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C) A)))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C) A)))))))
% 6.75/7.07 (assert (forall ((Z tptp.extended_enat) (X2 tptp.extended_enat) (Y2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.75/7.07 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.75/7.07 (assert (forall ((Z tptp.num) (X2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.75/7.07 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.75/7.07 (assert (= tptp.nat_triangle (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N3) (@ tptp.suc N3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))))
% 6.75/7.07 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.nat)) (X23 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X2) (@ tptp.some_P7363390416028606310at_nat X23)) (@ (@ tptp.plus_plus_nat (@ X2 X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((X2 (-> tptp.nat tptp.nat)) (X23 tptp.nat)) (= (@ (@ tptp.size_option_nat X2) (@ tptp.some_nat X23)) (@ (@ tptp.plus_plus_nat (@ X2 X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((X2 (-> tptp.num tptp.nat)) (X23 tptp.num)) (= (@ (@ tptp.size_option_num X2) (@ tptp.some_num X23)) (@ (@ tptp.plus_plus_nat (@ X2 X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.75/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)))
% 6.75/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.75/7.07 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) A)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) A)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) A)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) A)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) A)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex A) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B) A)) (@ (@ tptp.divide_divide_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B) A)) (@ (@ tptp.divide_divide_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_integer B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) (@ (@ tptp.times_3573771949741848930nteger C) A))) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) (@ (@ tptp.times_times_complex C) A))) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) (@ (@ tptp.times_times_real C) A))) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C) A))) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex C) A)) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) A)) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C) A)) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.divide6298287555418463151nteger B) A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B) A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B) A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ _let_1 (@ _let_1 A)) A)))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ _let_1 (@ _let_1 A)) A)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ _let_1 (@ _let_1 A)) A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) tptp.one_one_nat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N)) _let_1)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N))) (@ _let_1 N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N)) (not (@ _let_1 N))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (@ (@ tptp.divide6298287555418463151nteger B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B) A)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (= (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ _let_2 A))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ _let_2 A))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ _let_2 A))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ (@ tptp.divide_divide_nat N) _let_1))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N) _let_1)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N) M)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N) M)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N) M)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) (not (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (not (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (not (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int A) B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (or (@ (@ tptp.ord_less_nat M) N) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_real))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_rat))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) tptp.one_one_Code_integer))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) _let_1)) tptp.one_one_nat))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) _let_1)) tptp.one_one_int))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) tptp.one_one_Code_integer) A)))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_2 (= A tptp.zero_zero_real)))))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_2 (= A tptp.zero_zero_rat)))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_2 (= A tptp.zero_zero_int)))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer)) (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat)) (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int)) (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) C) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) C) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) C) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.75/7.07 (assert (= tptp.dvd_dvd_real (lambda ((A4 tptp.real) (B3 tptp.real)) (=> (= A4 tptp.zero_zero_real) (= B3 tptp.zero_zero_real)))))
% 6.75/7.07 (assert (= tptp.dvd_dvd_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (=> (= A4 tptp.zero_zero_rat) (= B3 tptp.zero_zero_rat)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B8 tptp.nat) (C5 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B8) C5)) (@ (@ tptp.dvd_dvd_nat B8) B) (@ (@ tptp.dvd_dvd_nat C5) C))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B8 tptp.int) (C5 tptp.int)) (and (= A (@ (@ tptp.times_times_int B8) C5)) (@ (@ tptp.dvd_dvd_int B8) B) (@ (@ tptp.dvd_dvd_int C5) C))))))
% 6.75/7.07 (assert (forall ((P6 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P6) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= P6 (@ (@ tptp.times_times_nat X4) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X4) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))))
% 6.75/7.07 (assert (forall ((P6 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P6) (@ (@ tptp.times_times_int A) B)) (not (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= P6 (@ (@ tptp.times_times_int X4) Y3)) (=> (@ (@ tptp.dvd_dvd_int X4) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real B) C))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat B) C))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B) (=> (@ (@ tptp.dvd_dvd_real C) D2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B) (=> (@ (@ tptp.dvd_dvd_rat C) D2) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real A) C))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat A) C))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.75/7.07 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B3 tptp.code_integer) (A4 tptp.code_integer)) (exists ((K2 tptp.code_integer)) (= A4 (@ (@ tptp.times_3573771949741848930nteger B3) K2))))))
% 6.75/7.07 (assert (= tptp.dvd_dvd_real (lambda ((B3 tptp.real) (A4 tptp.real)) (exists ((K2 tptp.real)) (= A4 (@ (@ tptp.times_times_real B3) K2))))))
% 6.75/7.07 (assert (= tptp.dvd_dvd_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (exists ((K2 tptp.rat)) (= A4 (@ (@ tptp.times_times_rat B3) K2))))))
% 6.75/7.07 (assert (= tptp.dvd_dvd_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (exists ((K2 tptp.nat)) (= A4 (@ (@ tptp.times_times_nat B3) K2))))))
% 6.75/7.07 (assert (= tptp.dvd_dvd_int (lambda ((B3 tptp.int) (A4 tptp.int)) (exists ((K2 tptp.int)) (= A4 (@ (@ tptp.times_times_int B3) K2))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (K tptp.code_integer)) (=> (= A (@ (@ tptp.times_3573771949741848930nteger B) K)) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K3 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K3))))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K3 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K3))))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K3 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K3))))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K3))))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K3 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K3))))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ _let_1 tptp.one_one_Code_integer))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer B))) (=> (@ _let_1 tptp.one_one_Code_integer) (@ _let_1 A)))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.75/7.07 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.75/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C)))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C)))))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger C) B)) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int C) B)) (@ _let_1 (@ (@ tptp.minus_minus_int B) C))))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X2))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y2) Z)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X2))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_complex Y2) Z)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X2))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y2) Z)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X2))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y2) Z)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X2))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y2) Z)))))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (= A B)))))))
% 6.75/7.07 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (= A B)))))))
% 6.75/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (= A B)))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (= A B)))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (= A B)))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (= A B)))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 D2)) (@ (@ tptp.divide6298287555418463151nteger B) D2)) (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D2) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D2)) (@ (@ tptp.divide_divide_nat B) D2)) (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D2) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D2)) (@ (@ tptp.divide_divide_int B) D2)) (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X2) Y2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.power_8256067586552552935nteger Y2) N)))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X2) Y2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y2) N)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X2) Y2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y2) N)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X2) Y2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y2) N)))))
% 6.75/7.07 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X2) Y2) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y2) N)))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (X1 tptp.nat) (X23 tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat X1) X23)) (@ (@ F X1) X23))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X1 tptp.nat) (X23 tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X23)) (@ (@ F X1) X23))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (X1 tptp.int) (X23 tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int X1) X23)) (@ (@ F X1) X23))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int Bool)) (X1 tptp.int) (X23 tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int X1) X23)) (@ (@ F X1) X23))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (X1 tptp.int) (X23 tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int X1) X23)) (@ (@ F X1) X23))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((K tptp.code_integer) (M tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N)))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N)))))))
% 6.75/7.07 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N)))))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B)))) (@ (@ tptp.dvd_dvd_int A) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) A)))) (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) B)))) (@ (@ tptp.dvd_dvd_Code_integer A) B))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B)))) (@ (@ tptp.dvd_dvd_nat A) B))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X4) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X4) Y3)))) (= (@ tptp.produc27273713700761075at_nat F) G))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X4) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X4) Y3)))) (= (@ tptp.produc8739625826339149834_nat_o F) G))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (G (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ F X4) Y3) (@ G (@ (@ tptp.product_Pair_int_int X4) Y3)))) (= (@ tptp.produc4245557441103728435nt_int F) G))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int Bool)) (G (-> tptp.product_prod_int_int Bool))) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ F X4) Y3) (@ G (@ (@ tptp.product_Pair_int_int X4) Y3)))) (= (@ tptp.produc4947309494688390418_int_o F) G))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (G (-> tptp.product_prod_int_int tptp.int))) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ F X4) Y3) (@ G (@ (@ tptp.product_Pair_int_int X4) Y3)))) (= (@ tptp.produc8211389475949308722nt_int F) G))))
% 6.75/7.07 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X) Y)) __flatten_var_0))) F)))
% 6.75/7.07 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X) Y)) __flatten_var_0))) F)))
% 6.75/7.07 (assert (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (lambda ((X tptp.int) (Y tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X) Y)))) F)))
% 6.75/7.07 (assert (forall ((F (-> tptp.product_prod_int_int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((X tptp.int) (Y tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X) Y)))) F)))
% 6.75/7.07 (assert (forall ((F (-> tptp.product_prod_int_int tptp.int))) (= (@ tptp.produc8211389475949308722nt_int (lambda ((X tptp.int) (Y tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X) Y)))) F)))
% 6.75/7.07 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc27273713700761075at_nat P) Z)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X4) Y3)) (not (@ Q (@ (@ P X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat Bool) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc8739625826339149834_nat_o P) Z)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X4) Y3)) (not (@ Q (@ (@ P X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Q (-> tptp.product_prod_int_int Bool)) (P (-> tptp.int tptp.int tptp.product_prod_int_int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4245557441103728435nt_int P) Z)) (not (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X4) Y3)) (not (@ Q (@ (@ P X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.int tptp.int Bool)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4947309494688390418_int_o P) Z)) (not (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X4) Y3)) (not (@ Q (@ (@ P X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Q (-> tptp.int Bool)) (P (-> tptp.int tptp.int tptp.int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc8211389475949308722nt_int P) Z)) (not (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X4) Y3)) (not (@ Q (@ (@ P X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) A)))) (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) B)))) (and (@ (@ tptp.dvd_dvd_Code_integer A) B) (not (@ (@ tptp.dvd_dvd_Code_integer B) A))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri6519982836138164636nteger M) A)) (@ _let_1 A)))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int M) A)) (@ _let_1 A)))))
% 6.75/7.07 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.75/7.07 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.75/7.07 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.75/7.07 (assert (forall ((D2 tptp.code_integer) (S tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X6 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D2) (@ (@ tptp.plus_p5714425477246183910nteger X6) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z3) X6) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.real) (S tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X6) S)))) (=> (@ (@ tptp.ord_less_real Z3) X6) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.rat) (S tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X6) S)))) (=> (@ (@ tptp.ord_less_rat Z3) X6) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.nat) (S tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X6) S)))) (=> (@ (@ tptp.ord_less_nat Z3) X6) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (S tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X6) S)))) (=> (@ (@ tptp.ord_less_int Z3) X6) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.code_integer) (S tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X6 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D2) (@ (@ tptp.plus_p5714425477246183910nteger X6) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z3) X6) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.real) (S tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X6) S))))) (=> (@ (@ tptp.ord_less_real Z3) X6) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.rat) (S tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X6) S))))) (=> (@ (@ tptp.ord_less_rat Z3) X6) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.nat) (S tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X6) S))))) (=> (@ (@ tptp.ord_less_nat Z3) X6) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (S tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X6) S))))) (=> (@ (@ tptp.ord_less_int Z3) X6) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.code_integer) (S tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X6 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D2) (@ (@ tptp.plus_p5714425477246183910nteger X6) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X6) Z3) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.real) (S tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X6) S)))) (=> (@ (@ tptp.ord_less_real X6) Z3) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.rat) (S tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X6) S)))) (=> (@ (@ tptp.ord_less_rat X6) Z3) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.nat) (S tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X6) S)))) (=> (@ (@ tptp.ord_less_nat X6) Z3) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (S tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X6) S)))) (=> (@ (@ tptp.ord_less_int X6) Z3) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.code_integer) (S tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X6 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D2) (@ (@ tptp.plus_p5714425477246183910nteger X6) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X6) Z3) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.real) (S tptp.real)) (exists ((Z3 tptp.real)) (forall ((X6 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X6) S))))) (=> (@ (@ tptp.ord_less_real X6) Z3) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.rat) (S tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X6 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X6) S))))) (=> (@ (@ tptp.ord_less_rat X6) Z3) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.nat) (S tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X6) S))))) (=> (@ (@ tptp.ord_less_nat X6) Z3) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (S tptp.int)) (exists ((Z3 tptp.int)) (forall ((X6 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X6) S))))) (=> (@ (@ tptp.ord_less_int X6) Z3) (= _let_1 _let_1)))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 6.75/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B) A) (@ (@ tptp.times_3573771949741848930nteger C) A)) (= B C)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B) A) (@ (@ tptp.times_times_nat C) A)) (= B C)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B) A) (@ (@ tptp.times_times_int C) A)) (= B C)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C)))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger C) B)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer) (and (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int)))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (D2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger C) D2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (D2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D2) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C) D2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D2) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C) D2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger B) C))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C)))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.times_times_nat (@ _let_1 B)) C)))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.times_times_int (@ _let_1 B)) C)))))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) C)) A) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) C)))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B) A)) C)))))
% 6.75/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B) A)) C)))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger C) B)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat C) B)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int C) B)) (@ _let_1 C))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger C) A)) (= B C)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat C) A)) (= B C)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int C) A)) (= B C)))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.75/7.07 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B3) A4) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (= tptp.dvd_dvd_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B3) A4) tptp.zero_zero_nat))))
% 6.75/7.07 (assert (= tptp.dvd_dvd_int (lambda ((A4 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B3) A4) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.power_8256067586552552935nteger Y2) M))))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y2) M))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y2) M))))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y2) M))))))
% 6.75/7.07 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y2) M))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (N tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer C) (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (@ (@ tptp.dvd_dvd_int C) (@ (@ tptp.minus_minus_int A) B)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M) N) (@ _let_1 M))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (not (@ (@ tptp.dvd_dvd_nat N) M))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (or (@ (@ tptp.ord_less_nat N) M) (@ _let_1 N))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N)))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 M)))))))
% 6.75/7.07 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N) (not (@ (@ tptp.dvd_dvd_int N) M))))))
% 6.75/7.07 (assert (forall ((D2 tptp.nat) (A tptp.nat) (B tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D2))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X2) (@ (@ tptp.plus_plus_nat (@ _let_2 Y2)) D2)) (= (@ _let_2 X2) (@ (@ tptp.plus_plus_nat (@ _let_1 Y2)) D2))) (exists ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X4) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D2)) (= (@ _let_3 X4) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D2)))))))))))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X4 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 X4) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D3)) (= (@ _let_2 X4) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D3))))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X4 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 X4)) (@ _let_2 Y3)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X4)) (@ _let_1 Y3)) D3)))))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C2 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C2)))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C2)))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C2 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C2)))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.code_integer Bool)) (L tptp.code_integer)) (= (exists ((X tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L) X))) (exists ((X tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L) (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.zero_z3403309356797280102nteger)) (@ P X))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.complex Bool)) (L tptp.complex)) (= (exists ((X tptp.complex)) (@ P (@ (@ tptp.times_times_complex L) X))) (exists ((X tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L) (@ (@ tptp.plus_plus_complex X) tptp.zero_zero_complex)) (@ P X))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X tptp.real)) (@ P (@ (@ tptp.times_times_real L) X))) (exists ((X tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X) tptp.zero_zero_real)) (@ P X))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X tptp.rat)) (@ P (@ (@ tptp.times_times_rat L) X))) (exists ((X tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X) tptp.zero_zero_rat)) (@ P X))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X))) (exists ((X tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X) tptp.zero_zero_nat)) (@ P X))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X tptp.int)) (@ P (@ (@ tptp.times_times_int L) X))) (exists ((X tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X) tptp.zero_zero_int)) (@ P X))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) C) (= B (@ (@ tptp.times_3573771949741848930nteger C) A)))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (= (@ (@ tptp.divide_divide_nat B) A) C) (= B (@ (@ tptp.times_times_nat C) A)))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (= (@ (@ tptp.divide_divide_int B) A) C) (= B (@ (@ tptp.times_times_int C) A)))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger C) B)))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C) B)))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C) B)))))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D2) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger D2) C)) (= (@ (@ tptp.times_3573771949741848930nteger B) C) (@ (@ tptp.times_3573771949741848930nteger A) D2)))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D2) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D2) C)) (= (@ (@ tptp.times_times_nat B) C) (@ (@ tptp.times_times_nat A) D2)))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D2) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D2) C)) (= (@ (@ tptp.times_times_int B) C) (@ (@ tptp.times_times_int A) D2)))))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))))
% 6.75/7.07 (assert (forall ((D2 tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) D4) (forall ((X6 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X6) T)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X6) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D2) D4) (forall ((X6 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X6) T)) (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X6) (@ (@ tptp.times_times_complex K4) D4))) T))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D2) D4) (forall ((X6 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X6) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X6) (@ (@ tptp.times_times_real K4) D4))) T))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D4) (forall ((X6 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X6) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K4) D4))) T))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X6 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X6) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K4) D4))) T))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) D4) (forall ((X6 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D2))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X6) T))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X6) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T)))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D2) D4) (forall ((X6 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_complex X6) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X6) (@ (@ tptp.times_times_complex K4) D4))) T)))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D2) D4) (forall ((X6 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X6) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X6) (@ (@ tptp.times_times_real K4) D4))) T)))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D4) (forall ((X6 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X6) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K4) D4))) T)))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X6 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X6) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K4) D4))) T)))))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) B)))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) B)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) B)))))
% 6.75/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.75/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.75/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= A (@ (@ tptp.divide6298287555418463151nteger C) B)) (= (@ (@ tptp.times_3573771949741848930nteger A) B) C)))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C) B)) (= (@ (@ tptp.times_times_nat A) B) C)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C) B)) (= (@ (@ tptp.times_times_int A) B) C)))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) C) (= A (@ (@ tptp.times_3573771949741848930nteger C) B))))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) C) (= A (@ (@ tptp.times_times_nat C) B))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) C) (= A (@ (@ tptp.times_times_int C) B))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K) N)))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X4 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) X4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D3))))))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int Z) N)))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N)) (not (@ (@ tptp.dvd_dvd_nat N) M)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D tptp.nat)) (@ (@ tptp.dvd_dvd_nat D) M)))))))
% 6.75/7.07 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.75/7.07 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.75/7.07 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B2 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B2 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B2) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B2)))))))))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_times_nat A) B2) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B2)))))))))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_times_int A) B2) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B2)))))))))))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2))))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2))))))))
% 6.75/7.07 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.75/7.07 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.75/7.07 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.75/7.07 (assert (= (lambda ((Y5 tptp.code_integer) (Z4 tptp.code_integer)) (= Y5 Z4)) (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B3)) (= (@ (@ tptp.divide6298287555418463151nteger A4) _let_1) (@ (@ tptp.divide6298287555418463151nteger B3) _let_1))))))))
% 6.75/7.07 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B3)) (= (@ (@ tptp.divide_divide_nat A4) _let_1) (@ (@ tptp.divide_divide_nat B3) _let_1))))))))
% 6.75/7.07 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A4 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B3)) (= (@ (@ tptp.divide_divide_int A4) _let_1) (@ (@ tptp.divide_divide_int B3) _let_1))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X2))) (=> (not (= X2 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X2) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X2))) (=> (not (= X2 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (=> (not (= X2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (X2 tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X2) (@ (@ tptp.power_8256067586552552935nteger X2) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (X2 tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X2) (@ (@ tptp.power_power_rat X2) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X2) (@ (@ tptp.power_power_nat X2) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X2) (@ (@ tptp.power_power_real X2) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (X2 tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X2) (@ (@ tptp.power_power_int X2) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X2) (@ (@ tptp.power_power_complex X2) N)))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X2) _let_1) (@ (@ tptp.divide_divide_nat Y2) _let_1)) (=> (= (@ _let_2 X2) (@ _let_2 Y2)) (= X2 Y2)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M)) M) (= N tptp.one_one_nat)))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N)) M) (= N tptp.one_one_nat)))))
% 6.75/7.07 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W))))))
% 6.75/7.07 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bitM W))))))
% 6.75/7.07 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bitM W))))))
% 6.75/7.07 (assert (forall ((Q2 tptp.nat) (N tptp.nat) (R tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q2))) (=> (@ _let_3 N) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N) Q2)) (@ _let_2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat _let_1) Q2)))))))))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.75/7.07 (assert (forall ((R tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R) N) (=> (@ (@ tptp.ord_less_eq_nat R) M) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M) R)) (= (@ (@ tptp.modulo_modulo_nat M) N) R))))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L)) (or (@ (@ tptp.dvd_dvd_int L) K) (and (= L tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) A)))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)) A)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)) A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.modulo364778990260209775nteger A) _let_1) tptp.zero_z3403309356797280102nteger)))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.modulo_modulo_nat A) _let_1) tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.modulo_modulo_int A) _let_1) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.modulo364778990260209775nteger A) _let_1) tptp.one_one_Code_integer)))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.modulo_modulo_nat A) _let_1) tptp.one_one_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.modulo_modulo_int A) _let_1) tptp.one_one_int)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se8260200283734997820nteger M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2793503036327961859nteger M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7882103937844011126it_nat M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1345352211410354436nteger M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2161824704523386999it_nat M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_Code_integer))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_nat))))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_int))))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z3403309356797280102nteger))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_integer))))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_nat))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_nat))))))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_int))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_int))))))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_integer))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 tptp.one_one_nat))))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 tptp.one_one_int))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 6.75/7.07 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N))))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_1 (= A tptp.zero_zero_rat))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))))
% 6.75/7.07 (assert (forall ((X2 (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X2) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X2) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((X2 (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X2) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) _let_3)) _let_2))))))))
% 6.75/7.07 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 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 L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 6.75/7.07 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 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 L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 6.75/7.07 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 6.75/7.07 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 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 L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 6.75/7.07 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 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 L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 6.75/7.07 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 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 L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 6.75/7.07 (assert (forall ((X8 tptp.set_Extended_enat)) (=> (not (= X8 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) X8) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) X8) (@ (@ tptp.ord_le72135733267957522d_enat X4) Xa))))) (not (@ tptp.finite4001608067531595151d_enat X8))))))
% 6.75/7.07 (assert (forall ((X8 tptp.set_real)) (=> (not (= X8 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) X8) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X8) (@ (@ tptp.ord_less_real X4) Xa))))) (not (@ tptp.finite_finite_real X8))))))
% 6.75/7.07 (assert (forall ((X8 tptp.set_rat)) (=> (not (= X8 tptp.bot_bot_set_rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) X8) (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) X8) (@ (@ tptp.ord_less_rat X4) Xa))))) (not (@ tptp.finite_finite_rat X8))))))
% 6.75/7.07 (assert (forall ((X8 tptp.set_num)) (=> (not (= X8 tptp.bot_bot_set_num)) (=> (forall ((X4 tptp.num)) (=> (@ (@ tptp.member_num X4) X8) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X8) (@ (@ tptp.ord_less_num X4) Xa))))) (not (@ tptp.finite_finite_num X8))))))
% 6.75/7.07 (assert (forall ((X8 tptp.set_nat)) (=> (not (= X8 tptp.bot_bot_set_nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) X8) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X8) (@ (@ tptp.ord_less_nat X4) Xa))))) (not (@ tptp.finite_finite_nat X8))))))
% 6.75/7.07 (assert (forall ((X8 tptp.set_int)) (=> (not (= X8 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) X8) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X8) (@ (@ tptp.ord_less_int X4) Xa))))) (not (@ tptp.finite_finite_int X8))))))
% 6.75/7.07 (assert (forall ((S3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S3) (=> (not (= S3 tptp.bot_bo7653980558646680370d_enat)) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) S3) (not (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) S3) (@ (@ tptp.ord_le72135733267957522d_enat Xa) X4))))))))))
% 6.75/7.07 (assert (forall ((S3 tptp.set_real)) (=> (@ tptp.finite_finite_real S3) (=> (not (= S3 tptp.bot_bot_set_real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) S3) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S3) (@ (@ tptp.ord_less_real Xa) X4))))))))))
% 6.75/7.07 (assert (forall ((S3 tptp.set_rat)) (=> (@ tptp.finite_finite_rat S3) (=> (not (= S3 tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) S3) (not (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) S3) (@ (@ tptp.ord_less_rat Xa) X4))))))))))
% 6.75/7.07 (assert (forall ((S3 tptp.set_num)) (=> (@ tptp.finite_finite_num S3) (=> (not (= S3 tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) S3) (not (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) S3) (@ (@ tptp.ord_less_num Xa) X4))))))))))
% 6.75/7.07 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (=> (not (= S3 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S3) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S3) (@ (@ tptp.ord_less_nat Xa) X4))))))))))
% 6.75/7.07 (assert (forall ((S3 tptp.set_int)) (=> (@ tptp.finite_finite_int S3) (=> (not (= S3 tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S3) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S3) (@ (@ tptp.ord_less_int Xa) X4))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (Y2 tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y2 (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X2) Y2) (=> (=> (= X2 tptp.zero_zero_nat) _let_1) (=> (=> (= X2 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X2 _let_2) (not (and (=> _let_8 (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 6.75/7.07 (assert (= tptp.divmod_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M3) N3))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M3)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q4)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M3) N3)) N3))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.75/7.07 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N3 tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A4) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N3 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger _let_2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A4) _let_1))))))))))
% 6.75/7.07 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A4) _let_1))) (@ (@ (@ tptp.if_int (= N3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int _let_2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))))))))))
% 6.75/7.07 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X2)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X2)) I))))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) I))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 6.75/7.07 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 6.75/7.07 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (=> (@ (@ F A) B) (@ (@ tptp.produc6590410687421337004_nat_o F) (@ (@ tptp.produc6161850002892822231at_nat A) B)))))
% 6.75/7.07 (assert (forall ((F (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (@ (@ F A) B) (@ (@ tptp.produc5703948589228662326_num_o F) (@ (@ tptp.product_Pair_num_num A) B)))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.num Bool)) (A tptp.nat) (B tptp.num)) (=> (@ (@ F A) B) (@ (@ tptp.produc4927758841916487424_num_o F) (@ (@ tptp.product_Pair_nat_num A) B)))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (@ (@ F A) B) (@ (@ tptp.produc6081775807080527818_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ F A) B) (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)))))
% 6.75/7.07 (assert (forall ((P6 tptp.produc859450856879609959at_nat) (C (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (= P6 (@ (@ tptp.produc6161850002892822231at_nat A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc6590410687421337004_nat_o C) P6))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_num_num) (C (-> tptp.num tptp.num Bool))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_num_num A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc5703948589228662326_num_o C) P6))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_nat_num) (C (-> tptp.nat tptp.num Bool))) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_nat_num A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc4927758841916487424_num_o C) P6))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat Bool))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= P6 (@ (@ tptp.product_Pair_nat_nat A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc6081775807080527818_nat_o C) P6))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_int_int) (C (-> tptp.int tptp.int Bool))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc4947309494688390418_int_o C) P6))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8296048397933160132t_real C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 6.75/7.07 (assert (forall ((Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1361121860356118632et_nat C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc6406642877701697732et_int C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real)) (A tptp.nat) (B tptp.num)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1435849484188172666t_real C) (@ (@ tptp.product_Pair_nat_num A) B)))))))
% 6.75/7.07 (assert (forall ((Z tptp.nat) (C (-> tptp.nat tptp.num tptp.set_nat)) (A tptp.nat) (B tptp.num)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc4130284055270567454et_nat C) (@ (@ tptp.product_Pair_nat_num A) B)))))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (C (-> tptp.nat tptp.num tptp.set_int)) (A tptp.nat) (B tptp.num)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc9175805072616146554et_int C) (@ (@ tptp.product_Pair_nat_num A) B)))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (C (-> tptp.nat tptp.nat tptp.set_real)) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc3668448655016342576t_real C) (@ (@ tptp.product_Pair_nat_nat A) B)))))))
% 6.75/7.07 (assert (forall ((Z tptp.nat) (C (-> tptp.nat tptp.nat tptp.set_nat)) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc6189476227299908564et_nat C) (@ (@ tptp.product_Pair_nat_nat A) B)))))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (C (-> tptp.nat tptp.nat tptp.set_int)) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc2011625207790711856et_int C) (@ (@ tptp.product_Pair_nat_nat A) B)))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (C (-> tptp.int tptp.int tptp.set_real)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc6452406959799940328t_real C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_num_num) (Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_num_num A3) B2)) (@ (@ tptp.member_real Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P6)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_num_num) (Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_num_num A3) B2)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P6)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_num_num) (Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_num_num A3) B2)) (@ (@ tptp.member_int Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P6)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_nat_num) (Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real))) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_nat_num A3) B2)) (@ (@ tptp.member_real Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P6)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_nat_num) (Z tptp.nat) (C (-> tptp.nat tptp.num tptp.set_nat))) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_nat_num A3) B2)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc4130284055270567454et_nat C) P6)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_nat_num) (Z tptp.int) (C (-> tptp.nat tptp.num tptp.set_int))) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_nat_num A3) B2)) (@ (@ tptp.member_int Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc9175805072616146554et_int C) P6)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_nat_nat) (Z tptp.real) (C (-> tptp.nat tptp.nat tptp.set_real))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= P6 (@ (@ tptp.product_Pair_nat_nat A3) B2)) (@ (@ tptp.member_real Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc3668448655016342576t_real C) P6)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_nat_nat) (Z tptp.nat) (C (-> tptp.nat tptp.nat tptp.set_nat))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= P6 (@ (@ tptp.product_Pair_nat_nat A3) B2)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc6189476227299908564et_nat C) P6)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_nat_nat) (Z tptp.int) (C (-> tptp.nat tptp.nat tptp.set_int))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= P6 (@ (@ tptp.product_Pair_nat_nat A3) B2)) (@ (@ tptp.member_int Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc2011625207790711856et_int C) P6)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_int_int) (Z tptp.real) (C (-> tptp.int tptp.int tptp.set_real))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ tptp.member_real Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc6452406959799940328t_real C) P6)))))
% 6.75/7.07 (assert (forall ((P6 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X2 tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A3) B2) P6) (@ (@ (@ C A3) B2) X2))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P6) X2))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.75/7.07 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.75/7.07 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.75/7.07 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.75/7.07 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.75/7.07 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 6.75/7.07 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) B))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= M N))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= M N))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= M N))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.times_times_int A) B))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) B))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.divide_divide_int A) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X2))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y2)) (@ _let_1 Y2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X2))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y2)) (@ _let_1 Y2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X2))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y2)) (@ _let_1 Y2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y2)) (@ _let_1 Y2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y2)) (@ _let_1 Y2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X2)) Y2) (@ (@ tptp.dvd_dvd_int X2) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X2)) Y2) (@ (@ tptp.dvd_dvd_real X2) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X2)) Y2) (@ (@ tptp.dvd_dvd_complex X2) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X2)) Y2) (@ (@ tptp.dvd_dvd_Code_integer X2) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X2)) Y2) (@ (@ tptp.dvd_dvd_rat X2) Y2))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.75/7.07 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 6.75/7.07 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 6.75/7.07 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 6.75/7.07 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 6.75/7.07 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 6.75/7.07 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X2 A))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.75/7.07 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.75/7.07 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.75/7.07 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 6.75/7.07 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.75/7.07 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.75/7.07 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.75/7.07 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.75/7.07 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.75/7.07 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 6.75/7.07 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.75/7.07 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.75/7.07 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 6.75/7.07 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) N)))
% 6.75/7.07 (assert (forall ((N tptp.nat) (X2 Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X2)) N)))
% 6.75/7.07 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X2)) N)))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (or P Q)) (@ (@ tptp.ord_max_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (or P Q)) (@ (@ tptp.ord_max_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (or P Q)) (@ (@ tptp.ord_max_Code_integer (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.75/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.75/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.75/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (let ((_let_2 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (let ((_let_2 (@ tptp.numeral_numeral_rat M))) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat _let_2)) (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat _let_2) _let_1)))))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.75/7.07 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 6.75/7.07 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.75/7.07 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.75/7.07 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.75/7.07 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 6.75/7.07 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.75/7.07 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.75/7.07 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.divide_divide_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X2))))
% 6.75/7.07 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X2))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat X2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X2))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int B) A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.75/7.07 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N) (@ tptp.zero_n2687167440665602831ol_nat (not (= N _let_1)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N) _let_1) _let_1))))
% 6.75/7.07 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.75/7.07 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X2)) I) X2))))
% 6.75/7.07 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) I) X2))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_numeral_dbl_int _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_numeral_dbl_real _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu7009210354673126013omplex _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu8804712462038260780nteger _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_numeral_dbl_rat _let_1))))))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.75/7.07 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.75/7.07 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.75/7.07 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.75/7.07 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.75/7.07 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.75/7.07 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.75/7.07 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.75/7.07 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.75/7.07 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.75/7.07 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= N tptp.one))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= N tptp.one))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= N tptp.one))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N tptp.one))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N tptp.one))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N tptp.one))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y2)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y2)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N))))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y2)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y2)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y2)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y2)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y2)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y2)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y2)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y2)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y2)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y2)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y2)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N) (@ tptp.pred_numeral K)))))
% 6.75/7.07 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.pred_numeral K)))))
% 6.75/7.07 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.75/7.07 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N) (@ tptp.pred_numeral K)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_num N) M))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_num N) M))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_num N) M))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_num N) M))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) (@ tptp.pred_numeral K))))))
% 6.75/7.07 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)))) (not (= M tptp.one)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)))) (not (= M tptp.one)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)))) (not (= M tptp.one)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (not (= M tptp.one)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M tptp.one)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M tptp.one)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M tptp.one)))))
% 6.75/7.07 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.75/7.07 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.75/7.07 (assert (forall ((P6 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P6))) P6)))
% 6.75/7.07 (assert (forall ((P6 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P6))) P6)))
% 6.75/7.07 (assert (forall ((P6 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P6))) P6)))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.plus_plus_int _let_1) _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.plus_plus_complex _let_1) _let_1) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.75/7.07 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.75/7.07 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.75/7.07 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.75/7.07 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.75/7.07 (assert (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 6.75/7.07 (assert (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.75/7.07 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.75/7.07 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.75/7.07 (assert (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)))
% 6.75/7.07 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.75/7.07 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.75/7.07 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.75/7.07 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.75/7.07 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.75/7.07 (assert (forall ((B Bool)) (= (@ (@ tptp.divide_divide_nat (@ tptp.zero_n2687167440665602831ol_nat B)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((B Bool)) (= (@ (@ tptp.divide_divide_int (@ tptp.zero_n2684676970156552555ol_int B)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat A) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.power_power_int A) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.power_power_real A) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.power_power_complex A) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.power_power_rat A) N)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X2)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2)))))
% 6.75/7.07 (assert (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 6.75/7.07 (assert (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.75/7.07 (assert (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int)))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_real)))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_complex)))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_Code_integer)))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_rat)))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int _let_1) N) _let_1)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real _let_1) N) _let_1)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex _let_1) N) _let_1)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N) _let_1)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat _let_1) N) _let_1)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N) tptp.one_one_real))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N) tptp.one_one_complex))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N) tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N) tptp.one_one_rat))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_ri6519982836138164636nteger tptp.zero_zero_nat) A) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_ri631733984087533419it_int tptp.zero_zero_nat) A) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.75/7.07 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ 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 L)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 6.75/7.07 (assert (forall ((P6 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P6) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (= P6 Q2))))
% 6.75/7.07 (assert (forall ((P6 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P6) (@ tptp.zero_n2684676970156552555ol_int Q2)) (= P6 Q2))))
% 6.75/7.07 (assert (forall ((P6 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P6) (@ tptp.zero_n356916108424825756nteger Q2)) (= P6 Q2))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n3304061248610475627l_real (and P Q)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (and P Q)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (and P Q)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (and P Q)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.75/7.07 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real)) (P6 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P6)) (not (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_num_num X4) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat)) (P6 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P6)) (not (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_num_num X4) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int)) (P6 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P6)) (not (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_num_num X4) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real)) (P6 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P6)) (not (forall ((X4 tptp.nat) (Y3 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_nat_num X4) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Z tptp.nat) (C (-> tptp.nat tptp.num tptp.set_nat)) (P6 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc4130284055270567454et_nat C) P6)) (not (forall ((X4 tptp.nat) (Y3 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_nat_num X4) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (C (-> tptp.nat tptp.num tptp.set_int)) (P6 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc9175805072616146554et_int C) P6)) (not (forall ((X4 tptp.nat) (Y3 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_nat_num X4) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (C (-> tptp.nat tptp.nat tptp.set_real)) (P6 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc3668448655016342576t_real C) P6)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= P6 (@ (@ tptp.product_Pair_nat_nat X4) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Z tptp.nat) (C (-> tptp.nat tptp.nat tptp.set_nat)) (P6 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc6189476227299908564et_nat C) P6)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= P6 (@ (@ tptp.product_Pair_nat_nat X4) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (C (-> tptp.nat tptp.nat tptp.set_int)) (P6 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc2011625207790711856et_int C) P6)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= P6 (@ (@ tptp.product_Pair_nat_nat X4) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (C (-> tptp.int tptp.int tptp.set_real)) (P6 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc6452406959799940328t_real C) P6)) (not (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int X4) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X4) Y3)))))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_eq_real B) (@ tptp.uminus_uminus_real A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_eq_rat B) (@ tptp.uminus_uminus_rat A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_eq_int B) (@ tptp.uminus_uminus_int A)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) A))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) A))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) A))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) A))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_int B) (@ tptp.uminus_uminus_int A)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_real B) (@ tptp.uminus_uminus_real A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_rat B) (@ tptp.uminus_uminus_rat A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_int B))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) A) (@ (@ tptp.times_times_real B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_real B))))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) A) (@ (@ tptp.times_times_complex B) B)) (or (= A B) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) A) (@ (@ tptp.times_3573771949741848930nteger B) B)) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) A) (@ (@ tptp.times_times_rat B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_rat B))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.times_times_real A) (@ tptp.uminus_uminus_real B)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.times_times_rat A) (@ tptp.uminus_uminus_rat B)))))
% 6.75/7.07 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.75/7.07 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.75/7.07 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.75/7.07 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.75/7.07 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))))
% 6.75/7.07 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A2 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))))
% 6.75/7.07 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A2 (@ (@ tptp.plus_plus_complex K) A)) (= (@ tptp.uminus1482373934393186551omplex A2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.75/7.07 (assert (forall ((A2 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A2 (@ (@ tptp.plus_p5714425477246183910nteger K) A)) (= (@ tptp.uminus1351360451143612070nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A))))))
% 6.75/7.07 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A2 (@ (@ tptp.plus_plus_rat K) A)) (= (@ tptp.uminus_uminus_rat A2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B)) A) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) B))))
% 6.75/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B)) A) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B))))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B))) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B))) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (A5 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A5) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A5)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A5 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A5) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A5)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.75/7.07 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (=> (@ (@ tptp.produc6590410687421337004_nat_o F) (@ (@ tptp.produc6161850002892822231at_nat A) B)) (@ (@ F A) B))))
% 6.75/7.07 (assert (forall ((F (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (@ (@ tptp.produc5703948589228662326_num_o F) (@ (@ tptp.product_Pair_num_num A) B)) (@ (@ F A) B))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.num Bool)) (A tptp.nat) (B tptp.num)) (=> (@ (@ tptp.produc4927758841916487424_num_o F) (@ (@ tptp.product_Pair_nat_num A) B)) (@ (@ F A) B))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.produc6081775807080527818_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.75/7.07 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (P6 tptp.produc859450856879609959at_nat)) (=> (@ (@ tptp.produc6590410687421337004_nat_o C) P6) (not (forall ((X4 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (=> (= P6 (@ (@ tptp.produc6161850002892822231at_nat X4) Y3)) (not (@ (@ C X4) Y3))))))))
% 6.75/7.07 (assert (forall ((C (-> tptp.num tptp.num Bool)) (P6 tptp.product_prod_num_num)) (=> (@ (@ tptp.produc5703948589228662326_num_o C) P6) (not (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_num_num X4) Y3)) (not (@ (@ C X4) Y3))))))))
% 6.75/7.07 (assert (forall ((C (-> tptp.nat tptp.num Bool)) (P6 tptp.product_prod_nat_num)) (=> (@ (@ tptp.produc4927758841916487424_num_o C) P6) (not (forall ((X4 tptp.nat) (Y3 tptp.num)) (=> (= P6 (@ (@ tptp.product_Pair_nat_num X4) Y3)) (not (@ (@ C X4) Y3))))))))
% 6.75/7.07 (assert (forall ((C (-> tptp.nat tptp.nat Bool)) (P6 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.produc6081775807080527818_nat_o C) P6) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= P6 (@ (@ tptp.product_Pair_nat_nat X4) Y3)) (not (@ (@ C X4) Y3))))))))
% 6.75/7.07 (assert (forall ((C (-> tptp.int tptp.int Bool)) (P6 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C) P6) (not (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int X4) Y3)) (not (@ (@ C X4) Y3))))))))
% 6.75/7.07 (assert (forall ((R2 (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat) (C tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o R2) (@ (@ tptp.product_Pair_nat_nat A) B)) C) (@ (@ (@ R2 A) B) C))))
% 6.75/7.07 (assert (forall ((C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P6 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P6) Z) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= P6 (@ (@ tptp.product_Pair_nat_nat X4) Y3)) (not (@ (@ (@ C X4) Y3) Z))))))))
% 6.75/7.07 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.75/7.07 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.75/7.07 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.75/7.07 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.75/7.07 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.75/7.07 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.75/7.07 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.75/7.07 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.75/7.07 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.75/7.07 (assert (forall ((P (-> tptp.complex Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P6)) (not (or (and P6 (not (@ P tptp.one_one_complex))) (and (not P6) (not (@ P tptp.zero_zero_complex))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.real Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P6)) (not (or (and P6 (not (@ P tptp.one_one_real))) (and (not P6) (not (@ P tptp.zero_zero_real))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.rat Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P6)) (not (or (and P6 (not (@ P tptp.one_one_rat))) (and (not P6) (not (@ P tptp.zero_zero_rat))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P6)) (not (or (and P6 (not (@ P tptp.one_one_nat))) (and (not P6) (not (@ P tptp.zero_zero_nat))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P6)) (not (or (and P6 (not (@ P tptp.one_one_int))) (and (not P6) (not (@ P tptp.zero_zero_int))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.code_integer Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P6)) (not (or (and P6 (not (@ P tptp.one_one_Code_integer))) (and (not P6) (not (@ P tptp.zero_z3403309356797280102nteger))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.complex Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P6)) (and (=> P6 (@ P tptp.one_one_complex)) (=> (not P6) (@ P tptp.zero_zero_complex))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.real Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P6)) (and (=> P6 (@ P tptp.one_one_real)) (=> (not P6) (@ P tptp.zero_zero_real))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.rat Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P6)) (and (=> P6 (@ P tptp.one_one_rat)) (=> (not P6) (@ P tptp.zero_zero_rat))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P6)) (and (=> P6 (@ P tptp.one_one_nat)) (=> (not P6) (@ P tptp.zero_zero_nat))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P6)) (and (=> P6 (@ P tptp.one_one_int)) (=> (not P6) (@ P tptp.zero_zero_int))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.code_integer Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P6)) (and (=> P6 (@ P tptp.one_one_Code_integer)) (=> (not P6) (@ P tptp.zero_z3403309356797280102nteger))))))
% 6.75/7.07 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P4 Bool)) (@ (@ (@ tptp.if_complex P4) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.75/7.07 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P4 Bool)) (@ (@ (@ tptp.if_real P4) tptp.one_one_real) tptp.zero_zero_real))))
% 6.75/7.07 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_rat P4) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.75/7.07 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_nat P4) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.75/7.07 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P4 Bool)) (@ (@ (@ tptp.if_int P4) tptp.one_one_int) tptp.zero_zero_int))))
% 6.75/7.07 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P4 Bool)) (@ (@ (@ tptp.if_Code_integer P4) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.75/7.07 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.75/7.07 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.75/7.07 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.75/7.07 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.75/7.07 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.75/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.75/7.07 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.75/7.07 (assert (forall ((W tptp.num) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X2)) (@ (@ tptp.times_times_int X2) (@ tptp.uminus_uminus_int _let_1))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real X2) (@ tptp.uminus_uminus_real _let_1))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (X2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex X2) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X2)) (@ (@ tptp.times_3573771949741848930nteger X2) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (X2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat X2) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.75/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B)))))))
% 6.75/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.int)) (= (= (@ (@ tptp.times_times_int X2) X2) tptp.one_one_int) (or (= X2 tptp.one_one_int) (= X2 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.times_times_real X2) X2) tptp.one_one_real) (or (= X2 tptp.one_one_real) (= X2 (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.75/7.07 (assert (forall ((X2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex X2) X2) tptp.one_one_complex) (or (= X2 tptp.one_one_complex) (= X2 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X2) X2) tptp.one_one_Code_integer) (or (= X2 tptp.one_one_Code_integer) (= X2 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat X2) X2) tptp.one_one_rat) (or (= X2 tptp.one_one_rat) (= X2 (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.75/7.07 (assert (forall ((B4 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B4 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((B4 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B4 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((B4 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B4 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((B4 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B4 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((B4 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B4 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))))
% 6.75/7.07 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))
% 6.75/7.07 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))
% 6.75/7.07 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))
% 6.75/7.07 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))
% 6.75/7.07 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))
% 6.75/7.07 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))
% 6.75/7.07 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))
% 6.75/7.07 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))
% 6.75/7.07 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))
% 6.75/7.07 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs2)) (= X4 X2))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs2)) X2) Xs2))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_o) (X2 Bool)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs2)) (= X4 X2))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs2)) X2) Xs2))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs2)) (= X4 X2))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs2)) X2) Xs2))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_option_nat) (N tptp.nat) (X2 tptp.option_nat)) (=> (= (@ tptp.size_s6086282163384603972on_nat Xs2) N) (=> (forall ((Y3 tptp.option_nat)) (=> (@ (@ tptp.member_option_nat Y3) (@ tptp.set_option_nat2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_option_nat N) X2))))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_real) (N tptp.nat) (X2 tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) N) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_real N) X2))))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_set_nat_rat) (N tptp.nat) (X2 tptp.set_nat_rat)) (=> (= (@ tptp.size_s3959913991096427681at_rat Xs2) N) (=> (forall ((Y3 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat Y3) (@ tptp.set_set_nat_rat2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replic5516892415368941373at_rat N) X2))))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_int) (N tptp.nat) (X2 tptp.int)) (=> (= (@ tptp.size_size_list_int Xs2) N) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_int N) X2))))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT N) X2))))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_o) (N tptp.nat) (X2 Bool)) (=> (= (@ tptp.size_size_list_o Xs2) N) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_o N) X2))))))
% 6.75/7.07 (assert (forall ((Xs2 tptp.list_nat) (N tptp.nat) (X2 tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs2) N) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_nat N) X2))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))))))
% 6.75/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))))))
% 6.75/7.07 (assert (forall ((U tptp.real) (X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X2) X2))))
% 6.75/7.07 (assert (= tptp.numeral_numeral_nat (lambda ((K2 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K2)))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (=> (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L) tptp.zero_zero_int)) (not (= (@ (@ tptp.modulo_modulo_int K) L) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int K))) (=> (not (= (@ _let_1 (@ tptp.uminus_uminus_int L)) tptp.zero_zero_int)) (not (= (@ _let_1 L) tptp.zero_zero_int))))))
% 6.75/7.07 (assert (= tptp.minus_minus_real (lambda ((X tptp.real) (Y tptp.real)) (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real Y)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.75/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.75/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.75/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.75/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.75/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.75/7.07 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.75/7.07 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.75/7.07 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= C (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))) (= (@ (@ tptp.times_times_real C) B) (@ tptp.uminus_uminus_real A))))))
% 6.75/7.07 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= C (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))) (= (@ (@ tptp.times_times_complex C) B) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C) B) (@ tptp.uminus_uminus_rat A))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) C) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C) B))))))
% 6.75/7.07 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) C) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C) B))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C) B))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B) (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.75/7.07 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B) (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) (@ tptp.uminus_uminus_real B))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) (@ tptp.uminus1482373934393186551omplex B))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B tptp.zero_zero_real)) (= A (@ tptp.uminus_uminus_real B))))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B tptp.zero_zero_complex)) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (@ tptp.uminus_uminus_rat B))))))
% 6.75/7.07 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int B) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) (@ tptp.uminus_uminus_int B))))
% 6.75/7.07 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real B) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) (@ tptp.uminus_uminus_real B))))
% 6.75/7.07 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.75/7.07 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat B) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) (@ tptp.uminus_uminus_rat B))))
% 6.75/7.07 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) B) (@ tptp.uminus_uminus_int B))))
% 6.75/7.07 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) B) (@ tptp.uminus_uminus_real B))))
% 6.75/7.07 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.75/7.07 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.75/7.07 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) B) (@ tptp.uminus_uminus_rat B))))
% 6.75/7.07 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.75/7.07 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.75/7.07 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.75/7.07 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.75/7.07 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ (@ tptp.power_power_int A) N)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.power_power_real A) N)))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ (@ tptp.power_power_complex A) N)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ (@ tptp.power_power_rat A) N)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X2)) _let_1) (@ (@ tptp.power_power_int X2) _let_1)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X2)) _let_1) (@ (@ tptp.power_power_real X2) _let_1)))))
% 6.75/7.07 (assert (forall ((X2 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X2)) _let_1) (@ (@ tptp.power_power_complex X2) _let_1)))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X2)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X2)) _let_1) (@ (@ tptp.power_power_rat X2) _let_1)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X2)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X2) _let_1))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X2)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X2) _let_1))))))
% 6.75/7.07 (assert (forall ((X2 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X2)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X2) _let_1))))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X2)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X2)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X2) _let_1))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X2) Y2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y2) (@ tptp.uminus_uminus_real X2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X2)) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X2)) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X2) Y2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.uminus_uminus_real X2)))))
% 6.75/7.07 (assert (= tptp.pred_numeral (lambda ((K2 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K2)) tptp.one_one_nat))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= _let_2 tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) B))))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= _let_1 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int B) _let_1)))))))))
% 6.75/7.07 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.75/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.75/7.07 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.75/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B))) (let ((_let_4 (@ (@ tptp.times_times_real A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.75/7.07 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.75/7.07 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.75/7.07 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X2) Z))) Y2) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real Y2) Z))) Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X2) Z))) Y2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex Y2) Z))) Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X2) Z))) Y2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat Y2) Z))) Z)))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X2) Z))) Y2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real Y2) Z))) Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X2) Z))) Y2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex Y2) Z))) Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X2) Z))) Y2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat Y2) Z))) Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.75/7.07 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.75/7.07 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.75/7.07 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.75/7.07 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 A)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X2) _let_1) (@ (@ tptp.power_power_int Y2) _let_1)) (or (= X2 Y2) (= X2 (@ tptp.uminus_uminus_int Y2)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X2) _let_1) (@ (@ tptp.power_power_real Y2) _let_1)) (or (= X2 Y2) (= X2 (@ tptp.uminus_uminus_real Y2)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X2) _let_1) (@ (@ tptp.power_power_complex Y2) _let_1)) (or (= X2 Y2) (= X2 (@ tptp.uminus1482373934393186551omplex Y2)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X2) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y2) _let_1)) (or (= X2 Y2) (= X2 (@ tptp.uminus1351360451143612070nteger Y2)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X2) _let_1) (@ (@ tptp.power_power_rat Y2) _let_1)) (or (= X2 Y2) (= X2 (@ tptp.uminus_uminus_rat Y2)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B4) N)) (@ (@ tptp.divide_divide_int A2) N))))))
% 6.75/7.07 (assert (forall ((B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.divide_divide_int _let_1) B) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.modulo_modulo_nat A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.modulo_modulo_int A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n356916108424825756nteger (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)))))
% 6.75/7.07 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.75/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.75/7.07 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.75/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.75/7.07 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.75/7.07 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (or (= A tptp.one_one_int) (= A (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (or (= A tptp.one_one_real) (= A (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.75/7.07 (assert (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (or (= A tptp.one_one_complex) (= A (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (or (= A tptp.one_one_Code_integer) (= A (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (or (= A tptp.one_one_rat) (= A (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (@ (@ tptp.power_power_rat _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.75/7.07 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.75/7.07 (assert (forall ((U tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) K))))
% 6.75/7.07 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))))
% 6.75/7.07 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) L))))))
% 6.75/7.07 (assert (forall ((B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ _let_1 B)))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))))))
% 6.75/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B)))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.if_int (= R tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q2))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q2) R)) (=> (not (= B tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))) (@ (@ _let_1 tptp.zero_zero_int) (@ (@ tptp.minus_minus_int B) R))))))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A3 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.nat) (B2 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B2)) (@ (@ tptp.times_times_nat _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A3 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.int) (B2 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B2)) (@ (@ tptp.times_times_int _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 6.75/7.07 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A3 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.code_integer) (B2 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B2)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 6.75/7.07 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X2) (=> (@ (@ tptp.ord_le3102999989581377725nteger X2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X2) (=> (@ (@ tptp.ord_less_eq_int X2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) (@ (@ tptp.power_power_complex A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) _let_1))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) L)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K) L) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.75/7.07 (assert (= tptp.divmod_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M3) N3)) (@ (@ tptp.modulo_modulo_nat M3) N3)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K3 tptp.int)) (=> (@ P K3) (=> (not (= K3 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K3 tptp.int)) (=> (@ P K3) (=> (not (= K3 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))))
% 6.75/7.07 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))))
% 6.75/7.07 (assert (= tptp.nat_set_decode (lambda ((X tptp.nat)) (@ tptp.collect_nat (lambda ((N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat _let_1) N3))))))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.75/7.07 (assert (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 6.75/7.07 (assert (forall ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) (@ tptp.uminus5710092332889474511et_nat Y2)) (@ (@ tptp.ord_less_eq_set_nat Y2) X2))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 6.75/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one)))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one)))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.75/7.07 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.75/7.07 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.75/7.07 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bitM K)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 6.75/7.07 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.75/7.07 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.75/7.07 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.75/7.07 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.75/7.07 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.75/7.07 (assert (forall ((Q2 tptp.int) (R tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q2) R)) (@ (@ tptp.plus_plus_int Q2) (@ tptp.zero_n2684676970156552555ol_int (not (= R tptp.zero_zero_int)))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu3811975205180677377ec_int _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu6075765906172075777c_real _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu6511756317524482435omplex _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu5831290666863070958nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu7757733837767384882nteger _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu3179335615603231917ec_rat _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu5851722552734809277nc_int _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu8295874005876285629c_real _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu8557863876264182079omplex _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu5831290666863070958nteger _let_1))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu5219082963157363817nc_rat _let_1))))))
% 6.75/7.07 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q4) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))
% 6.75/7.07 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))
% 6.75/7.07 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))
% 6.75/7.07 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))
% 6.75/7.07 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y2)) (@ tptp.uminus5710092332889474511et_nat X2)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y2) (@ tptp.uminus5710092332889474511et_nat X2)) (@ (@ tptp.ord_less_eq_set_nat X2) (@ tptp.uminus5710092332889474511et_nat Y2)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y2)) X2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.set_int) (Y2 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X2) Y2) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X2) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.set_Extended_enat) (Y2 tptp.set_Extended_enat)) (= (= (@ (@ tptp.minus_925952699566721837d_enat X2) Y2) tptp.bot_bo7653980558646680370d_enat) (@ (@ tptp.ord_le7203529160286727270d_enat X2) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X2) Y2) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X2) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))))))))
% 6.75/7.07 (assert (= tptp.ring_1_of_int_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K2) _let_1))))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K2) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))))
% 6.75/7.07 (assert (= tptp.ring_1_of_int_real (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))))
% 6.75/7.07 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))))
% 6.75/7.07 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.75/7.07 (assert (= tptp.ring_1_of_int_rat (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_rat (= K2 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.nat) (Y2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y2 (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X2) Y2) (=> (@ _let_2 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X2 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X2 _let_1) (=> (and (=> _let_8 (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 6.75/7.07 (assert (= tptp.int_ge_less_than (lambda ((D tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D) Z6) (@ (@ tptp.ord_less_int Z6) Z2))))))))
% 6.75/7.07 (assert (= tptp.int_ge_less_than2 (lambda ((D tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D) Z2) (@ (@ tptp.ord_less_int Z6) Z2))))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z) (@ tptp.numeral_numeral_rat N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.75/7.07 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.75/7.07 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 6.75/7.07 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 6.75/7.07 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 6.75/7.07 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.75/7.07 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y2)) (@ (@ tptp.ord_less_real X2) Y2)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (= (@ tptp.ln_ln_real X2) (@ tptp.ln_ln_real Y2)) (= X2 Y2)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X2) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X2) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X2) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X2) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 6.75/7.07 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 6.75/7.07 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 6.75/7.07 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z)) N))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (= (@ tptp.ln_ln_real X2) tptp.zero_zero_real) (= X2 tptp.one_one_real)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (= (@ _let_1 (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))))
% 6.75/7.07 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.75/7.07 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.75/7.07 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.75/7.07 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))))
% 6.75/7.07 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.75/7.07 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.75/7.07 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N) (@ tptp.ring_17405671764205052669omplex Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N) (@ tptp.ring_1_of_int_real Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N) (@ tptp.ring_1_of_int_rat Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y2)) (= _let_1 Y2)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y2) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y2) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y2) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (= (@ tptp.ring_1_of_int_int Y2) _let_1) (= Y2 _let_1)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.75/7.07 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.75/7.07 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.75/7.07 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.75/7.07 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.75/7.07 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.75/7.07 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (= (@ tptp.ring_1_of_int_int Y2) _let_1) (= Y2 _let_1)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y2) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y2) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X2))) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y2) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y2) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y2)) (= _let_1 Y2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N) (@ tptp.ring_1_of_int_real Y2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X2))) N) (@ tptp.ring_17405671764205052669omplex Y2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N) (@ tptp.ring_18347121197199848620nteger Y2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N) (@ tptp.ring_1_of_int_rat Y2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y2))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 6.75/7.07 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X2))) (= (@ (@ tptp.times_times_real _let_1) Y2) (@ (@ tptp.times_times_real Y2) _let_1)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) Y2) (@ (@ tptp.times_times_rat Y2) _let_1)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X2))) (= (@ (@ tptp.times_times_int _let_1) Y2) (@ (@ tptp.times_times_int Y2) _let_1)))))
% 6.75/7.07 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.75/7.07 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) X2))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) X2))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X2)) (=> (@ _let_1 X2) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))))
% 6.75/7.07 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2)))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) N) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) D2)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real D2))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y2))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (= (@ tptp.ln_ln_real X2) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (= X2 tptp.one_one_real)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y2))))))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real K)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.75/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)))))
% 6.75/7.07 (assert (= tptp.ord_less_eq_int (lambda ((N3 tptp.int) (M3 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N3)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M3)) tptp.one_one_real)))))
% 6.75/7.07 (assert (= tptp.ord_less_int (lambda ((N3 tptp.int) (M3 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N3)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M3)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D2))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X2)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X2) D2))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X2) D2))) _let_1))))))
% 6.75/7.07 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) Y2)) Y2)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))))
% 6.75/7.07 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2))))))
% 6.75/7.07 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2)))) tptp.one_one_real)))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2))) (@ tptp.uminus_uminus_real X2))))))
% 6.75/7.07 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K)))))
% 6.75/7.07 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ _let_1 K)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)))))))
% 6.75/7.07 (assert (= tptp.artanh_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X4)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X4) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y4)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X4)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X4)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X4) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y4)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X4)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.75/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.times_3573771949741848930nteger A) A)))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.times_times_real A) A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.times_times_rat A) A)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.times_times_int A) A)))))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.75/7.07 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.75/7.07 (assert (forall ((M tptp.real) (K tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M))) (= (@ _let_1 (@ tptp.abs_abs_real K)) (@ _let_1 K)))))
% 6.75/7.07 (assert (forall ((M tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M))) (= (@ _let_1 (@ tptp.abs_abs_int K)) (@ _let_1 K)))))
% 6.75/7.07 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer M))) (= (@ _let_1 (@ tptp.abs_abs_Code_integer K)) (@ _let_1 K)))))
% 6.75/7.07 (assert (forall ((M tptp.rat) (K tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat M))) (= (@ _let_1 (@ tptp.abs_abs_rat K)) (@ _let_1 K)))))
% 6.75/7.07 (assert (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))))
% 6.75/7.07 (assert (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))))
% 6.75/7.07 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.abs_abs_Code_integer M)) K) (@ (@ tptp.dvd_dvd_Code_integer M) K))))
% 6.75/7.07 (assert (forall ((M tptp.rat) (K tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M)) K) (@ (@ tptp.dvd_dvd_rat M) K))))
% 6.75/7.07 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) (@ tptp.tanh_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N)) (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X2)) (@ _let_1 X2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) (or (@ _let_1 A) (= B tptp.zero_zero_real))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) (or (@ _let_1 A) (= B tptp.zero_zero_rat))))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X2))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) (or (not (= A tptp.zero_zero_real)) (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N)) (or (not (= A tptp.zero_zero_rat)) (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N)) (or (not (= A tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((W tptp.num) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1))))))
% 6.75/7.07 (assert (forall ((W tptp.num) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1))))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.75/7.07 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (= (@ tptp.abs_abs_int X2) (@ tptp.abs_abs_int Y2)) (or (= X2 Y2) (= X2 (@ tptp.uminus_uminus_int Y2))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (= (@ tptp.abs_abs_real X2) (@ tptp.abs_abs_real Y2)) (or (= X2 Y2) (= X2 (@ tptp.uminus_uminus_real Y2))))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X2) (@ tptp.abs_abs_Code_integer Y2)) (or (= X2 Y2) (= X2 (@ tptp.uminus1351360451143612070nteger Y2))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (= (@ tptp.abs_abs_rat X2) (@ tptp.abs_abs_rat Y2)) (or (= X2 Y2) (= X2 (@ tptp.uminus_uminus_rat Y2))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 6.75/7.07 (assert (forall ((L tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L) K))))
% 6.75/7.07 (assert (forall ((L tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L) K))))
% 6.75/7.07 (assert (forall ((L tptp.code_integer) (K tptp.code_integer)) (=> (= (@ tptp.abs_abs_Code_integer L) (@ tptp.abs_abs_Code_integer K)) (@ (@ tptp.dvd_dvd_Code_integer L) K))))
% 6.75/7.07 (assert (forall ((L tptp.rat) (K tptp.rat)) (=> (= (@ tptp.abs_abs_rat L) (@ tptp.abs_abs_rat K)) (@ (@ tptp.dvd_dvd_rat L) K))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B))) (let ((_let_2 (@ tptp.abs_abs_Code_integer A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) C) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D2))))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B))) (let ((_let_2 (@ tptp.abs_abs_real A))) (=> (@ (@ tptp.ord_less_real _let_2) C) (=> (@ (@ tptp.ord_less_real _let_1) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D2))))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B))) (let ((_let_2 (@ tptp.abs_abs_rat A))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D2))))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D2))))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 6.75/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))))
% 6.75/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) tptp.one_one_real)))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) E2))) (= X2 tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) E2))) (= X2 tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (or (@ _let_1 B) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X2) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y2)) X2) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y2) X2))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y2)) X2) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y2) X2))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y2)) X2) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y2) X2))))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y2)) X2) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y2) X2))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.abs_abs_real B)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (or (= B A) (= B (@ tptp.uminus_uminus_real A)))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.abs_abs_Code_integer B)) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (or (= B A) (= B (@ tptp.uminus1351360451143612070nteger A)))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.abs_abs_rat B)) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (or (= B A) (= B (@ tptp.uminus_uminus_rat A)))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.abs_abs_int B)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (or (= B A) (= B (@ tptp.uminus_uminus_int A)))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.abs_abs_real A) B) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (or (= A B) (= A (@ tptp.uminus_uminus_real B)))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) B) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B)))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.abs_abs_rat A) B) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (or (= A B) (= A (@ tptp.uminus_uminus_rat B)))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.abs_abs_int A) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (or (= A B) (= A (@ tptp.uminus_uminus_int B)))))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.75/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X2)) Y2) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X2) Y2))))))
% 6.75/7.07 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X2)) Y2) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X2) Y2))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 6.75/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 6.75/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 6.75/7.07 (assert (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))
% 6.75/7.07 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 6.75/7.07 (assert (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))
% 6.75/7.07 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 6.75/7.07 (assert (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))
% 6.75/7.07 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 6.75/7.07 (assert (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))
% 6.75/7.07 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.75/7.07 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.75/7.07 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (A tptp.code_integer) (R tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) A))) R) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R)) X2) (@ (@ tptp.ord_le3102999989581377725nteger X2) (@ (@ tptp.plus_p5714425477246183910nteger A) R))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (A tptp.real) (R tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) A))) R) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R)) X2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real A) R))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (A tptp.rat) (R tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) A))) R) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R)) X2) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat A) R))))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (A tptp.int) (R tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) A))) R) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R)) X2) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.plus_plus_int A) R))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger C) D2)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D2)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat C) D2)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int C) D2)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D2))))))
% 6.75/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.75/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.75/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (A tptp.code_integer) (R tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) A))) R) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R)) X2) (@ (@ tptp.ord_le6747313008572928689nteger X2) (@ (@ tptp.plus_p5714425477246183910nteger A) R))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (A tptp.real) (R tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) A))) R) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R)) X2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real A) R))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (A tptp.rat) (R tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) A))) R) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R)) X2) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat A) R))))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (A tptp.int) (R tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) A))) R) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R)) X2) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.plus_plus_int A) R))))))
% 6.75/7.07 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 6.75/7.07 (assert (forall ((A tptp.real) (X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y4))) D3) (and (@ (@ tptp.ord_less_real A) Y4) (@ (@ tptp.ord_less_real Y4) B))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X2))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X2)))))
% 6.75/7.07 (assert (forall ((N tptp.int) (X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X2)))))
% 6.75/7.07 (assert (forall ((N tptp.int) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 6.75/7.07 (assert (forall ((N tptp.int) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2)))))
% 6.75/7.07 (assert (forall ((N tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X2)))))
% 6.75/7.07 (assert (forall ((N tptp.int) (X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X2)))))
% 6.75/7.07 (assert (forall ((N tptp.int) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X2)))))
% 6.75/7.07 (assert (forall ((N tptp.int) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2)))))
% 6.75/7.07 (assert (forall ((N tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X2)))))
% 6.75/7.07 (assert (forall ((A tptp.real) (X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y4))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y4) (@ (@ tptp.ord_less_eq_real Y4) B))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) (@ tptp.abs_abs_Code_integer Y2)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y2) _let_1))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) (@ tptp.abs_abs_rat Y2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1))))))
% 6.75/7.07 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_int Y2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1))))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X2) tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (= (= (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X2) tptp.one_one_rat))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X2) tptp.one_one_real))))
% 6.75/7.07 (assert (forall ((X2 tptp.int)) (= (= (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X2) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N) (@ (@ tptp.power_power_rat A) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N) (@ (@ tptp.power_power_real A) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N) (@ (@ tptp.power_power_int A) N)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.code_integer) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y2) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y2) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) Y2))))))
% 6.75/7.07 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) Y2))))))
% 6.75/7.07 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) Y2))))))
% 6.75/7.07 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) Y2))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X2 tptp.code_integer)) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X4) (@ (@ P X4) (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_Code_integer X2)) (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X2 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ P X4) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X2 tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (@ (@ P X4) (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_rat X2)) (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.75/7.07 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X2 tptp.int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ (@ P X4) (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X2)) (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat))))
% 6.75/7.07 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat))))
% 6.75/7.07 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X2)) tptp.one_one_int))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real Z3)))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat Z3)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real Z3)))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat Z3)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) X2))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z3)) X2))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_real Y2))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X2) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X2) _let_1)) (= (@ tptp.archim8280529875227126926d_real X2) Y2)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_rat Y2))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X2) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X2) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X2) Y2)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X2) N))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat N)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X2) N))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2))) X2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2))) X2))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X2)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2)))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2)))))
% 6.75/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X2)) (@ _let_1 X2)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 6.75/7.07 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 6.75/7.07 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) (@ tptp.arctan Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) (@ tptp.arctan Y2)))))
% 6.75/7.07 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y2) X2) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X2) Y2)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_int Y2))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X2)) (@ tptp.archim7778729529865785530nd_rat Y2)))))
% 6.75/7.07 (assert (= tptp.abs_abs_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I4)) I4))))
% 6.75/7.07 (assert (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.modulo_modulo_int K) L))) (@ tptp.abs_abs_int L)))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L 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 L))) (@ _let_2 (@ _let_1 L)))))))
% 6.75/7.07 (assert (forall ((K tptp.int) (L 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)) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 6.75/7.07 (assert (forall ((Z tptp.real) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_real Z))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real Z))))) (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real M)))))))
% 6.75/7.07 (assert (forall ((Z tptp.rat) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M)))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I2) (@ (@ tptp.ord_less_nat I2) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I2))) (@ F I2)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I2) (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ F I2) K)))))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X2) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) Z))) tptp.one_one_int)) D2))))))
% 6.75/7.07 (assert (forall ((D2 tptp.int) (X2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D2))) Z)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I2))) (@ F I2)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ F I2) K))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat))) (@ F I2)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ F I2) K))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X2)) (@ tptp.arctan Y2)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X2) Y2)))))))))
% 6.75/7.07 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2))) (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.75/7.07 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2))) (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 6.75/7.07 (assert (forall ((R tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R))) (=> (not (= R tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D2)))))))))
% 6.75/7.07 (assert (forall ((R tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (=> (not (= R tptp.zero_zero_real)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D2)))))))))
% 6.75/7.07 (assert (forall ((R tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R))) (=> (not (= R tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D2)))))))))
% 6.75/7.07 (assert (forall ((R tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R))) (=> (not (= R tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D2)))))))))
% 6.75/7.07 (assert (forall ((R tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int R))) (=> (not (= R tptp.zero_zero_int)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D2)))))))))
% 6.75/7.07 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int M) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N) (@ (@ tptp.plus_plus_int N) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A2)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.pred_numeral N)))))))
% 6.75/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ tptp.pred_numeral N)))))))
% 6.75/7.07 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.75/7.07 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N3 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A4) _let_1)))))))
% 6.75/7.07 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (A4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A4) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A4) _let_1)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N)) (@ _let_1 N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) tptp.one_one_int) tptp.one_one_int)))
% 6.75/7.07 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.75/7.07 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.75/7.07 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A2))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.abs_abs_real (@ F I4)))) A2))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.75/7.07 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.75/7.07 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A2))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.abs_abs_real (@ F I4)))) A2))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1745604003318907178nteger N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N))) _let_1)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q2)) (@ (@ tptp.bit_se2925701944663578781it_nat N) Q2)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) B)) (@ _let_1 B)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int) (R tptp.int) (S tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ tptp.bit_concat_bit N))) (= (= (@ (@ _let_2 K) L) (@ (@ _let_2 R) S)) (and (= (@ _let_1 K) (@ _let_1 R)) (= L S)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.75/7.07 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) K5)) (@ (@ tptp.groups1300246762558778688al_rat G) K5)))))
% 6.75/7.07 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K5)) (@ (@ tptp.groups2906978787729119204at_rat G) K5)))))
% 6.75/7.07 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G) K5)))))
% 6.75/7.07 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K5)) (@ (@ tptp.groups1935376822645274424al_nat G) K5)))))
% 6.75/7.07 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G) K5)))))
% 6.75/7.07 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K5)) (@ (@ tptp.groups1932886352136224148al_int G) K5)))))
% 6.75/7.07 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K5)) (@ (@ tptp.groups3539618377306564664at_int G) K5)))))
% 6.75/7.07 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4538972089207619220nt_int F) K5)) (@ (@ tptp.groups4538972089207619220nt_int G) K5)))))
% 6.75/7.07 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) K5)) (@ (@ tptp.groups3542108847815614940at_nat G) K5)))))
% 6.75/7.07 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K5) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) K5)) (@ (@ tptp.groups6591440286371151544t_real G) K5)))))
% 6.75/7.07 (assert (forall ((R tptp.int) (F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.times_times_int R) (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N3 tptp.int)) (@ (@ tptp.times_times_int R) (@ F N3)))) A2))))
% 6.75/7.07 (assert (forall ((R tptp.complex) (F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.times_times_complex R) (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N3 tptp.complex)) (@ (@ tptp.times_times_complex R) (@ F N3)))) A2))))
% 6.75/7.07 (assert (forall ((R tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_nat R) (@ F N3)))) A2))))
% 6.75/7.07 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_real R) (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real R) (@ F N3)))) A2))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (R tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) R) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N3 tptp.int)) (@ (@ tptp.times_times_int (@ F N3)) R))) A2))))
% 6.75/7.07 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F N3)) R))) A2))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (R tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) R) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F N3)) R))) A2))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) R))) A2))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (G (-> tptp.int tptp.int)) (B4 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) B4)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I4)) (@ G J3)))) B4))) A2))))
% 6.75/7.07 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B4 tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) B4)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I4 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I4)) (@ G J3)))) B4))) A2))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B4 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) B4)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I4)) (@ G J3)))) B4))) A2))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (B4 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) B4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I4)) (@ G J3)))) B4))) A2))))
% 6.75/7.07 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A2)) (@ (@ tptp.groups4538972089207619220nt_int H2) A2)))))
% 6.75/7.07 (assert (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A2)) (@ (@ tptp.groups7754918857620584856omplex H2) A2)))))
% 6.75/7.07 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A2)) (@ (@ tptp.groups3542108847815614940at_nat H2) A2)))))
% 6.75/7.07 (assert (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A2)) (@ (@ tptp.groups6591440286371151544t_real H2) A2)))))
% 6.75/7.07 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N3)) R))) A2))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N3)) R))) A2))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) A))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) A))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_real (@ F X4)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_real (@ F X4)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) tptp.zero_zero_real))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) tptp.zero_zero_rat))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_nat (@ F X4)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_nat (@ F X4)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) tptp.zero_zero_nat))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_int (@ F X4)) tptp.zero_zero_int))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) A2)) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_int (@ F X4)) tptp.zero_zero_int))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_int (@ F X4)) tptp.zero_zero_int))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) A2)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) A2)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1932886352136224148al_int F) A2)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups3539618377306564664at_int F) A2)))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int F) A2)))))
% 6.75/7.07 (assert (forall ((F (-> tptp.real tptp.rat)) (I5 tptp.set_real) (G (-> tptp.real tptp.rat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) I5) (@ (@ tptp.groups1300246762558778688al_rat G) I5)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G I))))))))
% 6.75/7.07 (assert (forall ((F (-> tptp.nat tptp.rat)) (I5 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) I5) (@ (@ tptp.groups2906978787729119204at_rat G) I5)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_nat I) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I) (@ G I))))))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.rat)) (I5 tptp.set_int) (G (-> tptp.int tptp.rat)) (I tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) I5) (@ (@ tptp.groups3906332499630173760nt_rat G) I5)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_int I) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I) (@ G I))))))))
% 6.75/7.07 (assert (forall ((F (-> tptp.complex tptp.rat)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) I5) (@ (@ tptp.groups5058264527183730370ex_rat G) I5)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G I))))))))
% 6.75/7.07 (assert (forall ((F (-> tptp.extended_enat tptp.rat)) (I5 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.rat)) (I tptp.extended_enat)) (=> (= (@ (@ tptp.groups1392844769737527556at_rat F) I5) (@ (@ tptp.groups1392844769737527556at_rat G) I5)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_Extended_enat I) I5) (=> (@ tptp.finite4001608067531595151d_enat I5) (= (@ F I) (@ G I))))))))
% 6.75/7.07 (assert (forall ((F (-> tptp.real tptp.nat)) (I5 tptp.set_real) (G (-> tptp.real tptp.nat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) I5) (@ (@ tptp.groups1935376822645274424al_nat G) I5)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G I))))))))
% 6.75/7.07 (assert (forall ((F (-> tptp.int tptp.nat)) (I5 tptp.set_int) (G (-> tptp.int tptp.nat)) (I tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I5) (@ (@ tptp.groups4541462559716669496nt_nat G) I5)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_int I) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I) (@ G I))))))))
% 6.75/7.07 (assert (forall ((F (-> tptp.complex tptp.nat)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) I5) (@ (@ tptp.groups5693394587270226106ex_nat G) I5)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G I))))))))
% 6.75/7.07 (assert (forall ((F (-> tptp.extended_enat tptp.nat)) (I5 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (I tptp.extended_enat)) (=> (= (@ (@ tptp.groups2027974829824023292at_nat F) I5) (@ (@ tptp.groups2027974829824023292at_nat G) I5)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_Extended_enat I) I5) (=> (@ tptp.finite4001608067531595151d_enat I5) (= (@ F I) (@ G I))))))))
% 6.75/7.07 (assert (forall ((F (-> tptp.real tptp.int)) (I5 tptp.set_real) (G (-> tptp.real tptp.int)) (I tptp.real)) (=> (= (@ (@ tptp.groups1932886352136224148al_int F) I5) (@ (@ tptp.groups1932886352136224148al_int G) I5)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G I))))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ _let_1 tptp.zero_zero_int)))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N) M)) _let_2) _let_1) A))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 6.75/7.07 (assert (forall ((S tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I (-> tptp.int tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.75/7.07 (assert (forall ((S tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.75/7.07 (assert (forall ((S tptp.set_int) (T tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (I (-> tptp.extended_enat tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S)) (@ (@ tptp.groups4148127829035722712t_real G) T))))))))
% 6.75/7.07 (assert (forall ((S tptp.set_complex) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.75/7.07 (assert (forall ((S tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.75/7.07 (assert (forall ((S tptp.set_complex) (T tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (I (-> tptp.extended_enat tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups4148127829035722712t_real G) T))))))))
% 6.75/7.07 (assert (forall ((S tptp.set_Extended_enat) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I (-> tptp.int tptp.extended_enat)) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) S)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.75/7.07 (assert (forall ((S tptp.set_Extended_enat) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.extended_enat)) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) S)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.75/7.07 (assert (forall ((S tptp.set_Extended_enat) (T tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (I (-> tptp.extended_enat tptp.extended_enat)) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) S)) (@ (@ tptp.groups4148127829035722712t_real G) T))))))))
% 6.75/7.07 (assert (forall ((S tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X4)))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F) A2) tptp.zero_zero_real) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) A2) (= (@ F X) tptp.zero_zero_real))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F) A2) tptp.zero_zero_real) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A2) (= (@ F X) tptp.zero_zero_real))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F) A2) tptp.zero_zero_real) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A2) (= (@ F X) tptp.zero_zero_real))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups4148127829035722712t_real F) A2) tptp.zero_zero_real) (forall ((X tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ F X) tptp.zero_zero_real))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups1300246762558778688al_rat F) A2) tptp.zero_zero_rat) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) A2) (= (@ F X) tptp.zero_zero_rat))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F) A2) tptp.zero_zero_rat) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A2) (= (@ F X) tptp.zero_zero_rat))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F) A2) tptp.zero_zero_rat) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A2) (= (@ F X) tptp.zero_zero_rat))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups5058264527183730370ex_rat F) A2) tptp.zero_zero_rat) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A2) (= (@ F X) tptp.zero_zero_rat))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups1392844769737527556at_rat F) A2) tptp.zero_zero_rat) (forall ((X tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ F X) tptp.zero_zero_rat))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (= (= (@ (@ tptp.groups1935376822645274424al_nat F) A2) tptp.zero_zero_nat) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) A2) (= (@ F X) tptp.zero_zero_nat))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G X4)))) (=> (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_real (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G X4)))) (=> (exists ((X6 tptp.complex)) (and (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_real (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G X4)))) (=> (exists ((X6 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X6) A2) (@ (@ tptp.ord_less_real (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups4148127829035722712t_real F) A2)) (@ (@ tptp.groups4148127829035722712t_real G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G X4)))) (=> (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A2) (@ (@ tptp.ord_less_rat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G X4)))) (=> (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_rat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G X4)))) (=> (exists ((X6 tptp.complex)) (and (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_rat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (G (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G X4)))) (=> (exists ((X6 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X6) A2) (@ (@ tptp.ord_less_rat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1392844769737527556at_rat F) A2)) (@ (@ tptp.groups1392844769737527556at_rat G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ G X4)))) (=> (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_nat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ G X4)))) (=> (exists ((X6 tptp.complex)) (and (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_nat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ G X4)))) (=> (exists ((X6 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X6) A2) (@ (@ tptp.ord_less_nat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups2027974829824023292at_nat F) A2)) (@ (@ tptp.groups2027974829824023292at_nat G) A2)))))))
% 6.75/7.07 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R2 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X22) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups2073611262835488442omplex H2) S3)) (@ (@ tptp.groups2073611262835488442omplex G) S3))))))))
% 6.75/7.07 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ (@ R2 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X22) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups3049146728041665814omplex H2) S3)) (@ (@ tptp.groups3049146728041665814omplex G) S3))))))))
% 6.75/7.07 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.complex)) (G (-> tptp.extended_enat tptp.complex))) (=> (@ (@ R2 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X22) Y23)))) (=> (@ tptp.finite4001608067531595151d_enat S3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups6818542070133387226omplex H2) S3)) (@ (@ tptp.groups6818542070133387226omplex G) S3))))))))
% 6.75/7.07 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R2 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X22) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups8778361861064173332t_real H2) S3)) (@ (@ tptp.groups8778361861064173332t_real G) S3))))))))
% 6.75/7.07 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R2 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X22) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups5808333547571424918x_real H2) S3)) (@ (@ tptp.groups5808333547571424918x_real G) S3))))))))
% 6.75/7.07 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ (@ R2 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X22) Y23)))) (=> (@ tptp.finite4001608067531595151d_enat S3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups4148127829035722712t_real H2) S3)) (@ (@ tptp.groups4148127829035722712t_real G) S3))))))))
% 6.75/7.07 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R2 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X22) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups2906978787729119204at_rat H2) S3)) (@ (@ tptp.groups2906978787729119204at_rat G) S3))))))))
% 6.75/7.07 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R2 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X22) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups3906332499630173760nt_rat H2) S3)) (@ (@ tptp.groups3906332499630173760nt_rat G) S3))))))))
% 6.75/7.07 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ (@ R2 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X22) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups5058264527183730370ex_rat H2) S3)) (@ (@ tptp.groups5058264527183730370ex_rat G) S3))))))))
% 6.75/7.07 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.rat)) (G (-> tptp.extended_enat tptp.rat))) (=> (@ (@ R2 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X22) Y23)))) (=> (@ tptp.finite4001608067531595151d_enat S3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups1392844769737527556at_rat H2) S3)) (@ (@ tptp.groups1392844769737527556at_rat G) S3))))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) (@ (@ tptp.groups8097168146408367636l_real G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups4148127829035722712t_real F) A2)) (@ (@ tptp.groups4148127829035722712t_real G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) (@ (@ tptp.groups1300246762558778688al_rat G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (G (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1392844769737527556at_rat F) A2)) (@ (@ tptp.groups1392844769737527556at_rat G) A2)))))))
% 6.75/7.07 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_nat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2)))))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) A)) (@ _let_1 A))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.real)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups4148127829035722712t_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_Extended_enat I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.rat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.rat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups1392844769737527556at_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_Extended_enat I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.nat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_nat)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.real)) (B4 tptp.real) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S) B4) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B4)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (B4 tptp.real) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S) B4) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B4)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (B4 tptp.real) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S) B4) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B4)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (B4 tptp.real) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups4148127829035722712t_real F) S) B4) (=> (@ (@ tptp.member_Extended_enat I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B4)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.rat)) (B4 tptp.rat) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S) B4) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B4)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B4 tptp.rat) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S) B4) (=> (@ (@ tptp.member_nat I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B4)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.rat)) (B4 tptp.rat) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S) B4) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B4)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.rat)) (B4 tptp.rat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S) B4) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B4)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (B4 tptp.rat) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups1392844769737527556at_rat F) S) B4) (=> (@ (@ tptp.member_Extended_enat I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B4)))))))
% 6.75/7.07 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.nat)) (B4 tptp.nat) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S) B4) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B4)))))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat N) (@ tptp.bit_se2002935070580805687sk_nat N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) (@ tptp.bit_se2000444600071755411sk_int N)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite4001608067531595151d_enat I5) (=> (@ (@ tptp.member_Extended_enat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups4148127829035722712t_real F) I5)))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite4001608067531595151d_enat I5) (=> (@ (@ tptp.member_Extended_enat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1392844769737527556at_rat F) I5)))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F) I5)))))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat I5) (=> (not (= I5 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups4148127829035722712t_real F) I5)))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat I5) (=> (not (= I5 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1392844769737527556at_rat F) I5)))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) I5)))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B4) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B4) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B4) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (A4 tptp.int)) (@ (@ tptp.modulo_modulo_int A4) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 6.75/7.07 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (A4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B2)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B2)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B2)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (=> (@ tptp.finite4001608067531595151d_enat B4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B4) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B2)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat F))) (=> (@ tptp.finite4001608067531595151d_enat B4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B4) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M))))
% 6.75/7.07 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.07 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.modulo_modulo_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 6.75/7.07 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) A))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) A))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) A))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B4) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) B4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B4) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) B4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) B4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (=> (@ tptp.finite4001608067531595151d_enat B4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B4) (=> (@ (@ tptp.member_Extended_enat B) (@ (@ tptp.minus_925952699566721837d_enat B4) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) B4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B4) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) B4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B4) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) B4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) B4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat F))) (=> (@ tptp.finite4001608067531595151d_enat B4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B4) (=> (@ (@ tptp.member_Extended_enat B) (@ (@ tptp.minus_925952699566721837d_enat B4) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) B4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B4) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) B4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.75/7.07 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B4) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) B4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.75/7.07 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.07 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.code_integer)) (A (-> tptp.real tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I4 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I4 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.75/7.07 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X2 I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X2) I5) tptp.one_one_real) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I4 tptp.real)) (@ (@ tptp.times_times_real (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X2 I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X2) I5) tptp.one_one_real) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I4 tptp.int)) (@ (@ tptp.times_times_real (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X2) I5) tptp.one_one_rat) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I4 tptp.real)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X2) I5) tptp.one_one_rat) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.rat)) (A (-> tptp.int tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I2)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat X2) I5) tptp.one_one_rat) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((I4 tptp.int)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.int)) (A (-> tptp.real tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X2 I2)))) (=> (= (@ (@ tptp.groups1932886352136224148al_int X2) I5) tptp.one_one_int) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups1932886352136224148al_int (lambda ((I4 tptp.real)) (@ (@ tptp.times_times_int (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.int)) (A (-> tptp.nat tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X2 I2)))) (=> (= (@ (@ tptp.groups3539618377306564664at_int X2) I5) tptp.one_one_int) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N)) (= N tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N)) (= N tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N)) (= N tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.75/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_complex (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_complex (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_real (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_rat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_nat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_int (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.75/7.08 (assert (forall ((W tptp.complex) (Y2 tptp.complex) (X2 tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X2))) (let ((_let_2 (@ tptp.times_times_complex W))) (= (= (@ (@ tptp.plus_plus_complex (@ _let_2 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_complex (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X2) (= Y2 Z)))))))
% 6.75/7.08 (assert (forall ((W tptp.real) (Y2 tptp.real) (X2 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X2))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X2) (= Y2 Z)))))))
% 6.75/7.08 (assert (forall ((W tptp.rat) (Y2 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X2))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X2) (= Y2 Z)))))))
% 6.75/7.08 (assert (forall ((W tptp.nat) (Y2 tptp.nat) (X2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X2))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X2) (= Y2 Z)))))))
% 6.75/7.08 (assert (forall ((W tptp.int) (Y2 tptp.int) (X2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X2))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X2) (= Y2 Z)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K)))))
% 6.75/7.08 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 6.75/7.08 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))))
% 6.75/7.08 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))))
% 6.75/7.08 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))))
% 6.75/7.08 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 6.75/7.08 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N3)) (@ (@ tptp.plus_plus_int K2) _let_1))) _let_1)))))
% 6.75/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer))))))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int))))))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat))))))))))
% 6.75/7.08 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))))
% 6.75/7.08 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X23)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.75/7.08 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ 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 L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_int)) (= (not (@ tptp.finite_finite_int S3)) (forall ((M3 tptp.int)) (exists ((N3 tptp.int)) (and (@ (@ tptp.ord_less_int M3) (@ tptp.abs_abs_int N3)) (@ (@ tptp.member_int N3) S3)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.75/7.08 (assert (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 6.75/7.08 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K2 tptp.zero_zero_int) (= L2 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K2 _let_2)) L2) (@ (@ (@ tptp.if_int (= L2 _let_2)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.75/7.08 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.pow K) L)))))
% 6.75/7.08 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_real (@ (@ tptp.pow K) L)))))
% 6.75/7.08 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_rat (@ (@ tptp.pow K) L)))))
% 6.75/7.08 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ (@ tptp.pow K) L)))))
% 6.75/7.08 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ (@ tptp.pow K) L)))))
% 6.75/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)))
% 6.75/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) B) _let_1))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B))) (= (@ (@ tptp.bit_se727722235901077358nd_nat _let_1) B) _let_1))))
% 6.75/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.75/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.75/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.75/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.75/7.08 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X2) tptp.zero_zero_int)))
% 6.75/7.08 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.08 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.75/7.08 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.75/7.08 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X2)))
% 6.75/7.08 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X2) (@ tptp.uminus_uminus_int tptp.one_one_int)) X2)))
% 6.75/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 6.75/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 6.75/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 6.75/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (or (@ _let_1 K) (@ _let_1 L))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) tptp.one_one_int) tptp.one_one_int)))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) tptp.one_one_nat) tptp.one_one_nat)))
% 6.75/7.08 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y2))) tptp.one_one_int)))
% 6.75/7.08 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) tptp.one_one_nat)))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.exp_real (@ tptp.ln_ln_real X2)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X2)) X2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.75/7.08 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y2))) tptp.zero_zero_int)))
% 6.75/7.08 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) tptp.zero_zero_nat)))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y2))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M))))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc M))))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc M))))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc M))))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc M))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.inc M)))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.inc M)))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.inc M)))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int) tptp.one_one_int)))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int)))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A2) tptp.zero_zero_complex))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A2) tptp.zero_zero_rat))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A2) tptp.zero_zero_real))))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y2))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y2))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y2))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.zero_zero_int)))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D2 (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D2 I4)))) A2) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D2 tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D2 I4)))) A2) tptp.zero_zero_complex))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat)) (D2 (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D2 I4)))) A2) (@ (@ tptp.divide_divide_rat (@ C tptp.zero_zero_nat)) (@ D2 tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D2 I4)))) A2) tptp.zero_zero_rat))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D2 (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D2 I4)))) A2) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D2 tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D2 I4)))) A2) tptp.zero_zero_real))))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y2))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y2)))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L)))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int B) C))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat B) C))))))
% 6.75/7.08 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B3) A4))))
% 6.75/7.08 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B3) A4))))
% 6.75/7.08 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int B))) (let ((_let_2 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat B))) (let ((_let_2 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.75/7.08 (assert (forall ((A2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex A2))) (= (@ (@ tptp.times_times_complex _let_1) A2) (@ (@ tptp.times_times_complex A2) _let_1)))))
% 6.75/7.08 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.exp_real A2))) (= (@ (@ tptp.times_times_real _let_1) A2) (@ (@ tptp.times_times_real A2) _let_1)))))
% 6.75/7.08 (assert (forall ((P (-> tptp.num Bool)) (X2 tptp.num)) (=> (@ P tptp.one) (=> (forall ((X4 tptp.num)) (=> (@ P X4) (@ P (@ tptp.inc X4)))) (@ P X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X2))) (= (@ _let_1 (@ tptp.inc Y2)) (@ tptp.inc (@ _let_1 Y2))))))
% 6.75/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (= (@ (@ tptp.bit_se3949692690581998587nteger A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X2))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (exists ((X4 tptp.real)) (= (@ tptp.exp_real X4) Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X2) Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y2)) X2))))
% 6.75/7.08 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y2)) Y2))))
% 6.75/7.08 (assert (forall ((Y2 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y2) Ya)) Z)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y2)) Z)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y2)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X2) Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X2) Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X2) Y2) (@ (@ tptp.times_times_complex Y2) X2)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X2) Y2)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (= (@ (@ tptp.times_times_real X2) Y2) (@ (@ tptp.times_times_real Y2) X2)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X2) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2)))))
% 6.75/7.08 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (A4 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A4) (@ tptp.bit_se2000444600071755411sk_int N3)))))
% 6.75/7.08 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (A4 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A4) (@ tptp.bit_se2002935070580805687sk_nat N3)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_option_nat) (G (-> tptp.option_nat tptp.nat)) (F (-> tptp.option_nat tptp.nat))) (=> (forall ((X4 tptp.option_nat)) (=> (@ (@ tptp.member_option_nat X4) A2) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups1921984841883549356at_nat (lambda ((X tptp.option_nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1921984841883549356at_nat F) A2)) (@ (@ tptp.groups1921984841883549356at_nat G) A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_set_nat_rat) (G (-> tptp.set_nat_rat tptp.nat)) (F (-> tptp.set_nat_rat tptp.nat))) (=> (forall ((X4 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X4) A2) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups207172935752626313at_nat (lambda ((X tptp.set_nat_rat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups207172935752626313at_nat F) A2)) (@ (@ tptp.groups207172935752626313at_nat G) A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.pow X2) tptp.one) X2)))
% 6.75/7.08 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X2)) (@ tptp.bit0 (@ tptp.inc X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X2)) (@ tptp.bit1 X2))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) tptp.one_one_nat) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) A2) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) A2) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.one_one_nat) (exists ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A2) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.complex)) (=> (@ (@ tptp.member_complex Y) A2) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2027974829824023292at_nat F) A2) tptp.one_one_nat) (exists ((X tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X) A2) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y) A2) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) tptp.one_one_nat) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A2) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A2) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.plus_plus_num X2) tptp.one) (@ tptp.inc X2))))
% 6.75/7.08 (assert (forall ((Y2 tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_int Y2) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y2)) Z)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_int Y2) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y2) Ya)) Z)))))
% 6.75/7.08 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) K))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2))) tptp.one_one_real)))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2))) tptp.one_one_complex)))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.times_times_num X2))) (= (@ _let_1 (@ tptp.inc Y2)) (@ (@ tptp.plus_plus_num (@ _let_1 Y2)) X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I5))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X2) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I5))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_int X2) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I5))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C)))) tptp.zero_zero_complex))))
% 6.75/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se3949692690581998587nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.complex)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (or (@ _let_1 K) (@ _let_1 L))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_complex (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_complex (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y2)) X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X2)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X2)) tptp.one_one_complex))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X2)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X2)) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X2)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X2)) tptp.one_one_rat))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X2)) tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X2)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X2)) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups2073611262835488442omplex G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_complex (@ G M)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_complex (@ F _let_1)) (@ F M)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 6.75/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.one_one_int) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.one_one_nat) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.complex)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_complex (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.75/7.08 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X)))) (let ((_let_2 (@ tptp.exp_real X))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.75/7.08 (assert (= tptp.tanh_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))) (let ((_let_2 (@ tptp.exp_complex X))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1))) _let_1)))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) Z)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.75/7.08 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) Z)) (@ (@ tptp.power_power_real (@ tptp.exp_real Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_complex (@ F N)) (@ F M))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F M))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F M))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F M))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.complex)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_complex (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M4) (exists ((N7 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N7) (@ (@ tptp.member_nat N7) S3))))) (not (@ tptp.finite_finite_nat S3)))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M3 tptp.nat)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (@ (@ tptp.member_nat N3) S3)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M3 tptp.nat)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.member_nat N3) S3)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 6.75/7.08 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 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))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X2))))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (D2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I4) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D2)))) _let_1)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X2)) (not (@ _let_2 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X2) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa2) Y2) (and (=> _let_5 (= Y2 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y2 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X2) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 6.75/7.08 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 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 K2)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K2) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X2 tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X2)))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X2 tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X2)))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X2 tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.log _let_1) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X2)))))))
% 6.75/7.08 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K2)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N3))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N)) (= M N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) (@ tptp.semiri681578069525770553at_rat N)) (= M N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat M) (@ tptp.semiri4216267220026989637d_enat N)) (= M N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.75/7.08 (assert (= (@ tptp.bit_se1146084159140164899it_int tptp.zero_zero_int) tptp.bot_bot_nat_o))
% 6.75/7.08 (assert (= (@ tptp.bit_se1148574629649215175it_nat tptp.zero_zero_nat) tptp.bot_bot_nat_o))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((U tptp.real) (Deg tptp.nat) (T tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (=> (= U (@ (@ tptp.power_power_real _let_1) Deg)) (=> (@ (@ tptp.vEBT_invar_vebt T) Deg) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_VEBT_height T))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ _let_2 (@ _let_2 U))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat M) tptp.zero_z5237406670263579293d_enat) (= M tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (@ tptp.semiri4216267220026989637d_enat N)) (= tptp.zero_zero_nat N))))
% 6.75/7.08 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.75/7.08 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.75/7.08 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.75/7.08 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.75/7.08 (assert (= (@ tptp.semiri4216267220026989637d_enat tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4216267220026989637d_enat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.numeral_numeral_nat N)) (@ tptp.numera1916890842035813515d_enat N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4216267220026989637d_enat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4216267220026989637d_enat N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat N) tptp.one_on7984719198319812577d_enat) (= N tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.semiri4216267220026989637d_enat N)) (= N tptp.one_one_nat))))
% 6.75/7.08 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.75/7.08 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.75/7.08 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.75/7.08 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.75/7.08 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.75/7.08 (assert (= (@ tptp.semiri4216267220026989637d_enat tptp.one_one_nat) tptp.one_on7984719198319812577d_enat))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4216267220026989637d_enat N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat M)) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.semiri4216267220026989637d_enat M)) N))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W) (@ tptp.semiri681578069525770553at_rat X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.semiri4216267220026989637d_enat B)) W) (@ tptp.semiri4216267220026989637d_enat X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X2) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X2) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X2) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X2) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat X2) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat X2) (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.semiri4216267220026989637d_enat B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.75/7.08 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.75/7.08 (assert (forall ((P Bool)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.75/7.08 (assert (forall ((P Bool)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n1046097342994218471d_enat P))))
% 6.75/7.08 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.75/7.08 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.semiri4216267220026989637d_enat M)) tptp.zero_z5237406670263579293d_enat) (= M tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.suc M)) (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.semiri4216267220026989637d_enat M)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) tptp.zero_zero_nat)))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (X2 tptp.extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X2) A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat W)))))
% 6.75/7.08 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.75/7.08 (assert (forall ((N tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) M))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X2) (= (@ _let_2 (@ (@ tptp.log A) X2)) (@ _let_1 X2))))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_real A) X2)))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) A))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_real X2) Y2)))))))))
% 6.75/7.08 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) A) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.semiri4216267220026989637d_enat N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.75/7.08 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) tptp.one_one_nat)))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y2) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y2) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.nat) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y2) _let_1) (= Y2 _let_1)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y2) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat Y2) (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat X2)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N) (@ tptp.semiri8010041392384452111omplex Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) (@ tptp.semiri1314217659103216013at_int Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N) (@ tptp.semiri5074537144036343181t_real Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y2)) (= _let_1 Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N) (@ tptp.semiri681578069525770553at_rat Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat X2)) N) (@ tptp.semiri4216267220026989637d_enat Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2)))))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) A))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_eq_real A) X2))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.power_power_real A) B)) (@ tptp.semiri5074537144036343181t_real B))))))
% 6.75/7.08 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N)))))
% 6.75/7.08 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N)))))
% 6.75/7.08 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N))))
% 6.75/7.08 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N)))))
% 6.75/7.08 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N)))))
% 6.75/7.08 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X2)) N)) (or (@ _let_1 X2) (= N tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 6.75/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))))
% 6.75/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)))))
% 6.75/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N)))))
% 6.75/7.08 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) _let_1) (@ (@ tptp.ord_less_nat X2) _let_1)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.75/7.08 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 6.75/7.08 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 6.75/7.08 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X2)) (@ _let_1 X2)))))
% 6.75/7.08 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) _let_1) (@ (@ tptp.ord_less_eq_nat X2) _let_1)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.75/7.08 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 6.75/7.08 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 6.75/7.08 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X2)) (@ _let_1 X2)))))
% 6.75/7.08 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 6.75/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.modulo_modulo_int A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.semiri1314217659103216013at_int M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.semiri1316708129612266289at_nat M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))) (= _let_1 _let_1))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N2)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) B)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B) N))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N2)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) B)) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B) N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat X2) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X2))) (= (@ (@ tptp.times_times_int _let_1) Y2) (@ (@ tptp.times_times_int Y2) _let_1)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X2))) (= (@ (@ tptp.times_times_real _let_1) Y2) (@ (@ tptp.times_times_real Y2) _let_1)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X2))) (= (@ (@ tptp.times_times_nat _let_1) Y2) (@ (@ tptp.times_times_nat Y2) _let_1)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) Y2) (@ (@ tptp.times_times_rat Y2) _let_1)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Y2 tptp.extended_enat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat X2))) (= (@ (@ tptp.times_7803423173614009249d_enat _let_1) Y2) (@ (@ tptp.times_7803423173614009249d_enat Y2) _let_1)))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int A) B)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B) N)))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) N) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B) N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L) N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se4203085406695923979it_int M) A)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N) (not (= M N))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) N) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (not (= M N))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B) _let_1)))))))
% 6.75/7.08 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X2)) (@ _let_1 X2)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X2))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X2))))
% 6.75/7.08 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N)) X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X2)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X2)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N) (= N tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N) (= N tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N)))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.semiri4216267220026989637d_enat N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M)) tptp.zero_z5237406670263579293d_enat))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M) A)) N) (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) A)) N) (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.suc N)) tptp.zero_z5237406670263579293d_enat))))
% 6.75/7.08 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.zero_n356916108424825756nteger B)) N) (and B (= N tptp.zero_zero_nat)))))
% 6.75/7.08 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B)) N) (and B (= N tptp.zero_zero_nat)))))
% 6.75/7.08 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B)) N) (and B (= N tptp.zero_zero_nat)))))
% 6.75/7.08 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4216267220026989637d_enat N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4216267220026989637d_enat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.08 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I)) (@ tptp.semiri5074537144036343181t_real J)))))
% 6.75/7.08 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.semiri4216267220026989637d_enat I)) (@ tptp.semiri4216267220026989637d_enat J)))))
% 6.75/7.08 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I)) (@ tptp.semiri681578069525770553at_rat J)))))
% 6.75/7.08 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I)) (@ tptp.semiri1316708129612266289at_nat J)))))
% 6.75/7.08 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.75/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) A) (@ (@ tptp.bit_se2923211474154528505it_int N) A)))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.75/7.08 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.75/7.08 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.08 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N))) Z))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X2) Y2)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X2)) (@ tptp.semiri1314217659103216013at_int Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X2) Y2)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.semiri5074537144036343181t_real Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X2) Y2)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ tptp.semiri1316708129612266289at_nat Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.ord_max_nat X2) Y2)) (@ (@ tptp.ord_max_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ tptp.semiri681578069525770553at_rat Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X2) Y2)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X2)) (@ tptp.semiri4216267220026989637d_enat Y2)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N) M)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 6.75/7.08 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.75/7.08 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat Y2) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) X2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool)) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((X4 tptp.vEBT_VEBT) (S4 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S4) (=> (forall ((Y4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_VEBT_VEBT X4) S4)))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X4 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.member_real Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X4) S4)))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X4 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X4) S4)))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X4 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X4) S4)))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X4 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X4) S4)))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool)) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat S3) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X4 tptp.extended_enat) (S4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S4) (=> (forall ((Y4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_Extended_enat X4) S4)))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool)) (F (-> tptp.vEBT_VEBT tptp.num))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((X4 tptp.vEBT_VEBT) (S4 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S4) (=> (forall ((Y4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_VEBT_VEBT X4) S4)))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X4 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.member_real Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X4) S4)))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X4 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X4) S4)))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.num))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X4 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X4) S4)))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B2 tptp.extended_enat) (A7 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A7) (=> (forall ((X6 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X6) A7) (@ (@ tptp.ord_le72135733267957522d_enat B2) X6))) (=> (@ P A7) (@ P (@ (@ tptp.insert_Extended_enat B2) A7)))))) (@ P A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B2 tptp.real) (A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A7) (@ (@ tptp.ord_less_real B2) X6))) (=> (@ P A7) (@ P (@ (@ tptp.insert_real B2) A7)))))) (@ P A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A2) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B2 tptp.rat) (A7 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A7) (=> (forall ((X6 tptp.rat)) (=> (@ (@ tptp.member_rat X6) A7) (@ (@ tptp.ord_less_rat B2) X6))) (=> (@ P A7) (@ P (@ (@ tptp.insert_rat B2) A7)))))) (@ P A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B2 tptp.num) (A7 tptp.set_num)) (=> (@ tptp.finite_finite_num A7) (=> (forall ((X6 tptp.num)) (=> (@ (@ tptp.member_num X6) A7) (@ (@ tptp.ord_less_num B2) X6))) (=> (@ P A7) (@ P (@ (@ tptp.insert_num B2) A7)))))) (@ P A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B2 tptp.nat) (A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A7) (@ (@ tptp.ord_less_nat B2) X6))) (=> (@ P A7) (@ P (@ (@ tptp.insert_nat B2) A7)))))) (@ P A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B2 tptp.int) (A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A7) (@ (@ tptp.ord_less_int B2) X6))) (=> (@ P A7) (@ P (@ (@ tptp.insert_int B2) A7)))))) (@ P A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B2 tptp.extended_enat) (A7 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A7) (=> (forall ((X6 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X6) A7) (@ (@ tptp.ord_le72135733267957522d_enat X6) B2))) (=> (@ P A7) (@ P (@ (@ tptp.insert_Extended_enat B2) A7)))))) (@ P A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B2 tptp.real) (A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A7) (@ (@ tptp.ord_less_real X6) B2))) (=> (@ P A7) (@ P (@ (@ tptp.insert_real B2) A7)))))) (@ P A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A2) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B2 tptp.rat) (A7 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A7) (=> (forall ((X6 tptp.rat)) (=> (@ (@ tptp.member_rat X6) A7) (@ (@ tptp.ord_less_rat X6) B2))) (=> (@ P A7) (@ P (@ (@ tptp.insert_rat B2) A7)))))) (@ P A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B2 tptp.num) (A7 tptp.set_num)) (=> (@ tptp.finite_finite_num A7) (=> (forall ((X6 tptp.num)) (=> (@ (@ tptp.member_num X6) A7) (@ (@ tptp.ord_less_num X6) B2))) (=> (@ P A7) (@ P (@ (@ tptp.insert_num B2) A7)))))) (@ P A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B2 tptp.nat) (A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A7) (@ (@ tptp.ord_less_nat X6) B2))) (=> (@ P A7) (@ P (@ (@ tptp.insert_nat B2) A7)))))) (@ P A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B2 tptp.int) (A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A7) (@ (@ tptp.ord_less_int X6) B2))) (=> (@ P A7) (@ P (@ (@ tptp.insert_int B2) A7)))))) (@ P A2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) X2)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X2)) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2)) (@ (@ tptp.power_power_real (@ tptp.exp_real X2)) N))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X2) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X2)) N))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X2) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.exp_real X2)) N))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A2)))) (let ((_let_4 (@ (@ tptp.member_real X2) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A2)))) (let ((_let_4 (@ (@ tptp.member_int X2) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (X2 tptp.extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Extended_enat X2) A2)))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X2) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A2)))) (let ((_let_4 (@ (@ tptp.member_real X2) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X2) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X2) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A2)))) (let ((_let_4 (@ (@ tptp.member_int X2) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (forall ((Y4 tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X2)))))))
% 6.75/7.08 (assert (forall ((M tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2)))))
% 6.75/7.08 (assert (= tptp.ord_less_int (lambda ((W2 tptp.int) (Z2 tptp.int)) (exists ((N3 tptp.nat)) (= Z2 (@ (@ tptp.plus_plus_int W2) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 6.75/7.08 (assert (forall ((D2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D2) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) D2)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real D2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.75/7.08 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N3 tptp.nat) (A4 tptp.int)) (@ (@ (@ (@ (@ tptp.if_nat_int_int (@ (@ tptp.bit_se1146084159140164899it_int A4) N3)) tptp.bit_se4203085406695923979it_int) tptp.bit_se7879613467334960850it_int) N3) A4))))
% 6.75/7.08 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N3 tptp.nat) (A4 tptp.nat)) (@ (@ (@ (@ (@ tptp.if_nat_nat_nat (@ (@ tptp.bit_se1148574629649215175it_nat A4) N3)) tptp.bit_se4205575877204974255it_nat) tptp.bit_se7882103937844011126it_nat) N3) A4))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X2) (@ (@ tptp.divide_divide_real (@ _let_1 X2)) (@ _let_1 B))))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L)) 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 L) (@ (@ tptp.minus_minus_nat N) M)))))))
% 6.75/7.08 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N2)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))))
% 6.75/7.08 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= K (@ tptp.semiri1314217659103216013at_int N2)))))))
% 6.75/7.08 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N2 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N2)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))))))
% 6.75/7.08 (assert (= tptp.ord_less_nat (lambda ((N3 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M3)))))
% 6.75/7.08 (assert (= tptp.ord_less_eq_nat (lambda ((N3 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M3)) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) tptp.zero_zero_int) (exists ((N2 tptp.nat)) (= X2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((T3 tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.ord_le3480810397992357184T_VEBT T3) S3) (=> (@ P T3) (exists ((X6 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X6) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) T3)) (@ P (@ (@ tptp.insert_VEBT_VEBT X6) T3))))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((T3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex T3) S3) (=> (@ P T3) (exists ((X6 tptp.complex)) (and (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex S3) T3)) (@ P (@ (@ tptp.insert_complex X6) T3))))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat T3) S3) (=> (@ P T3) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) (@ (@ tptp.minus_minus_set_nat S3) T3)) (@ P (@ (@ tptp.insert_nat X6) T3))))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int S3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((T3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int T3) S3) (=> (@ P T3) (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) (@ (@ tptp.minus_minus_set_int S3) T3)) (@ P (@ (@ tptp.insert_int X6) T3))))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat S3) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((T3 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat T3) S3) (=> (@ P T3) (exists ((X6 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X6) (@ (@ tptp.minus_925952699566721837d_enat S3) T3)) (@ P (@ (@ tptp.insert_Extended_enat X6) T3))))))) (@ P S3))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (B4 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_le3480810397992357184T_VEBT A2))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le3480810397992357184T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_3 tptp.bot_bo8194388402131092736T_VEBT))) B4)) (=> (not _let_2) (@ (@ tptp.ord_le4337996190870823476T_VEBT A2) B4)))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_option_nat) (X2 tptp.option_nat) (B4 tptp.set_option_nat)) (let ((_let_1 (@ tptp.member_option_nat X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_option_nat X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_le1792839605950587050on_nat A2))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le1792839605950587050on_nat (@ (@ tptp.minus_5999362281193037231on_nat A2) (@ _let_3 tptp.bot_bo5009843511495006442on_nat))) B4)) (=> (not _let_2) (@ (@ tptp.ord_le6937355464348597430on_nat A2) B4)))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_real X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_real A2))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B4)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A2) B4)))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_set_nat_rat) (X2 tptp.set_nat_rat) (B4 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_set_nat_rat X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_le1311537459589289991at_rat A2))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le1311537459589289991at_rat (@ (@ tptp.minus_1626877696091177228at_rat A2) (@ _let_3 tptp.bot_bo6797373522285170759at_rat))) B4)) (=> (not _let_2) (@ (@ tptp.ord_le4375437777232675859at_rat A2) B4)))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_int X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_int A2))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B4)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A2) B4)))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (X2 tptp.extended_enat) (B4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_Extended_enat X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_le2529575680413868914d_enat A2))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le2529575680413868914d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_3 tptp.bot_bo7653980558646680370d_enat))) B4)) (=> (not _let_2) (@ (@ tptp.ord_le7203529160286727270d_enat A2) B4)))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_nat X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_nat A2))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B4)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A2) B4)))))))))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int B))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat A) B)))) (let ((_let_4 (@ (@ tptp.ord_less_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) _let_1))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D2))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X2)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X2) D2))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X2) D2))) _let_1))))))
% 6.75/7.08 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I4)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I4) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))))))
% 6.75/7.08 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N3) K2) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N3)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 6.75/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) N))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N))))
% 6.75/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 6.75/7.08 (assert (forall ((A tptp.code_integer)) (=> (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))
% 6.75/7.08 (assert (forall ((A tptp.int)) (=> (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))
% 6.75/7.08 (assert (forall ((A tptp.nat)) (=> (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (@ _let_1 (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.plus_plus_real (@ _let_1 X2)) (@ _let_1 Y2)))))))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.minus_minus_real (@ _let_1 X2)) (@ _let_1 Y2)))))))))))
% 6.75/7.08 (assert (forall ((K tptp.int)) (not (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 M2) (@ _let_1 N2))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (not (@ _let_1 N2)))))))))))
% 6.75/7.08 (assert (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) E)))))))
% 6.75/7.08 (assert (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)))) E)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N))))))))
% 6.75/7.08 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.log _let_2))) (let ((_let_4 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_1))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_real _let_2) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) X2))) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_4))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_4)) (@ _let_3 (@ _let_3 U)))))))))))))
% 6.75/7.08 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (let ((_let_3 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_real _let_1) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_m_e_m_b_e_r T) X2))) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_3)) (@ _let_2 (@ _let_2 U))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X2) (@ tptp.semiri8010041392384452111omplex N)))) N) (@ tptp.exp_complex X2)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X2) (@ tptp.semiri5074537144036343181t_real N)))) N) (@ tptp.exp_real X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 C) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M4)) X2)) C))) (= X2 tptp.zero_zero_real)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.int)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups769130701875090982BT_int G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.complex)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups1794756597179926696omplex G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_complex (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (X2 tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.int))) (let ((_let_1 (@ tptp.groups769130701875090982BT_int G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))))
% 6.75/7.08 (assert (forall ((P (-> tptp.int Bool)) (X2 tptp.nat) (Y2 tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X2) Y2))) (and (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X2)) (@ tptp.semiri1314217659103216013at_int Y2)))) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ P tptp.zero_zero_int))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2)))) tptp.one_one_real)))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X2))))))
% 6.75/7.08 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A4 tptp.code_integer) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger A4) (@ (@ tptp.power_8256067586552552935nteger _let_1) N3))))))))
% 6.75/7.08 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A4 tptp.int) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int A4) (@ (@ tptp.power_power_int _let_1) N3))))))))
% 6.75/7.08 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat A4) (@ (@ tptp.power_power_nat _let_1) N3))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.real)) (C (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.groups2240296850493347238T_real C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real)) (C (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups8097168146408367636l_real C) (@ (@ tptp.minus_minus_set_real S3) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_2 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups5808333547571424918x_real C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.rat)) (C (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ (@ tptp.groups136491112297645522BT_rat C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups136491112297645522BT_rat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups136491112297645522BT_rat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat)) (C (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.groups1300246762558778688al_rat C) (@ (@ tptp.minus_minus_set_real S3) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_2 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat)) (C (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.groups5058264527183730370ex_rat C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.nat)) (C (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ (@ tptp.groups771621172384141258BT_nat C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups771621172384141258BT_nat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups771621172384141258BT_nat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.nat)) (C (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.groups1935376822645274424al_nat C) (@ (@ tptp.minus_minus_set_real S3) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_2 (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.nat)) (C (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups5693394587270226106ex_nat C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.int)) (C (-> tptp.vEBT_VEBT tptp.int))) (let ((_let_1 (@ (@ tptp.groups769130701875090982BT_int C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups769130701875090982BT_int (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups769130701875090982BT_int (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.bit_se727722235901077358nd_nat A) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.log A) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X2)))))))))))
% 6.75/7.08 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K2 tptp.int) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K2) (@ (@ tptp.power_power_int _let_1) N3))))))))
% 6.75/7.08 (assert (forall ((I tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (@ (@ tptp.member_VEBT_VEBT I) A2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups2240296850493347238T_real F) A2)))))))
% 6.75/7.08 (assert (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))))
% 6.75/7.08 (assert (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))))
% 6.75/7.08 (assert (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))))
% 6.75/7.08 (assert (forall ((I tptp.extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ (@ tptp.member_Extended_enat I) A2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat I) tptp.bot_bo7653980558646680370d_enat))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups4148127829035722712t_real F) A2)))))))
% 6.75/7.08 (assert (forall ((I tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ (@ tptp.member_VEBT_VEBT I) A2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups136491112297645522BT_rat F) A2)))))))
% 6.75/7.08 (assert (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups1300246762558778688al_rat F) A2)))))))
% 6.75/7.08 (assert (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups5058264527183730370ex_rat F) A2)))))))
% 6.75/7.08 (assert (forall ((I tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.member_nat I) A2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))))))
% 6.75/7.08 (assert (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) N))))))
% 6.75/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) N) (or (@ (@ tptp.bit_se9216721137139052372nteger A) N) (= N tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N) (= N tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (= N tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N) (or (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.minus_8373710615458151222nteger A) tptp.one_one_Code_integer)) N) (= N tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (or (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) N) (= N tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.minus_minus_nat A) tptp.one_one_nat)) N) (= N tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N))))))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N))))))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1148574629649215175it_nat _let_2) N))))))))))
% 6.75/7.08 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A4 tptp.code_integer) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A4) _let_1)) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)))))))))
% 6.75/7.08 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A4 tptp.int) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_int _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A4) _let_1)) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)))))))))
% 6.75/7.08 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_nat _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A4) _let_1)) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)))))))))
% 6.75/7.08 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M3 tptp.zero_zero_nat) (= N3 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N3) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 6.75/7.08 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M3)) (not (@ _let_2 N3))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (D2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A)) (@ (@ tptp.times_times_complex _let_1) D2))))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (D2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D2))))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (D2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (let ((_let_2 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat (@ _let_2 A)) (@ (@ tptp.times_times_rat _let_1) D2))))))))
% 6.75/7.08 (assert (forall ((A tptp.extended_enat) (D2 tptp.extended_enat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N))) (let ((_let_2 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_2 A)) (@ (@ tptp.times_7803423173614009249d_enat _let_1) D2))))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (D2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D2))))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (D2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A)) (@ (@ tptp.times_times_real _let_1) D2))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.75/7.08 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.plus_plus_int K2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K2) N3)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3))))))
% 6.75/7.08 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.minus_minus_int K2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N3))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N)))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (D2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D2)))) _let_1))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (D2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D2)))) _let_1))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X2))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X2 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X2)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X2))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X2 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X2)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X2))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X2 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X2)))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) _let_1))) N)) (@ tptp.exp_real X2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 X2) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X2)))))))
% 6.75/7.08 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_complex (= N3 tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M3 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M3)))) (@ (@ (@ tptp.if_complex (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_int (= N3 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M3 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M3)))) (@ (@ (@ tptp.if_int (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_real (= N3 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M3 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M3)))) (@ (@ (@ tptp.if_real (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M3 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M3)))) (@ (@ (@ tptp.if_nat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_rat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_rat) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((M3 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ tptp.semiri681578069525770553at_rat M3)))) (@ (@ (@ tptp.if_rat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.divmod_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (= tptp.semiri4216267220026989637d_enat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= N3 tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.produc2676513652042109336d_enat (lambda ((M3 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ tptp.semiri4216267220026989637d_enat M3)))) (@ (@ (@ tptp.if_Extended_enat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.divmod_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))))))
% 6.75/7.08 (assert (forall ((H2 tptp.real) (Z tptp.real) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)))) (let ((_let_4 (@ tptp.power_power_real Z))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z) H2))) (=> (not (= H2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N)) (@ _let_4 N))) H2)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H2)))))))))))))
% 6.75/7.08 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.power_power_complex Z))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z) H2))) (=> (not (= H2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N)) (@ _let_3 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (= (@ tptp.archim7802044766580827645g_real (@ _let_1 X2)) (@ tptp.archim7802044766580827645g_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X2) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N3)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ tptp.suc N3))))))))))
% 6.75/7.08 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_complex Z))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) Q4)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.75/7.08 (assert (forall ((H2 tptp.rat) (Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_rat Z))) (=> (not (= H2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) Q4)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.75/7.08 (assert (forall ((H2 tptp.real) (Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_real Z))) (=> (not (= H2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) Q4)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.75/7.08 (assert (forall ((I tptp.set_nat_rat) (K tptp.set_nat_rat)) (= (@ (@ tptp.member_set_nat_rat I) (@ tptp.set_or6234697943151750426at_rat K)) (@ (@ tptp.ord_less_set_nat_rat I) K))))
% 6.75/7.08 (assert (forall ((I tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I) K))))
% 6.75/7.08 (assert (forall ((I tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I) K))))
% 6.75/7.08 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I) K))))
% 6.75/7.08 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I) K))))
% 6.75/7.08 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I) K))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)) X2) (exists ((N3 tptp.int)) (= X2 (@ tptp.ring_1_of_int_rat N3))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)) X2) (exists ((N3 tptp.int)) (= X2 (@ tptp.ring_1_of_int_real N3))))))
% 6.75/7.08 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height T)) (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X2)) (@ tptp.set_ord_lessThan_rat Y2)) (@ (@ tptp.ord_less_eq_rat X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X2)) (@ tptp.set_ord_lessThan_num Y2)) (@ (@ tptp.ord_less_eq_num X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X2)) (@ tptp.set_ord_lessThan_int Y2)) (@ (@ tptp.ord_less_eq_int X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X2)) (@ tptp.set_ord_lessThan_nat Y2)) (@ (@ tptp.ord_less_eq_nat X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X2)) (@ tptp.set_or5984915006950818249n_real Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 6.75/7.08 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.75/7.08 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.75/7.08 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int))
% 6.75/7.08 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.complex)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) Z))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) Z))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real V)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.numeral_numeral_rat V)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X2))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 6.75/7.08 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.75/7.08 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N3)))) (@ F tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N3)))) (@ F tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X2))))
% 6.75/7.08 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X2))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X2))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X2))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A2)))))))
% 6.75/7.08 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X2))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X2))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.pred_numeral K))) (= (@ tptp.set_ord_lessThan_nat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_lessThan_nat _let_1))))))
% 6.75/7.08 (assert (= tptp.set_or6234697943151750426at_rat (lambda ((U2 tptp.set_nat_rat)) (@ tptp.collect_set_nat_rat (lambda ((X tptp.set_nat_rat)) (@ (@ tptp.ord_less_set_nat_rat X) U2))))))
% 6.75/7.08 (assert (= tptp.set_or6855495488841395556at_rat (lambda ((U2 (-> tptp.nat tptp.rat))) (@ tptp.collect_nat_rat (lambda ((X (-> tptp.nat tptp.rat))) (@ (@ tptp.ord_less_nat_rat X) U2))))))
% 6.75/7.08 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_rat X) U2))))))
% 6.75/7.08 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_num X) U2))))))
% 6.75/7.08 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_int X) U2))))))
% 6.75/7.08 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) U2))))))
% 6.75/7.08 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.ord_less_real X) U2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y2) X2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y2)) (@ tptp.archim7802044766580827645g_real X2)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y2) X2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y2)) (@ tptp.archim2889992004027027881ng_rat X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim2889992004027027881ng_rat Y2)) (@ (@ tptp.ord_less_rat X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim7802044766580827645g_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.75/7.08 (assert (forall ((M tptp.rat) (N tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N)) (@ (@ tptp.ord_less_rat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N)) (@ (@ tptp.ord_less_num M) N))))
% 6.75/7.08 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N)) (@ (@ tptp.ord_less_int M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.real) (N tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N)) (@ (@ tptp.ord_less_real M) N))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) A))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) A))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) Z) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real Z)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) Z) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat Z)))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) X2))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) Y2))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim2889992004027027881ng_rat Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) Y2))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim7802044766580827645g_real Y2)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.75/7.08 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N))) (=> (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X4)) (@ P X4))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 6.75/7.08 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X4)) (@ P X4))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 6.75/7.08 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R))) (@ (@ tptp.plus_plus_real R) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((R tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R))) (@ (@ tptp.plus_plus_rat R) tptp.one_one_rat))))
% 6.75/7.08 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R))) tptp.one_one_real)) R)))
% 6.75/7.08 (assert (forall ((R tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R))) tptp.one_one_rat)) R)))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (N tptp.nat) (R tptp.complex)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex F) _let_1)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) R)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F I4)) R))) _let_1)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (R tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) R)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I4)) R))) _let_1)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (R tptp.rat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat F) _let_1)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) R)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I4)) R))) _let_1)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (R tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) R)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I4)) R))) _let_1)))))
% 6.75/7.08 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I4))) (=> (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) T) (@ (@ tptp.ord_less_eq_real T) _let_1)) (@ P I4)))))))
% 6.75/7.08 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T) (@ (@ tptp.ord_less_eq_rat T) _let_1)) (@ P I4)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X2) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim2889992004027027881ng_rat X2) A) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (@ (@ tptp.ord_less_eq_rat X2) _let_1))))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.archim7802044766580827645g_real X2) Z))))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X2) Z))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (@ (@ tptp.ord_less_eq_rat X2) _let_1)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B))) (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) Z) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) Z) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X2))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_complex (@ _let_2 X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_rat (@ _let_2 X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_int (@ _let_2 X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_real (@ _let_2 X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (=> (not (= X2 tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (=> (not (= X2 tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (=> (not (= X2 tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((Q2 tptp.real) (P6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_eq_real P6) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P6) Q2)))) Q2)))))
% 6.75/7.08 (assert (forall ((Q2 tptp.rat) (P6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_eq_rat P6) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P6) Q2)))) Q2)))))
% 6.75/7.08 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M3) (@ (@ tptp.power_power_nat _let_1) N3))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X2))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X2 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N))) (@ _let_1 X2)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X2))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X2 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N))) (@ _let_1 X2)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X2))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X2 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N))) (@ _let_1 X2)))))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex) (H2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_complex Z))) (@ (@ tptp.times_times_complex (@ _let_2 P4)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.75/7.08 (assert (forall ((Z tptp.rat) (H2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_rat Z))) (@ (@ tptp.times_times_rat (@ _let_2 P4)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (H2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_int Z))) (@ (@ tptp.times_times_int (@ _let_2 P4)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.75/7.08 (assert (forall ((Z tptp.real) (H2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_real Z))) (@ (@ tptp.times_times_real (@ _let_2 P4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat) (Y2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y2) N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) Y2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_complex X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (N tptp.nat) (Y2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_rat Y2) N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) Y2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_rat X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y2) N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) Y2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_int X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat) (Y2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y2) N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) Y2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_real X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X2) _let_1)) (@ (@ tptp.power_power_complex Y2) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) Y2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X2) P4)) (@ (@ tptp.power_power_complex Y2) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (N tptp.nat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) Y2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X2) P4)) (@ (@ tptp.power_power_rat Y2) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) Y2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X2) P4)) (@ (@ tptp.power_power_int Y2) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) Y2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X2) P4)) (@ (@ tptp.power_power_real Y2) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) Z)) (@ (@ tptp.insert_nat N) _let_1))))))
% 6.75/7.08 (assert (forall ((Q2 tptp.real) (P6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P6) Q2)))) tptp.one_one_real)) Q2)) P6))))
% 6.75/7.08 (assert (forall ((Q2 tptp.rat) (P6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P6) Q2)))) tptp.one_one_rat)) Q2)) P6))))
% 6.75/7.08 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X2) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 6.75/7.08 (assert (forall ((N tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N))) (=> (@ (@ tptp.ord_less_rat _let_1) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X2) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_rat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) K5) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) K5))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_int (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) K5))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_nat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) K5))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_real (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) K5))))))
% 6.75/7.08 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) _let_1)))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) _let_1)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.times_times_complex (@ _let_1 X2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.times_times_rat (@ _let_1 X2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.times_times_int (@ _let_1 X2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_int X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ _let_1 X2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ F I4)) (@ G I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) tptp.one_one_nat)))) _let_1))))))
% 6.75/7.08 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.arctan X2) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 6.75/7.08 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V7735802525324610683m_real (@ _let_1 A)) (@ _let_1 (@ tptp.real_V7735802525324610683m_real A))))))
% 6.75/7.08 (assert (forall ((W tptp.num) (A tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) (@ tptp.real_V1022390504157884413omplex A)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 6.75/7.08 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.75/7.08 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X2)) (not (= X2 tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X2)) (not (= X2 tptp.zero_zero_complex)))))
% 6.75/7.08 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 6.75/7.08 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 6.75/7.08 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y2)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X2)) N))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X2)) N))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) Y2)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X2)) Y2)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y2)))))
% 6.75/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))))))
% 6.75/7.08 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))))))
% 6.75/7.08 (assert (forall ((W tptp.real) (N tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N) (@ (@ tptp.power_power_real Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))))
% 6.75/7.08 (assert (forall ((W tptp.complex) (N tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N) (@ (@ tptp.power_power_complex Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (R tptp.real) (Y2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y2)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y2))) (@ (@ tptp.times_times_real R) S))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (R tptp.real) (Y2 tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y2)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y2))) (@ (@ tptp.times_times_real R) S))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y2))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y2))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (R tptp.real) (Y2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y2)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y2))) (@ (@ tptp.plus_plus_real R) S))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (R tptp.real) (Y2 tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y2)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y2))) (@ (@ tptp.plus_plus_real R) S))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y2))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y2))) E))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y2))) E))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) C)))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) C)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y2))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y2))) E))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y2))) E))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y2))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y2))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (R tptp.real) (B tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R) S))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (R tptp.real) (B tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R) S))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X2) N))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X2)) N))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X2) N))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X2)) N))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y2))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y2) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y2))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y2) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B)))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B)))))
% 6.75/7.08 (assert (forall ((W tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.75/7.08 (assert (forall ((W tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D2)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) D2))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex C) D2)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) D2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X2) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X2) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((Z tptp.real) (W tptp.real) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real Z) M)) (@ (@ tptp.power_power_real W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z) W))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex) (W tptp.complex) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex Z) M)) (@ (@ tptp.power_power_complex W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z) W))))))))
% 6.75/7.08 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (= (@ tptp.suminf_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 6.75/7.08 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (= (@ tptp.suminf_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ F (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ F (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M3)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 6.75/7.08 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K)))) (@ tptp.summable_real F))))
% 6.75/7.08 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N3)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N3)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.75/7.08 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (@ tptp.power_power_real C)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((C tptp.complex)) (= (@ tptp.summable_complex (@ tptp.power_power_complex C)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N3)) C))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N3)) C))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N3)) (@ G N3))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ tptp.summable_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N3)) (@ G N3))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ tptp.summable_int (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N3)) (@ G N3))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N3)) (@ G N3))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) C))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N2))) (@ G N2))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N2))) (@ G N2))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N2))) (@ G N2)))) (@ tptp.summable_real F)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N2))) (@ G N2)))) (@ tptp.summable_complex F)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ G N2))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ G N2))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ G N2))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)))))))
% 6.75/7.08 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))))
% 6.75/7.08 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 6.75/7.08 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 6.75/7.08 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real F)) C) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) C)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))) (@ (@ tptp.times_times_real C) (@ tptp.suminf_real F))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (= (@ (@ tptp.plus_plus_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N3)) (@ G N3)))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (= (@ (@ tptp.plus_plus_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)) (@ tptp.suminf_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N3)) (@ G N3)))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (= (@ (@ tptp.plus_plus_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)) (@ tptp.suminf_int (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N3)) (@ G N3)))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (= (@ (@ tptp.plus_plus_complex (@ tptp.suminf_complex F)) (@ tptp.suminf_complex G)) (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N3)) (@ G N3)))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N3)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N3)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real X2) N3)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (X2 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex X2) N3)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N2))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N2))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N2))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N2))) (= (= (@ tptp.suminf_real F) tptp.zero_zero_real) (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_real)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N2))) (= (= (@ tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_nat)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N2))) (= (= (@ tptp.suminf_int F) tptp.zero_zero_int) (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_int)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F N2))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F N2))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F N2))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N3))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N3))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_int (@ F N3)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N3))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N3))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N3))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_complex Z) N3)))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_real Z) N3)))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_complex Z) N3)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_real Z) N3)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N3) M))) (@ (@ tptp.power_power_complex Z) N3)))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N3) M))) (@ (@ tptp.power_power_real Z) N3)))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))))))
% 6.75/7.08 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 6.75/7.08 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N2))) (@ G N2))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N3))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N2))) (@ G N2))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.abs_abs_real (@ F N3))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N2))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F)) (exists ((I4 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N2))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F)) (exists ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N2))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F)) (exists ((I4 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I4))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N2))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N2))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N2))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (@ tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) X2)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X2)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) X2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X2)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X2)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) X2)) (@ tptp.summable_int F)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) X2)) (@ tptp.summable_nat F)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) X2)) (@ tptp.summable_real F)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X2)))))
% 6.75/7.08 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real C)))))
% 6.75/7.08 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex C)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (I5 tptp.set_nat)) (=> (@ tptp.summable_int F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.member_nat N2) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) I5)) (@ tptp.suminf_int F)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (I5 tptp.set_nat)) (=> (@ tptp.summable_nat F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.member_nat N2) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) I5)) (@ tptp.suminf_nat F)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (I5 tptp.set_nat)) (=> (@ tptp.summable_real F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.member_nat N2) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) I5)) (@ tptp.suminf_real F)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex F) (@ (@ tptp.plus_plus_complex (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K))))) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real F) (@ (@ tptp.plus_plus_real (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K))))) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K)))) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex F)) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real X2) N3)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (X2 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex X2) N3)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M4)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))
% 6.75/7.08 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.75/7.08 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_complex Z) N3))))) Z))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_real Z) N3))))) Z))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_complex Z) N3))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3))))) (@ F tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_real Z) N3))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3))))) (@ F tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (E tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N9 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M2) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N7)))) E)))))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (E tptp.real)) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N9 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M2) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N7)))) E)))))))))))
% 6.75/7.08 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (=> (@ tptp.summable_real F) (exists ((N9 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N7) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N7)))))) R))))))))
% 6.75/7.08 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (=> (@ tptp.summable_complex F) (exists ((N9 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N7) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N7)))))) R))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I2)) tptp.one_one_real)) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ F I4)) (@ (@ tptp.power_power_real Z) I4))))))))))
% 6.75/7.08 (assert (forall ((R tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R) (=> (@ (@ tptp.ord_less_real R) R0) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N2))) (@ (@ tptp.power_power_real R0) N2))) M7)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N3))) (@ (@ tptp.power_power_real R) N3)))))))))
% 6.75/7.08 (assert (forall ((C tptp.real) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N2)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N2)))))) (@ tptp.summable_real F)))))
% 6.75/7.08 (assert (forall ((C tptp.real) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N2)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N2)))))) (@ tptp.summable_complex F)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M4)))) (=> (@ (@ tptp.ord_less_eq_nat N) I) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M4)))) (=> (@ (@ tptp.ord_less_eq_nat N) I) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M4)))) (=> (@ (@ tptp.ord_less_eq_nat N) I) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))))
% 6.75/7.08 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) _let_1)))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) _let_1)))
% 6.75/7.08 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.75/7.08 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.75/7.08 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) tptp.pi))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.zero_zero_real))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arctan Y2))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y2))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.bit0 _let_1))) (let ((_let_3 (@ tptp.bit1 tptp.one))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_1))) (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_3)))))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real _let_3)) (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_2))))))))) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_2)))))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_2)))) (= (@ (@ tptp.divide_divide_real tptp.pi) _let_3) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real _let_3) (@ tptp.arctan (@ _let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_2)))))) (@ tptp.arctan (@ _let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))))))))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D3))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ F (@ _let_2 _let_1))) (@ F (@ _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_real F))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X2) Xa2)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X2)) (not (@ _let_3 Xa2)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X2) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_6 (= Y2 (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y2 (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X2) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 6.75/7.08 (assert (forall ((K 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 K)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L))) (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 L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L)) (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 L) _let_1))))))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (not (= X2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T4 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T4))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M3)) (@ tptp.semiri2265585572941072030t_real M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))))
% 6.75/7.08 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.75/7.08 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.75/7.08 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.75/7.08 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 6.75/7.08 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.75/7.08 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.75/7.08 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.75/7.08 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.75/7.08 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.75/7.08 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 6.75/7.08 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 6.75/7.08 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.75/7.08 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.75/7.08 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 6.75/7.08 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.75/7.08 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.75/7.08 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri773545260158071498ct_rat _let_1) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri4449623510593786356d_enat _let_1) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat _let_1)) (@ tptp.semiri4449623510593786356d_enat N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X2))) (let ((_let_2 (@ tptp.cos_complex X2))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sin_real X2))) (let ((_let_2 (@ tptp.cos_real X2))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.75/7.08 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.75/7.08 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.75/7.08 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.75/7.08 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X2)) (@ tptp.cos_real X2))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1)) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1)) tptp.one_one_complex))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1)) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1)) tptp.one_one_complex))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.zero_zero_real)))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.one_one_real)))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X2)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 6.75/7.08 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 6.75/7.08 (assert (forall ((N tptp.int)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.one_one_real)))
% 6.75/7.08 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) tptp.zero_zero_real))
% 6.75/7.08 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.75/7.08 (assert (forall ((N tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex X2) Y2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X2)) (@ tptp.cos_complex Y2))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X2)) (@ tptp.sin_complex Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X2) Y2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.cos_real Y2))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.sin_real Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X2) Y2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X2)) (@ tptp.cos_complex Y2))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X2)) (@ tptp.sin_complex Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.cos_real Y2))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.sin_real Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (=> (= (@ tptp.cos_complex X2) tptp.one_one_complex) (= (@ tptp.sin_complex X2) tptp.zero_zero_complex))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (= (@ tptp.cos_real X2) tptp.one_one_real) (= (@ tptp.sin_real X2) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X2) Y2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X2)) (@ tptp.cos_complex Y2))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X2)) (@ tptp.sin_complex Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y2))) (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex X2) Y2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X2)) (@ tptp.cos_complex Y2))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X2)) (@ tptp.sin_complex Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X2) Y2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y2))) (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X2)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X2))) (@ tptp.cos_complex X2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X2)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X2))) (@ tptp.cos_real X2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (exists ((Y3 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.sin_real Y3) (@ tptp.sin_real X2)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real M)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) tptp.pi) (@ _let_1 (@ tptp.sin_real X2)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.75/7.08 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))))
% 6.75/7.08 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))))
% 6.75/7.08 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))))))
% 6.75/7.08 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))))))
% 6.75/7.08 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex Z) W)) _let_1)))))))
% 6.75/7.08 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real Z) W)) _let_1)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat N))) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.plus_plus_nat K) N)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_2)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 6.75/7.08 (assert (forall ((W tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (= (@ tptp.cos_complex (@ _let_2 W)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.sin_complex W)) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.75/7.08 (assert (forall ((W tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (= (@ tptp.cos_real (@ _let_2 W)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.sin_real W)) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.75/7.08 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real Y2) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y2)) (@ (@ tptp.ord_less_real Y2) X2)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.pi) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.pi) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri3624122377584611663nteger N)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.semiri5044797733671781792omplex (@ tptp.pred_numeral K))))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ tptp.pred_numeral K))))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int K)) (@ tptp.semiri1406184849735516958ct_int (@ tptp.pred_numeral K))))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real K)) (@ tptp.semiri2265585572941072030t_real (@ tptp.pred_numeral K))))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.semiri1408675320244567234ct_nat (@ tptp.pred_numeral K)))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) tptp.pi) (= X2 (@ tptp.cos_real T4)) (= Y2 (@ tptp.sin_real T4)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X2))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X2))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X2)))))))
% 6.75/7.08 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.75/7.08 (assert (exists ((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) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y4) tptp.zero_zero_real)) (= Y4 X4))))))
% 6.75/7.08 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y2) (=> (@ (@ tptp.ord_less_real Y2) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y2)) (@ tptp.cos_real X2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X2 (@ tptp.cos_real T4)) (= Y2 (@ tptp.sin_real T4)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X2 (@ tptp.cos_real T4)) (= Y2 (@ tptp.sin_real T4))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real _let_1) _let_1)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.one_one_real) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (=> (@ (@ tptp.ord_less_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X2 (@ tptp.cos_real T4)) (not (= Y2 (@ tptp.sin_real T4))))))))))))
% 6.75/7.08 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_complex (= M3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M3)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M3)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (= tptp.semiri4449623510593786356d_enat (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= M3 tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat M3)) (@ tptp.semiri4449623510593786356d_enat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_real (= M3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M3)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M3)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1406184849735516958ct_int N) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri773545260158071498ct_rat N) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri4449623510593786356d_enat N) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat N)) (@ tptp.semiri4449623510593786356d_enat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri2265585572941072030t_real N) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1408675320244567234ct_nat N) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))))
% 6.75/7.08 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X2))) tptp.one_one_real))))))
% 6.75/7.08 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X2)))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y2)) (@ tptp.sin_real X2))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X2) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y2)) (@ _let_1 Y2)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ _let_2 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) _let_1) (=> (= (@ tptp.sin_real X2) (@ tptp.sin_real Y2)) (= X2 Y2))))))))))
% 6.75/7.08 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.one_one_real) (exists ((X tptp.int)) (= X2 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 6.75/7.08 (assert (forall ((W tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (= (@ tptp.cos_complex (@ _let_2 W)) (@ (@ tptp.minus_minus_complex (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.cos_complex W)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_complex))))))
% 6.75/7.08 (assert (forall ((W tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (= (@ tptp.cos_real (@ _let_2 W)) (@ (@ tptp.minus_minus_real (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.cos_real W)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_real))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X2))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.cos_real X2))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_2)))) (= (@ tptp.cos_real (@ _let_3 X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2)) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y2) (=> (@ (@ tptp.ord_less_real Y2) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y2)) (@ tptp.sin_real X2))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ _let_2 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))))))))
% 6.75/7.08 (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 ((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) Y2) (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_eq_real Y4) _let_1) (= (@ tptp.sin_real Y4) Y2)) (= Y4 X4)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.one_one_real) (or (exists ((X tptp.nat)) (= X2 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X tptp.nat)) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 6.75/7.08 (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 ((K3 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K3) L4)) (=> (=> (not (and (@ (@ tptp.member_int K3) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K3) L4)))))) (@ (@ P A0) A1)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.literal tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_literal)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_literal))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 6.75/7.08 (assert (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B9 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M3)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B9) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real X2) T4) (@ (@ tptp.ord_less_real T4) tptp.zero_zero_real) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) X2) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M3)) (@ tptp.semiri2265585572941072030t_real M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4)) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (or (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.75/7.08 (assert (= tptp.cos_coeff (lambda ((N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N3) _let_1))) (@ tptp.semiri2265585572941072030t_real N3))) tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.cos_real X2) tptp.zero_zero_real) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.zero_zero_real) (or (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3)) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3)) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))
% 6.75/7.08 (assert (= tptp.sin_coeff (lambda ((N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N3)) 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 N3) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N3)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N)))))))))
% 6.75/7.08 (assert (forall ((R tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) R)))) (@ (@ tptp.power_power_nat N) R)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X2))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X2))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N3)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.sin_real X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X2) (@ (@ tptp.ord_less_eq_real X2) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 6.75/7.08 (assert (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))) (@ (@ tptp.power_power_real Z) N3)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N3))) (@ (@ tptp.power_power_complex Z) N3)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_real (@ X8 M4)) (@ X8 N2)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_set_nat (@ X8 M4)) (@ X8 N2)))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_rat (@ X8 M4)) (@ X8 N2)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_num (@ X8 M4)) (@ X8 N2)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_nat (@ X8 M4)) (@ X8 N2)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_int (@ X8 M4)) (@ X8 N2)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.75/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X2) tptp.zero_zero_real))) (let ((_let_2 (= X2 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X2) A)) (not (= X2 tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X2) tptp.one_one_real) (= X2 tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X2)) X2)))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y2)) Y2)))))
% 6.75/7.08 (assert (forall ((A (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N3)))) X2) (= (@ A tptp.zero_zero_nat) X2))))
% 6.75/7.08 (assert (forall ((A (-> tptp.nat tptp.real)) (X2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ A N3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N3)))) X2) (= (@ A tptp.zero_zero_nat) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X2)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S tptp.real) (T tptp.real)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ G N2))) (=> (@ (@ tptp.sums_real F) S) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S) T))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S tptp.nat) (T tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ G N2))) (=> (@ (@ tptp.sums_nat F) S) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S) T))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S tptp.int) (T tptp.int)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ G N2))) (=> (@ (@ tptp.sums_int F) S) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S) T))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) C))) (@ (@ tptp.times_times_real A) C)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))) (@ (@ tptp.times_times_real C) A)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (G (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ (@ tptp.sums_real F) A) (=> (@ (@ tptp.sums_real G) B) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N3)) (@ G N3)))) (@ (@ tptp.plus_plus_real A) B))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (G (-> tptp.nat tptp.nat)) (B tptp.nat)) (=> (@ (@ tptp.sums_nat F) A) (=> (@ (@ tptp.sums_nat G) B) (@ (@ tptp.sums_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N3)) (@ G N3)))) (@ (@ tptp.plus_plus_nat A) B))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (G (-> tptp.nat tptp.int)) (B tptp.int)) (=> (@ (@ tptp.sums_int F) A) (=> (@ (@ tptp.sums_int G) B) (@ (@ tptp.sums_int (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N3)) (@ G N3)))) (@ (@ tptp.plus_plus_int A) B))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (G (-> tptp.nat tptp.complex)) (B tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (=> (@ (@ tptp.sums_complex G) B) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N3)) (@ G N3)))) (@ (@ tptp.plus_plus_complex A) B))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N3)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N3)) C))) (@ (@ tptp.divide_divide_real A) C)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X2)) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y2) A)) (@ (@ tptp.powr_real X2) A)))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real A) B))))))
% 6.75/7.08 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) C))) (@ (@ tptp.times_times_real D2) C)) (@ (@ tptp.sums_real F) D2)))))
% 6.75/7.08 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))) (@ (@ tptp.times_times_real C) D2)) (@ (@ tptp.sums_real F) D2)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y2) A)))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y2) A)) (@ (@ tptp.powr_real X2) A)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (@ _let_1 (@ (@ tptp.powr_real X2) Y2)))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.powr_real A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (= (@ _let_1 X2) (@ _let_1 Y2)) (= X2 Y2)))))))
% 6.75/7.08 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N3)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))))
% 6.75/7.08 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ F tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (S tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) S) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex S) (@ F tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) L) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L) (@ F tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (L tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) L) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L) (@ F tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (L tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) L) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L) (@ F tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (L tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) L) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex L) (@ F tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ F I2) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S) (@ (@ tptp.sums_real F) S)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.75/7.08 (assert (forall ((W tptp.real) (Z1 tptp.real) (Z22 tptp.real)) (let ((_let_1 (@ tptp.powr_real W))) (= (@ _let_1 (@ (@ tptp.minus_minus_real Z1) Z22)) (@ (@ tptp.divide_divide_real (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N3 M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N3)))) (@ (@ tptp.power_power_complex Z) M))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N3 M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N3)))) (@ (@ tptp.power_power_real Z) M))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N3 M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N3)))) (@ (@ tptp.power_power_int Z) M))))
% 6.75/7.08 (assert (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N3)))) (@ A tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ A N3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N3)))) (@ A tptp.zero_zero_nat))))
% 6.75/7.08 (assert (= tptp.tan_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex X)))))
% 6.75/7.08 (assert (= tptp.tan_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X)) (@ tptp.cos_real X)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X2) N)))))
% 6.75/7.08 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.log B) X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y2)) X2))))))
% 6.75/7.08 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X2)) Y2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B) Y2)))))))
% 6.75/7.08 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B) Y2)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X2)) Y2))))))
% 6.75/7.08 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y2)) X2) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.log B) X2)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (N tptp.nat) (S tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex S) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (N tptp.nat) (S tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) (@ (@ tptp.minus_minus_complex S) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.sums_complex F) S))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.sums_real F) S))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (S tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.sums_complex F) S) (@ (@ tptp.sums_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) (@ (@ tptp.minus_minus_complex S) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real) (N tptp.nat)) (=> (@ (@ tptp.sums_real F) S) (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.complex)) (S3 tptp.complex) (A2 tptp.set_nat) (S5 tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.sums_complex G) S3) (=> (@ tptp.finite_finite_nat A2) (=> (= S5 (@ (@ tptp.plus_plus_complex S3) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N3)) (@ G N3)))) A2))) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat N3) A2)) (@ F N3)) (@ G N3)))) S5))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (S3 tptp.real) (A2 tptp.set_nat) (S5 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G) S3) (=> (@ tptp.finite_finite_nat A2) (=> (= S5 (@ (@ tptp.plus_plus_real S3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N3)) (@ G N3)))) A2))) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat N3) A2)) (@ F N3)) (@ G N3)))) S5))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)))))
% 6.75/7.08 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y2)) X2) (@ (@ tptp.ord_less_eq_real Y2) (@ (@ tptp.log B) X2)))))))
% 6.75/7.08 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B) Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X2)) Y2))))))
% 6.75/7.08 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X2)) Y2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B) Y2)))))))
% 6.75/7.08 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real Y2) (@ (@ tptp.log B) X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y2)) X2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X2) A)) A))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X2)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X2))))))
% 6.75/7.08 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.75/7.08 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real (@ _let_1 X2)) Y2) (@ _let_1 (@ (@ tptp.times_times_real X2) (@ (@ tptp.powr_real B) Y2)))))))))))
% 6.75/7.08 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real Y2) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y2)) X2))))))))))
% 6.75/7.08 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real Y2) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y2)) X2))))))))))
% 6.75/7.08 (assert (= tptp.powr_real (lambda ((X tptp.real) (A4 tptp.real)) (@ (@ (@ tptp.if_real (= X tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A4) (@ tptp.ln_ln_real X)))))))
% 6.75/7.08 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ (@ tptp.sums_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 6.75/7.08 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ (@ tptp.sums_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 6.75/7.08 (assert (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N3)))) tptp.one_one_real))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y2) (@ tptp.tan_real X4)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X2)))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (exists ((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) Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X2) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y2) (=> (@ (@ tptp.ord_less_real Y2) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y2)) (@ _let_1 Y2)))))))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 Y2) (=> (@ _let_1 _let_2) (=> (@ _let_3 X2) (=> (@ (@ tptp.ord_less_real X2) _let_2) (= (@ _let_1 X2) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y2)) (@ tptp.tan_real X2))))))))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y2) (=> (@ (@ tptp.ord_less_real Y2) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y2)) (@ tptp.tan_real X2))))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (exists ((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) Y2) (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_real Y4) _let_1) (= (@ tptp.tan_real Y4) Y2)) (= Y4 X4)))))))))
% 6.75/7.08 (assert (= (@ tptp.tan_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y2)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y2)))))
% 6.75/7.08 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real (@ _let_1 X2)) Y2) (@ _let_1 (@ (@ tptp.times_times_real X2) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y2))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y2))) (let ((_let_2 (@ tptp.cos_complex X2))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X2)) (@ tptp.tan_complex Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X2) Y2))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y2))) (let ((_let_2 (@ tptp.cos_real X2))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y2)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) Y2))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ (@ tptp.sums_real G) X2) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N3)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) _let_1)))))) X2))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (X2 tptp.real) (F (-> tptp.nat tptp.real)) (Y2 tptp.real)) (=> (@ (@ tptp.sums_real G) X2) (=> (@ (@ tptp.sums_real F) Y2) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N3)) (@ F (@ (@ tptp.divide_divide_nat N3) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X2) Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat N)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X2)))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X4) Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X2)) tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (=> (@ _let_2 Y2) (=> (@ (@ tptp.ord_less_real Y2) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (=> (@ (@ tptp.ord_less_real Y2) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y2))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X2))) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (=> (= (@ tptp.tan_real X2) Y2) (= (@ tptp.arctan Y2) X2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X2)) X2))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arctan Y2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_real _let_1) _let_2) (= (@ tptp.tan_real _let_1) Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y2))) (let ((_let_2 (@ tptp.cos_complex X2))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.tan_complex X2)) (@ tptp.tan_complex Y2))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X2) Y2))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y2))) (let ((_let_2 (@ tptp.cos_real X2))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y2))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) Y2))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y2))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X2) Y2))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y2))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ (@ tptp.minus_minus_real X2) Y2))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y2))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X2) Y2))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y2))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ (@ tptp.plus_plus_real X2) Y2))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (exists ((Z3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z3) (@ (@ tptp.ord_less_real Z3) _let_1) (= (@ tptp.tan_real Z3) X2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N3)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.cos_real X2))))
% 6.75/7.08 (assert (= tptp.tan_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))
% 6.75/7.08 (assert (= tptp.tan_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))
% 6.75/7.08 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X7 (-> tptp.nat tptp.real))) (or (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X7 (@ tptp.suc N3))) (@ X7 N3)))))))
% 6.75/7.08 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X7 (-> tptp.nat tptp.set_nat))) (or (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X7 (@ tptp.suc N3))) (@ X7 N3)))))))
% 6.75/7.08 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X7 (-> tptp.nat tptp.rat))) (or (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X7 (@ tptp.suc N3))) (@ X7 N3)))))))
% 6.75/7.08 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X7 (-> tptp.nat tptp.num))) (or (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X7 (@ tptp.suc N3))) (@ X7 N3)))))))
% 6.75/7.08 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X7 (-> tptp.nat tptp.nat))) (or (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X7 (@ tptp.suc N3))) (@ X7 N3)))))))
% 6.75/7.08 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X7 (-> tptp.nat tptp.int))) (or (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X7 (@ tptp.suc N3))) (@ X7 N3)))))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 (@ tptp.suc N2))) (@ X8 N2))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X8 (@ tptp.suc N2))) (@ X8 N2))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 (@ tptp.suc N2))) (@ X8 N2))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 (@ tptp.suc N2))) (@ X8 N2))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 (@ tptp.suc N2))) (@ X8 N2))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 (@ tptp.suc N2))) (@ X8 N2))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 N2)) (@ X8 (@ tptp.suc N2)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X8 N2)) (@ X8 (@ tptp.suc N2)))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 N2)) (@ X8 (@ tptp.suc N2)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 N2)) (@ X8 (@ tptp.suc N2)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 N2)) (@ X8 (@ tptp.suc N2)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 N2)) (@ X8 (@ tptp.suc N2)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.75/7.08 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X7 (-> tptp.nat tptp.real))) (or (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.ord_less_eq_real (@ X7 M3)) (@ X7 N3)))) (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.ord_less_eq_real (@ X7 N3)) (@ X7 M3))))))))
% 6.75/7.08 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X7 (-> tptp.nat tptp.set_nat))) (or (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.ord_less_eq_set_nat (@ X7 M3)) (@ X7 N3)))) (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.ord_less_eq_set_nat (@ X7 N3)) (@ X7 M3))))))))
% 6.75/7.08 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X7 (-> tptp.nat tptp.rat))) (or (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.ord_less_eq_rat (@ X7 M3)) (@ X7 N3)))) (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.ord_less_eq_rat (@ X7 N3)) (@ X7 M3))))))))
% 6.75/7.08 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X7 (-> tptp.nat tptp.num))) (or (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.ord_less_eq_num (@ X7 M3)) (@ X7 N3)))) (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.ord_less_eq_num (@ X7 N3)) (@ X7 M3))))))))
% 6.75/7.08 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X7 (-> tptp.nat tptp.nat))) (or (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.ord_less_eq_nat (@ X7 M3)) (@ X7 N3)))) (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.ord_less_eq_nat (@ X7 N3)) (@ X7 M3))))))))
% 6.75/7.08 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X7 (-> tptp.nat tptp.int))) (or (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.ord_less_eq_int (@ X7 M3)) (@ X7 N3)))) (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N3) (@ (@ tptp.ord_less_eq_int (@ X7 N3)) (@ X7 M3))))))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_real (@ X8 N2)) (@ X8 M4)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_set_nat (@ X8 N2)) (@ X8 M4)))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_rat (@ X8 N2)) (@ X8 M4)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_num (@ X8 N2)) (@ X8 M4)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_nat (@ X8 N2)) (@ X8 M4)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.75/7.08 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_int (@ X8 N2)) (@ X8 M4)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N3)) (@ (@ tptp.power_power_complex X2) N3)))) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N3)) (@ C N3))) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.minus_minus_nat N3) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N3)) (@ (@ tptp.power_power_complex X2) N3))))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N3)) (@ (@ tptp.power_power_real X2) N3)))) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ C N3))) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N3) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N3)) (@ (@ tptp.power_power_real X2) N3))))))))
% 6.75/7.08 (assert (= tptp.arcosh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X2) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X2)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z) N))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))))
% 6.75/7.08 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z) N))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))))
% 6.75/7.08 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.times_times_rat _let_2) Z)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z) N))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (= (@ tptp.sqrt X2) (@ tptp.sqrt Y2)) (= X2 Y2))))
% 6.75/7.08 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sqrt X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sqrt X2) tptp.one_one_real) (= X2 tptp.one_one_real))))
% 6.75/7.08 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.75/7.08 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real))
% 6.75/7.08 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X2) tptp.one_one_real) (= X2 tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X2) tptp.one_one_complex) (= X2 tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.numeral_numeral_real W)) (@ tptp.numera6690914467698888265omplex W))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.times_times_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y2)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y2)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1803761363581548252l_real X2)) N))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_complex (@ tptp.real_V4546457046886955230omplex X2)) N))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 6.75/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.75/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.75/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.75/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.75/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X2) X2)) (@ tptp.abs_abs_real X2))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.75/7.08 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))))
% 6.75/7.08 (assert (= (@ tptp.cos_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.75/7.08 (assert (= (@ tptp.cos_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X2)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X2)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (B tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real B))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X2)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) _let_1))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (B tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.numera6690914467698888265omplex B))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) (@ tptp.numeral_numeral_real B))))))
% 6.75/7.08 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.75/7.08 (assert (= (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.zero_zero_complex))
% 6.75/7.08 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.75/7.08 (assert (= (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.one_one_complex))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X2) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) K))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.times_times_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.sqrt X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X2) N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X2) N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X2) N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X2) N))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_real))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_rat))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_real)))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_rat)))))))
% 6.75/7.08 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 6.75/7.08 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 6.75/7.08 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 6.75/7.08 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 6.75/7.08 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y2))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sqrt X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.divide_divide_real X2) _let_1) _let_1)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X2) Y2))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X2) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X2) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X2) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X2) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X2))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X2))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.75/7.08 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N)))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N)))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N)))))
% 6.75/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N)))))
% 6.75/7.08 (assert (= tptp.diffs_int (lambda ((C3 (-> tptp.nat tptp.int)) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C3 _let_1))))))
% 6.75/7.08 (assert (= tptp.diffs_real (lambda ((C3 (-> tptp.nat tptp.real)) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C3 _let_1))))))
% 6.75/7.08 (assert (= tptp.diffs_rat (lambda ((C3 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ C3 _let_1))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N)))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N)))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N)))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N)))))))
% 6.75/7.08 (assert (forall ((A tptp.extended_enat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s3181272606743183617d_enat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 N)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ tptp.semiri4216267220026989637d_enat N)))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ _let_1 N))))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) (@ _let_1 N))))))
% 6.75/7.08 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) (@ _let_1 N))))))
% 6.75/7.08 (assert (forall ((Z tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) (@ _let_1 N))))))
% 6.75/7.08 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) (@ _let_1 N))))))
% 6.75/7.08 (assert (forall ((Z tptp.extended_enat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s3181272606743183617d_enat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat Z) (@ tptp.semiri4216267220026989637d_enat N))) (@ _let_1 N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N) K))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N) K))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N) K))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N) K))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N) K))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K2))))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K2))))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K2))))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat)))))
% 6.75/7.08 (assert (forall ((Z tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N))) M))))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) M))))))
% 6.75/7.08 (assert (forall ((Z tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) M))))))
% 6.75/7.08 (assert (forall ((Z tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) M))))))
% 6.75/7.08 (assert (forall ((Z tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) M))))))
% 6.75/7.08 (assert (forall ((Z tptp.extended_enat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s3181272606743183617d_enat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 N)) (@ (@ tptp.comm_s3181272606743183617d_enat (@ (@ tptp.plus_p3455044024723400733d_enat Z) (@ tptp.semiri4216267220026989637d_enat N))) M))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y2) (@ (@ tptp.ord_less_real X2) (@ tptp.sqrt Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) Y2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt Y2)))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (=> (forall ((X4 tptp.complex)) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N3)) (@ (@ tptp.power_power_complex X4) N3))))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N3)) (@ (@ tptp.power_power_complex X2) N3)))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (forall ((X4 tptp.real)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ C N3)) (@ (@ tptp.power_power_real X4) N3))))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N3)) (@ (@ tptp.power_power_real X2) N3)))))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) (@ tptp.sqrt _let_1))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.complex)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.extended_enat)) (let ((_let_1 (@ tptp.comm_s3181272606743183617d_enat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 M)) (@ (@ tptp.comm_s3181272606743183617d_enat (@ (@ tptp.plus_p3455044024723400733d_enat Z) (@ tptp.semiri4216267220026989637d_enat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) Y2)))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (= (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (= (@ tptp.sqrt X2) Y2)))))
% 6.75/7.08 (assert (forall ((U tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) U) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) U))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) X2) (= Y2 tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) Y2) (= X2 tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) C)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real B) D2)) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real C) _let_1)) (@ (@ tptp.power_power_real D2) _let_1))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.sqrt Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y2))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_2)) _let_2)))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_2)) _let_2)))))
% 6.75/7.08 (assert (forall ((M tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.cos_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X2))) (@ tptp.real_V1803761363581548252l_real (@ tptp.cos_real (@ _let_1 X2)))))))
% 6.75/7.08 (assert (forall ((M tptp.int) (X2 tptp.real)) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X2))) (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X2))))))
% 6.75/7.08 (assert (forall ((M tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.sin_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X2))) (@ tptp.real_V1803761363581548252l_real (@ tptp.sin_real (@ _let_1 X2)))))))
% 6.75/7.08 (assert (forall ((M tptp.int) (X2 tptp.real)) (= (@ tptp.sin_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X2))) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X2))))))
% 6.75/7.08 (assert (forall ((R tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))))
% 6.75/7.08 (assert (forall ((R tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))))
% 6.75/7.08 (assert (forall ((R tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 6.75/7.08 (assert (forall ((R tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))))
% 6.75/7.08 (assert (forall ((R tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ tptp.semiri5044797733671781792omplex N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ tptp.semiri3624122377584611663nteger N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) Y2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))) (@ (@ tptp.plus_plus_real X2) Y2))))))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.bit1 tptp.one))) (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.power_power_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) N) (= (@ tptp.sqrt (@ _let_3 N)) (@ _let_3 (@ (@ tptp.divide_divide_nat N) _let_2)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real Y2))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ tptp.sqrt X2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.bit1 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((B tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K)))))
% 6.75/7.08 (assert (forall ((B tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K)))))
% 6.75/7.08 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K)))))
% 6.75/7.08 (assert (forall ((B tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K)))))
% 6.75/7.08 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K)))))
% 6.75/7.08 (assert (forall ((B tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 6.75/7.08 (assert (forall ((B tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K)))))
% 6.75/7.08 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))))
% 6.75/7.08 (assert (forall ((B tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 6.75/7.08 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 6.75/7.08 (assert (= tptp.cos_real (lambda ((X tptp.real)) (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))))
% 6.75/7.08 (assert (= tptp.cos_complex (lambda ((X tptp.complex)) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X)))))
% 6.75/7.08 (assert (= tptp.sin_real (lambda ((X tptp.real)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))))
% 6.75/7.08 (assert (= tptp.sin_complex (lambda ((X tptp.complex)) (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) K5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X4)) K5) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ C N3)) (@ (@ tptp.power_power_real X4) N3)))))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N3)) (@ (@ tptp.power_power_real X2) N3))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) K5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) K5) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N3)) (@ (@ tptp.power_power_complex X4) N3)))))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N3)) (@ (@ tptp.power_power_complex X2) N3))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) N) (@ (@ tptp.power_power_real X2) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X2) Y2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (U tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y2)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2)))) U))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (= (@ tptp.arcosh_real X2) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X2)) (@ (@ tptp.divide_divide_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (U tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X2) _let_4) (=> (@ (@ tptp.ord_less_real Y2) _let_4) (=> (@ _let_3 X2) (=> (@ _let_3 Y2) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2)))) U)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sin_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.75/7.08 (assert (= tptp.arctan (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.plus_plus_real tptp.one_one_real))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real X) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri5044797733671781792omplex _let_3) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex _let_2) _let_3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N))) (@ tptp.semiri5044797733671781792omplex N))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri773545260158071498ct_rat _let_3) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat _let_2) _let_3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N))) (@ tptp.semiri773545260158071498ct_rat N))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri2265585572941072030t_real _let_3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real _let_2) _let_3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) N))) (@ tptp.semiri2265585572941072030t_real N))))))))
% 6.75/7.08 (assert (= tptp.arsinh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K2)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.75/7.08 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.75/7.08 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.comm_s4028243227959126397er_rat Z) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K2)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.75/7.08 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A4 tptp.complex) (N3 tptp.nat)) (@ (@ (@ tptp.if_complex (= N3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A4) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_complex)))))
% 6.75/7.08 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N3 tptp.nat)) (@ (@ (@ tptp.if_int (= N3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_int)))))
% 6.75/7.08 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N3 tptp.nat)) (@ (@ (@ tptp.if_real (= N3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_real)))))
% 6.75/7.08 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N3 tptp.nat)) (@ (@ (@ tptp.if_rat (= N3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A4) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_rat)))))
% 6.75/7.08 (assert (= tptp.comm_s3181272606743183617d_enat (lambda ((A4 tptp.extended_enat) (N3 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= N3 tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ (@ (@ tptp.set_fo2538466533108834004d_enat (lambda ((O tptp.nat) (__flatten_var_0 tptp.extended_enat)) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A4) (@ tptp.semiri4216267220026989637d_enat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_on7984719198319812577d_enat)))))
% 6.75/7.08 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_nat)))))
% 6.75/7.08 (assert (= tptp.arsinh_real (lambda ((X tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A2) tptp.one_one_nat)))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups6464643781859351333omplex G) tptp.bot_bot_set_nat) tptp.one_one_complex)))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)))
% 6.75/7.08 (assert (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups7440179247065528705omplex G) tptp.bot_bot_set_int) tptp.one_one_complex)))
% 6.75/7.08 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups2316167850115554303t_real G) tptp.bot_bot_set_int) tptp.one_one_real)))
% 6.75/7.08 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) tptp.bot_bot_set_int) tptp.one_one_rat)))
% 6.75/7.08 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) tptp.bot_bot_set_int) tptp.one_one_nat)))
% 6.75/7.08 (assert (forall ((G (-> tptp.extended_enat tptp.complex))) (= (@ (@ tptp.groups4622424608036095791omplex G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_complex)))
% 6.75/7.08 (assert (forall ((G (-> tptp.extended_enat tptp.real))) (= (@ (@ tptp.groups97031904164794029t_real G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_real)))
% 6.75/7.08 (assert (forall ((G (-> tptp.extended_enat tptp.rat))) (= (@ (@ tptp.groups2245840878043517529at_rat G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_rat)))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups4622424608036095791omplex G) A2) tptp.one_one_complex))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups2316167850115554303t_real G) A2) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups97031904164794029t_real G) A2) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups73079841787564623at_rat G) A2) tptp.one_one_rat))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups1072433553688619179nt_rat G) A2) tptp.one_one_rat))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S3))) (=> (@ tptp.finite4001608067531595151d_enat S3) (and (=> _let_1 (= (@ (@ tptp.groups4622424608036095791omplex (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4622424608036095791omplex (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S3))) (=> (@ tptp.finite4001608067531595151d_enat S3) (and (=> _let_1 (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S3))) (=> (@ tptp.finite4001608067531595151d_enat S3) (and (=> _let_1 (= (@ (@ tptp.groups4622424608036095791omplex (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4622424608036095791omplex (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S3))) (=> (@ tptp.finite4001608067531595151d_enat S3) (and (=> _let_1 (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (X2 tptp.extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X2) A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.75/7.08 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.75/7.08 (assert (= (@ tptp.arcsin (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (= (@ G X4) tptp.one_one_nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) A2) tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (= (@ G X4) tptp.one_one_int))) (= (@ (@ tptp.groups705719431365010083at_int G) A2) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (= (@ G X4) tptp.one_one_int))) (= (@ (@ tptp.groups1705073143266064639nt_int G) A2) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((G (-> tptp.real tptp.complex)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups713298508707869441omplex G) A2) tptp.one_one_complex)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (= (@ G A3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (= (@ G A3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.int tptp.complex)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (= (@ G A3) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A2) tptp.one_one_real)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (= (@ G A3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (= (@ G A3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G) A2) tptp.one_one_real)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (= (@ G A3) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.real tptp.rat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups4061424788464935467al_rat G) A2) tptp.one_one_rat)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (= (@ G A3) tptp.one_one_rat)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups73079841787564623at_rat G) A2) tptp.one_one_rat)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (= (@ G A3) tptp.one_one_rat)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.int tptp.rat)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups1072433553688619179nt_rat G) A2) tptp.one_one_rat)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (= (@ G A3) tptp.one_one_rat)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.real tptp.nat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups4696554848551431203al_nat G) A2) tptp.one_one_nat)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (= (@ G A3) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) A2)) (@ (@ tptp.groups708209901874060359at_nat H2) A2)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ (@ tptp.times_times_int (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) A2)) (@ (@ tptp.groups705719431365010083at_int H2) A2)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ (@ tptp.times_times_int (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G) A2)) (@ (@ tptp.groups1705073143266064639nt_int H2) A2)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) N) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ (@ tptp.power_power_nat (@ F X)) N))) A2))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A2)) N) (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ (@ tptp.power_power_int (@ F X)) N))) A2))))
% 6.75/7.08 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) N) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ (@ tptp.power_power_int (@ F X)) N))) A2))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) A))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A2)) A))))
% 6.75/7.08 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) A))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.groups73079841787564623at_rat G) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat G) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) (@ (@ tptp.groups4694064378042380927al_int G) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat G) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups4696554848551431203al_nat F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ (@ tptp.groups4694064378042380927al_int F) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_complex))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_rat))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups713298508707869441omplex G) (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A2) (@ P X))))) (@ (@ tptp.groups713298508707869441omplex (lambda ((X tptp.real)) (@ (@ (@ tptp.if_complex (@ P X)) (@ G X)) tptp.one_one_complex))) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A2) (@ P X))))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((X tptp.nat)) (@ (@ (@ tptp.if_complex (@ P X)) (@ G X)) tptp.one_one_complex))) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups7440179247065528705omplex G) (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A2) (@ P X))))) (@ (@ tptp.groups7440179247065528705omplex (lambda ((X tptp.int)) (@ (@ (@ tptp.if_complex (@ P X)) (@ G X)) tptp.one_one_complex))) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups3708469109370488835omplex G) (@ tptp.collect_complex (lambda ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A2) (@ P X))))) (@ (@ tptp.groups3708469109370488835omplex (lambda ((X tptp.complex)) (@ (@ (@ tptp.if_complex (@ P X)) (@ G X)) tptp.one_one_complex))) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups4622424608036095791omplex G) (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X) A2) (@ P X))))) (@ (@ tptp.groups4622424608036095791omplex (lambda ((X tptp.extended_enat)) (@ (@ (@ tptp.if_complex (@ P X)) (@ G X)) tptp.one_one_complex))) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups1681761925125756287l_real G) (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A2) (@ P X))))) (@ (@ tptp.groups1681761925125756287l_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_real (@ P X)) (@ G X)) tptp.one_one_real))) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A2) (@ P X))))) (@ (@ tptp.groups129246275422532515t_real (lambda ((X tptp.nat)) (@ (@ (@ tptp.if_real (@ P X)) (@ G X)) tptp.one_one_real))) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups2316167850115554303t_real G) (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A2) (@ P X))))) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X tptp.int)) (@ (@ (@ tptp.if_real (@ P X)) (@ G X)) tptp.one_one_real))) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups766887009212190081x_real G) (@ tptp.collect_complex (lambda ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A2) (@ P X))))) (@ (@ tptp.groups766887009212190081x_real (lambda ((X tptp.complex)) (@ (@ (@ tptp.if_real (@ P X)) (@ G X)) tptp.one_one_real))) A2)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups97031904164794029t_real G) (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X) A2) (@ P X))))) (@ (@ tptp.groups97031904164794029t_real (lambda ((X tptp.extended_enat)) (@ (@ (@ tptp.if_real (@ P X)) (@ G X)) tptp.one_one_real))) A2)))))
% 6.75/7.08 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_real C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((A4 tptp.nat)) (@ (@ tptp.power_power_real C) (@ F A4)))) A2))))
% 6.75/7.08 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_complex C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((A4 tptp.nat)) (@ (@ tptp.power_power_complex C) (@ F A4)))) A2))))
% 6.75/7.08 (assert (forall ((C tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_nat C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((A4 tptp.nat)) (@ (@ tptp.power_power_nat C) (@ F A4)))) A2))))
% 6.75/7.08 (assert (forall ((C tptp.int) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((A4 tptp.nat)) (@ (@ tptp.power_power_int C) (@ F A4)))) A2))))
% 6.75/7.08 (assert (forall ((C tptp.int) (F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((A4 tptp.int)) (@ (@ tptp.power_power_int C) (@ F A4)))) A2))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_real X4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_nat X4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_int X4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_real X4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) tptp.one_one_rat))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_nat X4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) tptp.one_one_rat))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_int X4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) tptp.one_one_rat))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_real X4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_int X4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_real X4) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) tptp.one_one_int))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_nat X4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) tptp.one_one_nat))))
% 6.75/7.08 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R2 tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X22) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups6464643781859351333omplex H2) S3)) (@ (@ tptp.groups6464643781859351333omplex G) S3))))))))
% 6.75/7.08 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ (@ R2 tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X22) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups7440179247065528705omplex H2) S3)) (@ (@ tptp.groups7440179247065528705omplex G) S3))))))))
% 6.75/7.08 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ (@ R2 tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X22) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups3708469109370488835omplex H2) S3)) (@ (@ tptp.groups3708469109370488835omplex G) S3))))))))
% 6.75/7.08 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.complex)) (G (-> tptp.extended_enat tptp.complex))) (=> (@ (@ R2 tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X22) Y23)))) (=> (@ tptp.finite4001608067531595151d_enat S3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups4622424608036095791omplex H2) S3)) (@ (@ tptp.groups4622424608036095791omplex G) S3))))))))
% 6.75/7.08 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ (@ R2 tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X22) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups129246275422532515t_real H2) S3)) (@ (@ tptp.groups129246275422532515t_real G) S3))))))))
% 6.75/7.08 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R2 tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X22) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups2316167850115554303t_real H2) S3)) (@ (@ tptp.groups2316167850115554303t_real G) S3))))))))
% 6.75/7.08 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R2 tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X22) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups766887009212190081x_real H2) S3)) (@ (@ tptp.groups766887009212190081x_real G) S3))))))))
% 6.75/7.08 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ (@ R2 tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X22) Y23)))) (=> (@ tptp.finite4001608067531595151d_enat S3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups97031904164794029t_real H2) S3)) (@ (@ tptp.groups97031904164794029t_real G) S3))))))))
% 6.75/7.08 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R2 tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_rat X15) Y15)) (@ (@ tptp.times_times_rat X22) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups73079841787564623at_rat H2) S3)) (@ (@ tptp.groups73079841787564623at_rat G) S3))))))))
% 6.75/7.08 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R2 tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_rat X15) Y15)) (@ (@ tptp.times_times_rat X22) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R2 (@ H2 X4)) (@ G X4)))) (@ (@ R2 (@ (@ tptp.groups1072433553688619179nt_rat H2) S3)) (@ (@ tptp.groups1072433553688619179nt_rat G) S3))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A2)))) (let ((_let_4 (@ (@ tptp.member_real X2) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X2) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X2) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A2)))) (let ((_let_4 (@ (@ tptp.member_int X2) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (X2 tptp.extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Extended_enat X2) A2)))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X2) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A2)))) (let ((_let_4 (@ (@ tptp.member_real X2) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X2) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X2) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A2)))) (let ((_let_4 (@ (@ tptp.member_int X2) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 6.75/7.08 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_real) (S3 tptp.set_real) (I (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T6 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T6) T5)))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T6) T5)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T6) T5)) (@ (@ tptp.member_real (@ I B2)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) T5) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups713298508707869441omplex H2) T6)))))))))))))
% 6.75/7.08 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_nat) (S3 tptp.set_real) (I (-> tptp.nat tptp.real)) (J (-> tptp.real tptp.nat)) (T6 tptp.set_nat) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_nat (@ J A3)) (@ (@ tptp.minus_minus_set_nat T6) T5)))) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat T6) T5)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat T6) T5)) (@ (@ tptp.member_real (@ I B2)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) T5) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups6464643781859351333omplex H2) T6)))))))))))))
% 6.75/7.08 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_int) (S3 tptp.set_real) (I (-> tptp.int tptp.real)) (J (-> tptp.real tptp.int)) (T6 tptp.set_int) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T6) T5)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T6) T5)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T6) T5)) (@ (@ tptp.member_real (@ I B2)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T5) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups7440179247065528705omplex H2) T6)))))))))))))
% 6.75/7.08 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_complex) (S3 tptp.set_real) (I (-> tptp.complex tptp.real)) (J (-> tptp.real tptp.complex)) (T6 tptp.set_complex) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_complex (@ J A3)) (@ (@ tptp.minus_811609699411566653omplex T6) T5)))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T6) T5)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T6) T5)) (@ (@ tptp.member_real (@ I B2)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) T5) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups3708469109370488835omplex H2) T6)))))))))))))
% 6.75/7.08 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_Extended_enat) (S3 tptp.set_real) (I (-> tptp.extended_enat tptp.real)) (J (-> tptp.real tptp.extended_enat)) (T6 tptp.set_Extended_enat) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_Extended_enat (@ J A3)) (@ (@ tptp.minus_925952699566721837d_enat T6) T5)))) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat T6) T5)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat T6) T5)) (@ (@ tptp.member_real (@ I B2)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) T5) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups4622424608036095791omplex H2) T6)))))))))))))
% 6.75/7.08 (assert (forall ((S5 tptp.set_nat) (T5 tptp.set_real) (S3 tptp.set_nat) (I (-> tptp.real tptp.nat)) (J (-> tptp.nat tptp.real)) (T6 tptp.set_real) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_nat S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat S3) S5)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat S3) S5)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T6) T5)))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T6) T5)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T6) T5)) (@ (@ tptp.member_nat (@ I B2)) (@ (@ tptp.minus_minus_set_nat S3) S5)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) S5) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) T5) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups6464643781859351333omplex G) S3) (@ (@ tptp.groups713298508707869441omplex H2) T6)))))))))))))
% 6.75/7.08 (assert (forall ((S5 tptp.set_nat) (T5 tptp.set_nat) (S3 tptp.set_nat) (I (-> tptp.nat tptp.nat)) (J (-> tptp.nat tptp.nat)) (T6 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat S5) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat S3) S5)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat S3) S5)) (@ (@ tptp.member_nat (@ J A3)) (@ (@ tptp.minus_minus_set_nat T6) T5)))) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat T6) T5)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat T6) T5)) (@ (@ tptp.member_nat (@ I B2)) (@ (@ tptp.minus_minus_set_nat S3) S5)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) S5) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) T5) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups6464643781859351333omplex G) S3) (@ (@ tptp.groups6464643781859351333omplex H2) T6)))))))))))))
% 6.75/7.08 (assert (forall ((S5 tptp.set_nat) (T5 tptp.set_int) (S3 tptp.set_nat) (I (-> tptp.int tptp.nat)) (J (-> tptp.nat tptp.int)) (T6 tptp.set_int) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_nat S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat S3) S5)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat S3) S5)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T6) T5)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T6) T5)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T6) T5)) (@ (@ tptp.member_nat (@ I B2)) (@ (@ tptp.minus_minus_set_nat S3) S5)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) S5) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T5) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups6464643781859351333omplex G) S3) (@ (@ tptp.groups7440179247065528705omplex H2) T6)))))))))))))
% 6.75/7.08 (assert (forall ((S5 tptp.set_nat) (T5 tptp.set_complex) (S3 tptp.set_nat) (I (-> tptp.complex tptp.nat)) (J (-> tptp.nat tptp.complex)) (T6 tptp.set_complex) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite_finite_nat S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat S3) S5)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat S3) S5)) (@ (@ tptp.member_complex (@ J A3)) (@ (@ tptp.minus_811609699411566653omplex T6) T5)))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T6) T5)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T6) T5)) (@ (@ tptp.member_nat (@ I B2)) (@ (@ tptp.minus_minus_set_nat S3) S5)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) S5) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) T5) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups6464643781859351333omplex G) S3) (@ (@ tptp.groups3708469109370488835omplex H2) T6)))))))))))))
% 6.75/7.08 (assert (forall ((S5 tptp.set_nat) (T5 tptp.set_Extended_enat) (S3 tptp.set_nat) (I (-> tptp.extended_enat tptp.nat)) (J (-> tptp.nat tptp.extended_enat)) (T6 tptp.set_Extended_enat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite_finite_nat S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat S3) S5)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat S3) S5)) (@ (@ tptp.member_Extended_enat (@ J A3)) (@ (@ tptp.minus_925952699566721837d_enat T6) T5)))) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat T6) T5)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat T6) T5)) (@ (@ tptp.member_nat (@ I B2)) (@ (@ tptp.minus_minus_set_nat S3) S5)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) S5) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) T5) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups6464643781859351333omplex G) S3) (@ (@ tptp.groups4622424608036095791omplex H2) T6)))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ tptp.collect_nat (lambda ((X tptp.nat)) (= (@ G X) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G X) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X tptp.complex)) (= (@ G X) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (= (@ G X) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ tptp.collect_nat (lambda ((X tptp.nat)) (= (@ G X) tptp.one_one_real))))) (@ _let_1 A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G X) tptp.one_one_real))))) (@ _let_1 A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X tptp.complex)) (= (@ G X) tptp.one_one_real))))) (@ _let_1 A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (= (@ G X) tptp.one_one_real))))) (@ _let_1 A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ tptp.collect_nat (lambda ((X tptp.nat)) (= (@ G X) tptp.one_one_rat))))) (@ _let_1 A2))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G X) tptp.one_one_rat))))) (@ _let_1 A2))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1681761925125756287l_real F) I5)))))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups129246275422532515t_real F) I5)))))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2316167850115554303t_real F) I5)))))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups766887009212190081x_real F) I5)))))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite4001608067531595151d_enat I5) (=> (@ (@ tptp.member_Extended_enat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups97031904164794029t_real F) I5)))))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups4061424788464935467al_rat F) I5)))))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups73079841787564623at_rat F) I5)))))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1072433553688619179nt_rat F) I5)))))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups225925009352817453ex_rat F) I5)))))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite4001608067531595151d_enat I5) (=> (@ (@ tptp.member_Extended_enat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2245840878043517529at_rat F) I5)))))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) I5)))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) I5)))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) I5)))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) I5)))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat I5) (=> (not (= I5 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups97031904164794029t_real F) I5)))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) I5)))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) I5)))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) I5)))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) I5)))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat I5) (=> (not (= I5 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups2245840878043517529at_rat F) I5)))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B4) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B4) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B4) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex H2))) (let ((_let_2 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex H2))) (let ((_let_2 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C4) B4)) (= (@ H2 B2) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex H2))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B4 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex)) (H2 (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex H2))) (let ((_let_2 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B4) C4) (=> (forall ((A3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A3) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat C4) B4)) (= (@ H2 B2) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real H2))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real H2))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C4) B4)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real H2))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B4 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real H2))) (let ((_let_2 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B4) C4) (=> (forall ((A3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A3) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat C4) B4)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat H2))) (let ((_let_2 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_rat))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.rat)) (H2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat H2))) (let ((_let_2 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C4) B4)) (= (@ H2 B2) tptp.one_one_rat))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex H2))) (let ((_let_2 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex H2))) (let ((_let_2 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C4) B4)) (= (@ H2 B2) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex H2))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B4 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex)) (H2 (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex H2))) (let ((_let_2 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B4) C4) (=> (forall ((A3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A3) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat C4) B4)) (= (@ H2 B2) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real H2))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real H2))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C4) B4)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real H2))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B4 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real H2))) (let ((_let_2 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B4) C4) (=> (forall ((A3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A3) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat C4) B4)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat H2))) (let ((_let_2 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.75/7.08 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.rat)) (H2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat H2))) (let ((_let_2 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C4) B4)) (= (@ H2 B2) tptp.one_one_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_complex))) (= (@ _let_1 S3) (@ _let_1 T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ G X4) tptp.one_one_complex))) (= (@ _let_1 S3) (@ _let_1 T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_Extended_enat) (S3 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat T6) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S3) T6) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T6) S3)) (= (@ G X4) tptp.one_one_complex))) (= (@ _let_1 S3) (@ _let_1 T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_real))) (= (@ _let_1 S3) (@ _let_1 T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ G X4) tptp.one_one_real))) (= (@ _let_1 S3) (@ _let_1 T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_Extended_enat) (S3 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat T6) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S3) T6) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T6) S3)) (= (@ G X4) tptp.one_one_real))) (= (@ _let_1 S3) (@ _let_1 T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_rat))) (= (@ _let_1 S3) (@ _let_1 T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ G X4) tptp.one_one_rat))) (= (@ _let_1 S3) (@ _let_1 T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_Extended_enat) (S3 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat G))) (=> (@ tptp.finite4001608067531595151d_enat T6) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S3) T6) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T6) S3)) (= (@ G X4) tptp.one_one_rat))) (= (@ _let_1 S3) (@ _let_1 T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_nat))) (= (@ _let_1 S3) (@ _let_1 T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_complex))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ G X4) tptp.one_one_complex))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_Extended_enat) (S3 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat T6) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S3) T6) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T6) S3)) (= (@ G X4) tptp.one_one_complex))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_real))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ G X4) tptp.one_one_real))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_Extended_enat) (S3 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat T6) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S3) T6) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T6) S3)) (= (@ G X4) tptp.one_one_real))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_rat))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ G X4) tptp.one_one_rat))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_Extended_enat) (S3 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat G))) (=> (@ tptp.finite4001608067531595151d_enat T6) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S3) T6) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T6) S3)) (= (@ G X4) tptp.one_one_rat))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_nat))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ H2 X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups713298508707869441omplex H2) T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ H2 X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups7440179247065528705omplex G) S3) (@ (@ tptp.groups7440179247065528705omplex H2) T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ H2 X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups3708469109370488835omplex G) S3) (@ (@ tptp.groups3708469109370488835omplex H2) T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_Extended_enat) (S3 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.complex)) (G (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite4001608067531595151d_enat T6) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S3) T6) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T6) S3)) (= (@ H2 X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups4622424608036095791omplex G) S3) (@ (@ tptp.groups4622424608036095791omplex H2) T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ H2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1681761925125756287l_real G) S3) (@ (@ tptp.groups1681761925125756287l_real H2) T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ H2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups2316167850115554303t_real G) S3) (@ (@ tptp.groups2316167850115554303t_real H2) T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ H2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups766887009212190081x_real G) S3) (@ (@ tptp.groups766887009212190081x_real H2) T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_Extended_enat) (S3 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat T6) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S3) T6) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T6) S3)) (= (@ H2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups97031904164794029t_real G) S3) (@ (@ tptp.groups97031904164794029t_real H2) T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ H2 X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups4061424788464935467al_rat G) S3) (@ (@ tptp.groups4061424788464935467al_rat H2) T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ H2 X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) S3) (@ (@ tptp.groups1072433553688619179nt_rat H2) T6))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ G X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups713298508707869441omplex G) T6) (@ (@ tptp.groups713298508707869441omplex H2) S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups7440179247065528705omplex G) T6) (@ (@ tptp.groups7440179247065528705omplex H2) S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ G X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups3708469109370488835omplex G) T6) (@ (@ tptp.groups3708469109370488835omplex H2) S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_Extended_enat) (S3 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex)) (H2 (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite4001608067531595151d_enat T6) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S3) T6) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T6) S3)) (= (@ G X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups4622424608036095791omplex G) T6) (@ (@ tptp.groups4622424608036095791omplex H2) S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1681761925125756287l_real G) T6) (@ (@ tptp.groups1681761925125756287l_real H2) S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups2316167850115554303t_real G) T6) (@ (@ tptp.groups2316167850115554303t_real H2) S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups766887009212190081x_real G) T6) (@ (@ tptp.groups766887009212190081x_real H2) S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_Extended_enat) (S3 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat T6) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S3) T6) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T6) S3)) (= (@ G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups97031904164794029t_real G) T6) (@ (@ tptp.groups97031904164794029t_real H2) S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ G X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups4061424788464935467al_rat G) T6) (@ (@ tptp.groups4061424788464935467al_rat H2) S3))))))))
% 6.75/7.08 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.rat)) (H2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) T6) (@ (@ tptp.groups1072433553688619179nt_rat H2) S3))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G M)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G M)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G M)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G M)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.75/7.08 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N3 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 6.75/7.08 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N3 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 6.75/7.08 (assert (= tptp.semiri4449623510593786356d_enat (lambda ((N3 tptp.nat)) (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 6.75/7.08 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N3 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 6.75/7.08 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N3 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I2)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I2)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I2)))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I2)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((I2 tptp.extended_enat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_Extended_enat I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I2)))))) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups97031904164794029t_real F) A2)) (@ (@ tptp.groups97031904164794029t_real G) A2)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I2)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G) A2)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I2)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.groups225925009352817453ex_rat G) A2)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I2)))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.groups73079841787564623at_rat G) A2)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I2)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat G) A2)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (G (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((I2 tptp.extended_enat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_Extended_enat I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I2)))))) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2245840878043517529at_rat F) A2)) (@ (@ tptp.groups2245840878043517529at_rat G) A2)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3455450783089532116nteger F) A2)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3827104343326376752nteger F) A2)) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.code_integer))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups8682486955453173170nteger F) A2)) (exists ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.code_integer))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups845124408420398302nteger F) A2)) (exists ((X tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (exists ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (exists ((X tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups858564598930262913ex_int F) A2)) (exists ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2878480467620962989at_int F) A2)) (exists ((X tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups2703838992350267259T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (X2 tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (X2 tptp.int)) (let ((_let_1 (@ tptp.insert_int X2))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X2))) (let ((_let_2 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups5726676334696518183BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (X2 tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat)) (X2 tptp.int)) (let ((_let_1 (@ tptp.insert_int X2))) (let ((_let_2 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.rat)) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X2))) (let ((_let_2 (@ tptp.groups2245840878043517529at_rat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X2) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X2) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X2) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat X2) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X2) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (X2 tptp.extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X2) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X2) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X2) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X2) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat X2) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y2)) (@ (@ tptp.ord_less_real X2) Y2))))))
% 6.75/7.08 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A4 tptp.nat) (B3 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B3) A4)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F3) (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) B3) (@ (@ F3 A4) Acc2))))))
% 6.75/7.08 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X2))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb) Xc) Y2) (and (=> _let_2 (= Y2 Xc)) (=> (not _let_2) (= Y2 (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (@ (@ X2 Xa2) Xc))))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.real)) (C (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.groups2703838992350267259T_real C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real)) (C (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups1681761925125756287l_real C) (@ (@ tptp.minus_minus_set_real S3) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_2 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups766887009212190081x_real C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real)) (C (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.groups129246275422532515t_real C) (@ (@ tptp.minus_minus_set_nat S3) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_2 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real)) (C (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.groups2316167850115554303t_real C) (@ (@ tptp.minus_minus_set_int S3) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_2 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.real)) (C (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.groups97031904164794029t_real C) (@ (@ tptp.minus_925952699566721837d_enat S3) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S3))) (=> (@ tptp.finite4001608067531595151d_enat S3) (and (=> _let_2 (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.rat)) (C (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ (@ tptp.groups5726676334696518183BT_rat C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups5726676334696518183BT_rat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5726676334696518183BT_rat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat)) (C (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.groups4061424788464935467al_rat C) (@ (@ tptp.minus_minus_set_real S3) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_2 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat)) (C (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.groups225925009352817453ex_rat C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups225925009352817453ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups225925009352817453ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat)) (C (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.groups73079841787564623at_rat C) (@ (@ tptp.minus_minus_set_nat S3) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_2 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real F))) (=> (@ tptp.finite4001608067531595151d_enat B4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B4) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat F))) (=> (@ tptp.finite4001608067531595151d_enat B4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B4) (=> (forall ((B2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B2)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.75/7.08 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B2)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.complex)) (A tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.groups127312072573709053omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.complex)) (A tptp.real)) (let ((_let_1 (@ tptp.groups713298508707869441omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups3708469109370488835omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (A tptp.nat)) (let ((_let_1 (@ tptp.groups6464643781859351333omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.complex)) (A tptp.int)) (let ((_let_1 (@ tptp.groups7440179247065528705omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_int A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.complex)) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.groups4622424608036095791omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (A tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.groups2703838992350267259T_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (A tptp.real)) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (A tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X2)) tptp.zero_zero_real))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.75/7.08 (assert (forall ((A tptp.extended_enat) (N tptp.nat)) (= (@ (@ tptp.comm_s3181272606743183617d_enat A) (@ tptp.suc N)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ tptp.semiri4216267220026989637d_enat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.75/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.75/7.08 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A4 tptp.complex) (N3 tptp.nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat N3) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 6.75/7.08 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N3 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N3) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 6.75/7.08 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N3 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N3) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 6.75/7.08 (assert (= tptp.comm_s3181272606743183617d_enat (lambda ((A4 tptp.extended_enat) (N3 tptp.nat)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A4) (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.minus_minus_nat N3) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 6.75/7.08 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N3) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 6.75/7.08 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N3) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_complex))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_rat))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.75/7.08 (assert (forall ((A tptp.extended_enat) (N tptp.nat)) (= (@ (@ tptp.comm_s3181272606743183617d_enat A) (@ tptp.suc N)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.75/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y2))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arcsin Y2))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_eq_real _let_2) _let_1))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X2)) X2))))))
% 6.75/7.08 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N3 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 6.75/7.08 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N3 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 6.75/7.08 (assert (= tptp.semiri4449623510593786356d_enat (lambda ((N3 tptp.nat)) (@ tptp.semiri4216267220026989637d_enat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 6.75/7.08 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N3 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 6.75/7.08 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N3 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y2))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y2) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y2)) X2))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) Y2) (@ _let_1 (@ tptp.sin_real Y2)))))))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.sin_real _let_1) Y2)))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) _let_2) (= (@ tptp.sin_real _let_1) Y2))))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 6.75/7.08 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I4 tptp.complex)) (@ (@ tptp.plus_plus_complex I4) tptp.one_one_complex))) N3) tptp.zero_zero_complex))))
% 6.75/7.08 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I4 tptp.int)) (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))) N3) tptp.zero_zero_int))))
% 6.75/7.08 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I4 tptp.real)) (@ (@ tptp.plus_plus_real I4) tptp.one_one_real))) N3) tptp.zero_zero_real))))
% 6.75/7.08 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) N3) tptp.zero_zero_nat))))
% 6.75/7.08 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I4 tptp.rat)) (@ (@ tptp.plus_plus_rat I4) tptp.one_one_rat))) N3) tptp.zero_zero_rat))))
% 6.75/7.08 (assert (= tptp.semiri4216267220026989637d_enat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.semiri8563196900006977889d_enat (lambda ((I4 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat I4) tptp.one_on7984719198319812577d_enat))) N3) tptp.zero_z5237406670263579293d_enat))))
% 6.75/7.08 (assert (forall ((R tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R) K2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R) _let_1))))))
% 6.75/7.08 (assert (forall ((R tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R) K2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat R) _let_1))))))
% 6.75/7.08 (assert (forall ((R tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R) K2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R) _let_1))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X2)) X2) (exists ((N3 tptp.int)) (= X2 (@ tptp.ring_1_of_int_real N3))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X2)) X2) (exists ((N3 tptp.int)) (= X2 (@ tptp.ring_1_of_int_rat N3))))))
% 6.75/7.08 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.75/7.08 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.75/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.75/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.75/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.75/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.75/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.75/7.08 (assert (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int))
% 6.75/7.08 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups1707563613775114915nt_nat F) A2) tptp.one_one_nat) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A2) (= (@ F X) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.one_one_nat) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A2) (= (@ F X) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2880970938130013265at_nat F) A2) tptp.one_one_nat) (forall ((X tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ F X) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups708209901874060359at_nat F) A2) tptp.one_one_nat) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A2) (= (@ F X) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (forall ((X tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X))))))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X2))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real V)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X2) (@ tptp.numeral_numeral_rat V)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat))))
% 6.75/7.08 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.75/7.08 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 6.75/7.08 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B)))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X2))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X2))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.75/7.08 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.75/7.08 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int B)))))
% 6.75/7.08 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B)))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X2))))
% 6.75/7.08 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.75/7.08 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int B)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X2))) X2)))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X2))) X2)))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y2)) (@ (@ tptp.ord_less_rat X2) Y2))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X2))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real Z)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat Z)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y2))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y2))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) Y2)))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) X2)))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) (@ tptp.ring_1_of_int_real Z))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.ring_1_of_int_rat Z))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real K)) (@ tptp.ring_1_of_int_real L))) (@ (@ tptp.divide_divide_int K) L))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K)) (@ tptp.ring_1_of_int_rat L))) (@ (@ tptp.divide_divide_int K) L))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X2))) (=> (= X2 (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X2))) (=> (= X2 (@ tptp.ring_1_of_int_rat _let_1)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (= (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) _let_1) (@ (@ tptp.plus_plus_real (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (= (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) _let_1) (@ (@ tptp.plus_plus_rat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (= (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) _let_1) (@ (@ tptp.plus_plus_complex (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_complex A) _let_2) (@ (@ tptp.plus_plus_complex (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_2) (@ (@ tptp.plus_plus_real (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_2) (@ (@ tptp.plus_plus_rat (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex A) K)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ _let_1 tptp.one_one_complex)) K))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real A) K)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ _let_1 tptp.one_one_real)) K))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ _let_1 tptp.one_one_rat)) K))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex A) _let_3) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real A) _let_3) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat A) _let_3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex _let_3) A) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real _let_3) A) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat _let_3) A) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real K))) (=> (@ (@ tptp.ord_less_eq_real _let_1) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) _let_1)) K)) (@ (@ tptp.gbinomial_real A) K))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat K))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) _let_1)) K)) (@ (@ tptp.gbinomial_rat A) K))))))
% 6.75/7.08 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_real R) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R))) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) N))))))
% 6.75/7.08 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real R) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R))) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R)))))
% 6.75/7.08 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R)))))
% 6.75/7.08 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.75/7.08 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I4))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T) (@ (@ tptp.ord_less_real T) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I4)))))))
% 6.75/7.08 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T) (@ (@ tptp.ord_less_rat T) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P I4)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X2) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim3151403230148437115or_rat X2) A) (and (@ (@ tptp.ord_less_eq_rat _let_1) X2) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) Z))))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X2) (=> (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X2) Z))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X2))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X2))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X2))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y2)) (@ tptp.arccos X2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X2)) (@ tptp.arccos Y2)) (@ (@ tptp.ord_less_real Y2) X2))))))
% 6.75/7.08 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) N))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_2)) (@ (@ tptp.gbinomial_complex _let_1) _let_2)) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.gbinomial_complex A) K)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_2)) (@ (@ tptp.gbinomial_real _let_1) _let_2)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.gbinomial_real A) K)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A) K)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ (@ tptp.gbinomial_complex A) _let_1)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) K))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ (@ tptp.gbinomial_real A) _let_1)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) K))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ (@ tptp.gbinomial_rat A) _let_1)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) K))))))
% 6.75/7.08 (assert (forall ((B tptp.int) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real A) (@ tptp.ring_1_of_int_real B))) (@ (@ tptp.divide_divide_int (@ tptp.archim6058952711729229775r_real A)) B)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex M)) K)) (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M)) K)) (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M)) K)) (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_option_nat) (F (-> tptp.option_nat tptp.real))) (=> (@ tptp.finite5523153139673422903on_nat I5) (=> (forall ((I2 tptp.option_nat)) (=> (@ (@ tptp.member_option_nat I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups6579596140936342515t_real F) I5)) (@ (@ tptp.groups4518532050878116744t_real (lambda ((X tptp.option_nat)) (@ tptp.ln_ln_real (@ F X)))) I5))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups1681761925125756287l_real F) I5)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X tptp.real)) (@ tptp.ln_ln_real (@ F X)))) I5))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_set_nat_rat) (F (-> tptp.set_nat_rat tptp.real))) (=> (@ tptp.finite6430367030675640852at_rat I5) (=> (forall ((I2 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups2125999189389939536t_real F) I5)) (@ (@ tptp.groups4357547368389691109t_real (lambda ((X tptp.set_nat_rat)) (@ tptp.ln_ln_real (@ F X)))) I5))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups2316167850115554303t_real F) I5)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X tptp.int)) (@ tptp.ln_ln_real (@ F X)))) I5))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups766887009212190081x_real F) I5)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X tptp.complex)) (@ tptp.ln_ln_real (@ F X)))) I5))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat I5) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups97031904164794029t_real F) I5)) (@ (@ tptp.groups4148127829035722712t_real (lambda ((X tptp.extended_enat)) (@ tptp.ln_ln_real (@ F X)))) I5))))))
% 6.75/7.08 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups129246275422532515t_real F) I5)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X tptp.nat)) (@ tptp.ln_ln_real (@ F X)))) I5))))))
% 6.75/7.08 (assert (forall ((Q2 tptp.real) (P6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P6) Q2)))) Q2)) P6))))
% 6.75/7.08 (assert (forall ((Q2 tptp.rat) (P6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P6) Q2)))) Q2)) P6))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arccos Y2))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K)) (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K)) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))) (@ (@ tptp.gbinomial_complex A) K)))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.gbinomial_real A) K)))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))) (@ (@ tptp.gbinomial_rat A) K)))))))
% 6.75/7.08 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex K2)) A4)) tptp.one_one_complex)) K2)))))
% 6.75/7.08 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real K2)) A4)) tptp.one_one_real)) K2)))))
% 6.75/7.08 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K2)) A4)) tptp.one_one_rat)) K2)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) K)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) K)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) K)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X2)) tptp.zero_zero_real))))))
% 6.75/7.08 (assert (forall ((Q2 tptp.real) (P6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_real P6) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P6) Q2)))) tptp.one_one_real)) Q2)))))
% 6.75/7.08 (assert (forall ((Q2 tptp.rat) (P6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_rat P6) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P6) Q2)))) tptp.one_one_rat)) Q2)))))
% 6.75/7.08 (assert (= tptp.archim8280529875227126926d_real (lambda ((X tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (K tptp.nat)) (= (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (K tptp.nat)) (= (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (K tptp.nat)) (= (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A) K) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A) K) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.75/7.08 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex A4)) K2))) (@ tptp.semiri5044797733671781792omplex K2)))))
% 6.75/7.08 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K2 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat A4)) K2))) (@ tptp.semiri773545260158071498ct_rat K2)))))
% 6.75/7.08 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real A4)) K2))) (@ tptp.semiri2265585572941072030t_real K2)))))
% 6.75/7.08 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A4) (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) K2)) (@ tptp.semiri5044797733671781792omplex K2)))))
% 6.75/7.08 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K2 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A4) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2)) (@ tptp.semiri773545260158071498ct_rat K2)))))
% 6.75/7.08 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A4) (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) K2)) (@ tptp.semiri2265585572941072030t_real K2)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_complex A) _let_1) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups6464643781859351333omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri5044797733671781792omplex _let_1))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_1) (@ (@ tptp.divide_divide_rat (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri773545260158071498ct_rat _let_1))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_1) (@ (@ tptp.divide_divide_real (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2265585572941072030t_real _let_1))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_nat A) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_int A) _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X2)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X2) (@ (@ tptp.ord_less_real X2) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A) K) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A) K) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) _let_2))))) tptp.one_one_int))))))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 6.75/7.08 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A4) (@ tptp.semiri8010041392384452111omplex L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K2))))))
% 6.75/7.08 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A4) (@ tptp.semiri681578069525770553at_rat L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K2))))))
% 6.75/7.08 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A4) (@ tptp.semiri5074537144036343181t_real L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K2))))))
% 6.75/7.08 (assert (forall ((Theta tptp.real)) (not (forall ((K3 tptp.int)) (not (= (@ tptp.arccos (@ tptp.cos_real Theta)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Theta) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real K3)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K2))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K2))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K2))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.75/7.08 (assert (= tptp.binomial (lambda ((N3 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N3) K2))) (let ((_let_2 (@ tptp.ord_less_nat N3))) (@ (@ (@ tptp.if_nat (@ _let_2 K2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2))) (@ (@ tptp.binomial N3) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N3) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K2)))))))))
% 6.75/7.08 (assert (= tptp.archim8280529875227126926d_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.archim2898591450579166408c_real X))) (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim6058952711729229775r_real X)))))
% 6.75/7.08 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X tptp.rat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.archimedean_frac_rat X))) (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim3151403230148437115or_rat X)))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (= (@ (@ tptp.groups2073611262835488442omplex (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) (@ tptp.semiri8010041392384452111omplex M))) tptp.one_one_complex))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_complex _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (= (@ (@ tptp.groups2906978787729119204at_rat (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat _let_2) (@ tptp.semiri681578069525770553at_rat M))) tptp.one_one_rat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ (@ tptp.groups6591440286371151544t_real (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) (@ tptp.semiri5074537144036343181t_real M))) tptp.one_one_real))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_real _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) N)))))))
% 6.75/7.08 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_ord_atMost_real K)) (@ (@ tptp.ord_less_eq_real I) K))))
% 6.75/7.08 (assert (forall ((I tptp.set_nat_rat) (K tptp.set_nat_rat)) (= (@ (@ tptp.member_set_nat_rat I) (@ tptp.set_or3094126398206284534at_rat K)) (@ (@ tptp.ord_le2679597024174929757at_rat I) K))))
% 6.75/7.08 (assert (forall ((I tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ tptp.set_or4236626031148496127et_nat K)) (@ (@ tptp.ord_less_eq_set_nat I) K))))
% 6.75/7.08 (assert (forall ((I tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I) (@ tptp.set_ord_atMost_rat K)) (@ (@ tptp.ord_less_eq_rat I) K))))
% 6.75/7.08 (assert (forall ((I tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I) (@ tptp.set_ord_atMost_num K)) (@ (@ tptp.ord_less_eq_num I) K))))
% 6.75/7.08 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_atMost_int K)) (@ (@ tptp.ord_less_eq_int I) K))))
% 6.75/7.08 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_atMost_nat K)) (@ (@ tptp.ord_less_eq_nat I) K))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 6.75/7.08 (assert (forall ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_or4236626031148496127et_nat X2)) (@ tptp.set_or4236626031148496127et_nat Y2)) (@ (@ tptp.ord_less_eq_set_nat X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X2)) (@ tptp.set_ord_atMost_rat Y2)) (@ (@ tptp.ord_less_eq_rat X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X2)) (@ tptp.set_ord_atMost_num Y2)) (@ (@ tptp.ord_less_eq_num X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X2)) (@ tptp.set_ord_atMost_int Y2)) (@ (@ tptp.ord_less_eq_int X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X2)) (@ tptp.set_ord_atMost_nat Y2)) (@ (@ tptp.ord_less_eq_nat X2) Y2))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N))) (= (@ (@ tptp.binomial (@ tptp.suc N)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.75/7.08 (assert (forall ((L tptp.set_nat) (H2 tptp.set_nat) (H3 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat L) H2)) (@ tptp.set_or4236626031148496127et_nat H3)) (or (not (@ (@ tptp.ord_less_eq_set_nat L) H2)) (@ (@ tptp.ord_less_eq_set_nat H2) H3)))))
% 6.75/7.08 (assert (forall ((L tptp.rat) (H2 tptp.rat) (H3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L) H2)) (@ tptp.set_ord_atMost_rat H3)) (or (not (@ (@ tptp.ord_less_eq_rat L) H2)) (@ (@ tptp.ord_less_eq_rat H2) H3)))))
% 6.75/7.08 (assert (forall ((L tptp.num) (H2 tptp.num) (H3 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num L) H2)) (@ tptp.set_ord_atMost_num H3)) (or (not (@ (@ tptp.ord_less_eq_num L) H2)) (@ (@ tptp.ord_less_eq_num H2) H3)))))
% 6.75/7.08 (assert (forall ((L tptp.nat) (H2 tptp.nat) (H3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L) H2)) (@ tptp.set_ord_atMost_nat H3)) (or (not (@ (@ tptp.ord_less_eq_nat L) H2)) (@ (@ tptp.ord_less_eq_nat H2) H3)))))
% 6.75/7.08 (assert (forall ((L tptp.int) (H2 tptp.int) (H3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L) H2)) (@ tptp.set_ord_atMost_int H3)) (or (not (@ (@ tptp.ord_less_eq_int L) H2)) (@ (@ tptp.ord_less_eq_int H2) H3)))))
% 6.75/7.08 (assert (forall ((L tptp.real) (H2 tptp.real) (H3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L) H2)) (@ tptp.set_ord_atMost_real H3)) (or (not (@ (@ tptp.ord_less_eq_real L) H2)) (@ (@ tptp.ord_less_eq_real H2) H3)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.complex)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_complex (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)) (@ (@ tptp.ord_less_eq_nat K) N))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 6.75/7.08 (assert (= tptp.set_or3094126398206284534at_rat (lambda ((U2 tptp.set_nat_rat)) (@ tptp.collect_set_nat_rat (lambda ((X tptp.set_nat_rat)) (@ (@ tptp.ord_le2679597024174929757at_rat X) U2))))))
% 6.75/7.08 (assert (= tptp.set_or5632376147039224640at_rat (lambda ((U2 (-> tptp.nat tptp.rat))) (@ tptp.collect_nat_rat (lambda ((X (-> tptp.nat tptp.rat))) (@ (@ tptp.ord_less_eq_nat_rat X) U2))))))
% 6.75/7.08 (assert (= tptp.set_or4236626031148496127et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) U2))))))
% 6.75/7.08 (assert (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) U2))))))
% 6.75/7.08 (assert (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) U2))))))
% 6.75/7.08 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) U2))))))
% 6.75/7.08 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) U2))))))
% 6.75/7.08 (assert (forall ((R tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R) K2)) K2))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R) N))) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M)) tptp.one_one_nat)) M))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) K)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (R tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (@ _let_1 K))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K)) (@ (@ tptp.times_times_nat (@ _let_3 K)) (@ (@ tptp.binomial _let_2) M)))))))))
% 6.75/7.08 (assert (forall ((R tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) R)) (@ (@ tptp.power_power_nat N) R)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.minus_minus_nat M) K2)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N)) M)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (R tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K2)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R) K2))))) (@ tptp.set_ord_atMost_nat R)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N)) R))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N)) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K2))) (@ (@ tptp.power_power_nat A) K2))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X2)) tptp.one_one_real)))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ tptp.archimedean_frac_rat X2)) tptp.one_one_rat)))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ tptp.archim2898591450579166408c_real X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ tptp.archimedean_frac_rat X2))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A) B))))) (let ((_let_2 (@ tptp.suc A))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B)) (@ _let_1 A)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K))) _let_1))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.minus_minus_nat M) K)))))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B)) N) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K2))) (@ (@ tptp.power_power_complex A) K2))) (@ (@ tptp.power_power_complex B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K2))) (@ (@ tptp.power_power_int A) K2))) (@ (@ tptp.power_power_int B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat A) B)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K2))) (@ (@ tptp.power_power_rat A) K2))) (@ (@ tptp.power_power_rat B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (N tptp.nat)) (= (@ (@ tptp.power_8040749407984259932d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) N) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.binomial N) K2))) (@ (@ tptp.power_8040749407984259932d_enat A) K2))) (@ (@ tptp.power_8040749407984259932d_enat B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K2))) (@ (@ tptp.power_power_nat A) K2))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K2))) (@ (@ tptp.power_power_real A) K2))) (@ (@ tptp.power_power_real B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) B)) N) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K2))) (@ (@ tptp.comm_s2602460028002588243omplex A) K2))) (@ (@ tptp.comm_s2602460028002588243omplex B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K2))) (@ (@ tptp.comm_s4660882817536571857er_int A) K2))) (@ (@ tptp.comm_s4660882817536571857er_int B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) B)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K2))) (@ (@ tptp.comm_s4028243227959126397er_rat A) K2))) (@ (@ tptp.comm_s4028243227959126397er_rat B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) B)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K2))) (@ (@ tptp.comm_s7457072308508201937r_real A) K2))) (@ (@ tptp.comm_s7457072308508201937r_real B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N) K2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) N))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat (@ tptp.pred_numeral K)))))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat A)) (@ tptp.set_ord_lessThan_rat B)) (@ (@ tptp.ord_less_rat A) B))))
% 6.75/7.08 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num A)) (@ tptp.set_ord_lessThan_num B)) (@ (@ tptp.ord_less_num A) B))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int A)) (@ tptp.set_ord_lessThan_int B)) (@ (@ tptp.ord_less_int A) B))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat A)) (@ tptp.set_ord_lessThan_nat B)) (@ (@ tptp.ord_less_nat A) B))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real A)) (@ tptp.set_or5984915006950818249n_real B)) (@ (@ tptp.ord_less_real A) B))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I4)) (@ tptp.semiri8010041392384452111omplex I4))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I4)) (@ tptp.semiri4939895301339042750nteger I4))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I4)) (@ tptp.semiri1314217659103216013at_int I4))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I4)) (@ tptp.semiri681578069525770553at_rat I4))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ tptp.semiri5074537144036343181t_real I4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) K))))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat I4) (@ (@ tptp.binomial N) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.binomial N) K)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I4)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I4)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I4)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I4)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (D2 (-> tptp.nat tptp.complex))) (= (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex X) I4)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ D2 I4)) (@ (@ tptp.power_power_complex X) I4)))) _let_1)))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ C I4) (@ D2 I4)))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (D2 (-> tptp.nat tptp.real))) (= (forall ((X tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real X) I4)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ D2 I4)) (@ (@ tptp.power_power_real X) I4)))) _let_1)))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ C I4) (@ D2 I4)))))))
% 6.75/7.08 (assert (forall ((A (-> tptp.nat tptp.int)) (B4 tptp.int)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int A) (@ tptp.set_ord_atMost_nat N2))) B4)) (@ tptp.summable_int A)))))
% 6.75/7.08 (assert (forall ((A (-> tptp.nat tptp.nat)) (B4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat A) (@ tptp.set_ord_atMost_nat N2))) B4)) (@ tptp.summable_nat A)))))
% 6.75/7.08 (assert (forall ((A (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real A) (@ tptp.set_ord_atMost_nat N2))) B4)) (@ tptp.summable_real A)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real K))) K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri681578069525770553at_rat K))) K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X2) X2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X2) X2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat)))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (forall ((X tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex X) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ C I4) tptp.zero_zero_complex))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat)) (= (forall ((X tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real X) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ C I4) tptp.zero_zero_real))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (K tptp.nat)) (=> (forall ((W3 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex W3) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ C K) tptp.zero_zero_complex)))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (K tptp.nat)) (=> (forall ((W3 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real W3) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ C K) tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X2)) (@ tptp.archim2898591450579166408c_real Y2)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X2) Y2)))) (let ((_let_3 (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X2)) (@ tptp.archimedean_frac_rat Y2)))) (let ((_let_2 (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X2) Y2)))) (let ((_let_3 (@ (@ tptp.ord_less_rat _let_1) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_complex (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.75/7.08 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K2))) K2))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) N))))
% 6.75/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K2))) K2))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) N))))
% 6.75/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K2))) K2))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) N))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ 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)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K2) I4)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ 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)) N))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K2) I4)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ 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)) N))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K2) I4)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ 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)) N))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K2) I4)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N) _let_1))) (let ((_let_3 (@ tptp.binomial N))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I4))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I4))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I4))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I4))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I4))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I4))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_rat (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I4))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I4))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K))))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K))))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ (@ tptp.times_times_complex (@ _let_2 X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ (@ tptp.times_times_rat (@ _let_2 X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ (@ tptp.times_times_real (@ _let_2 X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex X) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (not (= (@ C I4) tptp.zero_zero_complex)))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real X) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (not (= (@ C I4) tptp.zero_zero_real)))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.complex)) (K tptp.nat) (N tptp.nat)) (=> (not (= (@ C K) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex Z2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.real)) (K tptp.nat) (N tptp.nat)) (=> (not (= (@ C K) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real Z2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.complex)) (A tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex A) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex) (not (forall ((B2 (-> tptp.nat tptp.complex))) (not (forall ((Z5 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z5) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ B2 I4)) (@ (@ tptp.power_power_complex Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.rat)) (A tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat A) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat) (not (forall ((B2 (-> tptp.nat tptp.rat))) (not (forall ((Z5 tptp.rat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z5) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ B2 I4)) (@ (@ tptp.power_power_rat Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.int)) (A tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ C I4)) (@ (@ tptp.power_power_int A) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int) (not (forall ((B2 (-> tptp.nat tptp.int))) (not (forall ((Z5 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ C I4)) (@ (@ tptp.power_power_int Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z5) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ B2 I4)) (@ (@ tptp.power_power_int Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.real)) (A tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real A) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real) (not (forall ((B2 (-> tptp.nat tptp.real))) (not (forall ((Z5 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z5) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ B2 I4)) (@ (@ tptp.power_power_real Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (A tptp.complex)) (exists ((B2 (-> tptp.nat tptp.complex))) (forall ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex Z5) I4)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z5) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ B2 I4)) (@ (@ tptp.power_power_complex Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex A) I4)))) _let_1))))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.rat)) (N tptp.nat) (A tptp.rat)) (exists ((B2 (-> tptp.nat tptp.rat))) (forall ((Z5 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat Z5) I4)))) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z5) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ B2 I4)) (@ (@ tptp.power_power_rat Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat A) I4)))) _let_1))))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.int)) (N tptp.nat) (A tptp.int)) (exists ((B2 (-> tptp.nat tptp.int))) (forall ((Z5 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ C I4)) (@ (@ tptp.power_power_int Z5) I4)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z5) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ B2 I4)) (@ (@ tptp.power_power_int Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ C I4)) (@ (@ tptp.power_power_int A) I4)))) _let_1))))))))
% 6.75/7.08 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (A tptp.real)) (exists ((B2 (-> tptp.nat tptp.real))) (forall ((Z5 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real Z5) I4)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z5) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ B2 I4)) (@ (@ tptp.power_power_real Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real A) I4)))) _let_1))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I4) J3)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K2) I4)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I4) J3)) N))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K2) I4)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I4) J3)) N))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K2) I4)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.75/7.08 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I4) J3)) N))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K2) I4)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.75/7.08 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K2)))) (=> (@ tptp.summable_real (lambda ((K2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K2)))) (@ tptp.summable_complex (lambda ((K2 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I4)) (@ B (@ (@ tptp.minus_minus_nat K2) I4))))) (@ tptp.set_ord_atMost_nat K2))))))))
% 6.75/7.08 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K2)))) (=> (@ tptp.summable_real (lambda ((K2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K2)))) (@ tptp.summable_real (lambda ((K2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A I4)) (@ B (@ (@ tptp.minus_minus_nat K2) I4))))) (@ tptp.set_ord_atMost_nat K2))))))))
% 6.75/7.08 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K2)))) (=> (@ tptp.summable_real (lambda ((K2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K2)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)) (@ tptp.suminf_complex (lambda ((K2 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I4)) (@ B (@ (@ tptp.minus_minus_nat K2) I4))))) (@ tptp.set_ord_atMost_nat K2)))))))))
% 6.75/7.08 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K2)))) (=> (@ tptp.summable_real (lambda ((K2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K2)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A I4)) (@ B (@ (@ tptp.minus_minus_nat K2) I4))))) (@ tptp.set_ord_atMost_nat K2)))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A I2) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ (@ tptp.power_power_nat X2) I4)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X2) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K2)) (@ B (@ (@ tptp.minus_minus_nat R5) K2))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X2)) N)))))
% 6.75/7.08 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N3 tptp.nat)) N3)))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X2)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X2)))))
% 6.75/7.08 (assert (= tptp.divide_divide_real (lambda ((X tptp.real) (Y tptp.real)) (@ (@ tptp.times_times_real X) (@ tptp.inverse_inverse_real Y)))))
% 6.75/7.08 (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 ((N2 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.75/7.08 (assert (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3)))) (and (not (= N3 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))))
% 6.75/7.08 (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 ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sqrt X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.divide_divide_real _let_1) X2) (@ tptp.inverse_inverse_real _let_1))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X2)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X2))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ _let_1 (@ tptp.inverse_inverse_real X2)) (@ tptp.uminus_uminus_real (@ _let_1 X2))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X2) (@ tptp.inverse_inverse_real X2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (=> (@ (@ tptp.ord_less_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T4)) (@ tptp.sin_real T4)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X2)) tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) (@ tptp.sinh_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X2)) (@ _let_1 X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y2)) (@ (@ tptp.ord_less_real Y2) X2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y2)) (@ (@ tptp.ord_less_real X2) Y2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y2))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real A) _let_2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real B)) _let_2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X2) Y2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ tptp.inverse_inverse_real X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) (@ tptp.inverse_inverse_real X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)) (@ tptp.cot_real X2))))
% 6.75/7.08 (assert (= tptp.arctan (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.tan_real X) Y))))))))
% 6.75/7.08 (assert (= tptp.arcsin (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.sin_real X) Y))))))))
% 6.75/7.08 (assert (forall ((L 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 L))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))) _let_1)))))))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (I tptp.int)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real I)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I)))))))))))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.75/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W) Z)))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 6.75/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.75/7.08 (assert (forall ((V tptp.num) (V3 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V3)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V3))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) (@ tptp.nat2 Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y2))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X2))) A) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real A)))))
% 6.75/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.75/7.08 (assert (forall ((V tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) tptp.one_one_nat) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) tptp.one_one_int)))))
% 6.75/7.08 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 6.75/7.08 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.75/7.08 (assert (= tptp.numeral_numeral_nat (lambda ((I4 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I4)))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y2)))))
% 6.75/7.08 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (=> (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L)) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L))))))
% 6.75/7.08 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M3) (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) Z))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X2)) N) (@ (@ tptp.ord_less_eq_int X2) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B))) (@ (@ tptp.plus_plus_nat A) B))))
% 6.75/7.08 (assert (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (@ (@ tptp.dvd_dvd_int L) K)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.modulo_modulo_int K) L)) (@ tptp.sgn_sgn_int L))))))
% 6.75/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W) Z))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W))) (@ tptp.nat2 (@ tptp.abs_abs_int Z))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X2))))))
% 6.75/7.08 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.75/7.08 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 6.75/7.08 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 6.75/7.08 (assert (= tptp.divide_divide_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 6.75/7.08 (assert (= tptp.sgn_sgn_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (= I4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.75/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.75/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int W) Z)))))
% 6.75/7.08 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N3 tptp.nat)) (=> (= I (@ tptp.semiri1314217659103216013at_int N3)) (@ P N3))) (=> (@ (@ tptp.ord_less_int I) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) K)))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z7)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))))
% 6.75/7.08 (assert (forall ((V tptp.int) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) (@ _let_3 _let_1)) (@ (@ tptp.divide_divide_int _let_2) _let_1))))))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int K) L)))) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X2) Y2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y2))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X2) Y2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y2))))))
% 6.75/7.08 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.dvd_dvd_int L) K) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K)) (@ tptp.sgn_sgn_int L))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L)))))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X2) Y2)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y2))))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.divide_divide_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) A) (@ (@ tptp.ord_less_eq_nat X2) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.modulo_modulo_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.75/7.08 (assert (= tptp.divide_divide_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) (@ tptp.sgn_sgn_int L2))) (@ 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 L2) K2))))))))))))
% 6.75/7.08 (assert (= tptp.modulo_modulo_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L2))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) _let_3)) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K2))))) _let_2)))))))))))
% 6.75/7.08 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((W tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1314217659103216013at_int M))))))
% 6.75/7.08 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z7)))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A) B))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B) A))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A) B))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) N)))))
% 6.75/7.08 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z7))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z7)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z7) tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (@ tptp.nat2 _let_1)))))))))))
% 6.75/7.08 (assert (forall ((R tptp.int) (L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R) (@ tptp.sgn_sgn_int L)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R)) (@ tptp.abs_abs_int L)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) L)) R)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R)))))))
% 6.75/7.08 (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)))))))))))))
% 6.75/7.08 (assert (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A33 tptp.product_prod_int_int)) (or (exists ((K2 tptp.int)) (and (= A12 K2) (= A23 tptp.zero_zero_int) (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K2)))) (exists ((L2 tptp.int) (K2 tptp.int) (Q4 tptp.int)) (and (= A12 K2) (= A23 L2) (= A33 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K2 (@ (@ tptp.times_times_int Q4) L2)))) (exists ((R5 tptp.int) (L2 tptp.int) (K2 tptp.int) (Q4 tptp.int)) (and (= A12 K2) (= A23 L2) (= A33 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L2)) (= K2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L2)) R5))))))))
% 6.75/7.08 (assert (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L))) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L)))) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L) K)))))))))
% 6.75/7.08 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.nat2 K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K))))))
% 6.75/7.08 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real))))))
% 6.75/7.08 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))))
% 6.75/7.08 (assert (forall ((L 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 L))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))))))))))))))))
% 6.75/7.08 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K2 _let_2) (= L2 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X2)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X2))))))
% 6.75/7.08 (assert (forall ((S tptp.vEBT_VEBT) (M tptp.nat) (Listy tptp.list_VEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M))))) (=> (@ (@ tptp.vEBT_invar_vebt S) M) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Listy)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (= M (@ tptp.suc N)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Listy)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height X4)) (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N)))))) (=> (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height S)) _let_1) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT S) (@ tptp.set_VEBT_VEBT2 Listy))))) _let_1)))))))))
% 6.75/7.08 (assert (forall ((T tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 TreeList))) (=> (@ (@ tptp.member_VEBT_VEBT T) _let_1) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_height T)) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary) _let_1))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X14 tptp.vEBT_VEBT) (M tptp.nat) (X13 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_VEBT_height X14))) (let ((_let_2 (@ tptp.times_times_nat N))) (@ (@ tptp.ord_less_eq_nat (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat M) (@ _let_2 (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.insert_nat _let_1) (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13)))))))))))
% 6.75/7.08 (assert (forall ((I tptp.nat) (X13 tptp.list_VEBT_VEBT) (Foo tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT X13)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_height (@ (@ tptp.nth_VEBT_VEBT X13) I))) (@ (@ tptp.ord_max_nat Foo) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13))))))))
% 6.75/7.08 (assert (forall ((I tptp.nat) (X13 tptp.list_VEBT_VEBT) (N tptp.nat) (X14 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT X13)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ tptp.vEBT_VEBT_height (@ (@ tptp.nth_VEBT_VEBT X13) I)))) (@ tptp.suc (@ tptp.suc (@ _let_1 (@ (@ tptp.ord_max_nat (@ tptp.vEBT_VEBT_height X14)) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13))))))))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int K) L)) (and (@ _let_1 K) (@ _let_1 L))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L) N)))))
% 6.75/7.08 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se1409905431419307370or_int K) L)))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X2) Y2)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y2)) (@ (@ tptp.bit_se1409905431419307370or_int X2) Y2)) (@ (@ tptp.plus_plus_int X2) Y2))))
% 6.75/7.08 (assert (forall ((Uu tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (@ tptp.vEBT_VEBT_height (@ (@ (@ (@ tptp.vEBT_Node Uu) Deg) TreeList) Summary)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary) (@ tptp.set_VEBT_VEBT2 TreeList))))))))
% 6.75/7.08 (assert (= tptp.sgn_sgn_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (= A4 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A4)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.75/7.08 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_height X2) Y2) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B2))) (not (= Y2 tptp.zero_zero_nat))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList2) Summary2)) (not (= Y2 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary2) (@ tptp.set_VEBT_VEBT2 TreeList2))))))))))))))
% 6.75/7.08 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K2) N3)) M3))))))))
% 6.75/7.08 (assert (forall ((A tptp.real) (N tptp.nat) (X2 tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) X2) (=> (= X2 (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int X2) _let_1) (=> (@ (@ tptp.ord_less_int Y2) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X2) Y2)) _let_1)))))))
% 6.75/7.08 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 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))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K2)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.75/7.08 (assert (forall ((Y2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2)))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 6.75/7.08 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 6.75/7.08 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 6.75/7.08 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.75/7.08 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 6.75/7.08 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.75/7.08 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.75/7.08 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.75/7.08 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y2 tptp.one))))) (let ((_let_3 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X2) Xa2) Y2) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y2 (@ tptp.bit1 M4)))))) (=> (=> _let_3 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (not (= Y2 _let_1)))))) (=> (=> (exists ((N2 tptp.num)) (= X2 (@ tptp.bit0 N2))) (=> _let_1 (not (= Y2 (@ tptp.bit0 tptp.one))))) (=> (forall ((N2 tptp.num)) (=> (= X2 (@ tptp.bit0 N2)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M4)))))))) (=> (forall ((N2 tptp.num)) (=> (= X2 (@ tptp.bit0 N2)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M4)) (not (= Y2 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N2) M4)))))))) (=> (=> (exists ((N2 tptp.num)) (= X2 (@ tptp.bit1 N2))) _let_2) (=> (forall ((N2 tptp.num)) (=> (= X2 (@ tptp.bit1 N2)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M4)))))))) (not (forall ((N2 tptp.num)) (=> (= X2 (@ tptp.bit1 N2)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M4)) (not (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M4)))))))))))))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.75/7.08 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M3)) (not (@ _let_2 N3))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 6.75/7.08 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N3) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N3) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1))))))))))
% 6.75/7.08 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.75/7.08 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) tptp.one_one_complex))
% 6.75/7.08 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.real_V4546457046886955230omplex tptp.pi))) tptp.imaginary_unit)) tptp.one_one_complex))
% 6.75/7.08 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2)))))
% 6.75/7.08 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2)))))
% 6.75/7.08 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.75/7.08 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.75/7.08 (assert (= (@ tptp.cis (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)))
% 6.75/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.cis A)) N) (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))))
% 6.75/7.08 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N3) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N3) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1))))))))))
% 6.75/7.08 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M3)) (not (@ _let_2 N3)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 6.75/7.08 (assert (= (@ tptp.arg (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.75/7.08 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K2 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K2))) (@ tptp.semiri5074537144036343181t_real N))))) (@ tptp.set_ord_lessThan_nat N)) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))))))
% 6.75/7.08 (assert (= (@ tptp.csqrt tptp.imaginary_unit) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.imaginary_unit)) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int K) L)) (= (@ _let_1 K) (@ _let_1 L))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) N) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L) N))))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X2) Y2)))))))
% 6.75/7.08 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int X2) _let_1) (=> (@ (@ tptp.ord_less_int Y2) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X2) Y2)) _let_1)))))))
% 6.75/7.08 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 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))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K2)) (not (@ _let_2 L2)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex) (X2 tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X2)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.arg Z) X2))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (=> (not (= Z tptp.zero_zero_complex)) (and (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis _let_1)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi))))))
% 6.75/7.08 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L2)) (@ (@ (@ tptp.if_int (= L2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K2)) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))))))
% 6.75/7.08 (assert (= tptp.arg (lambda ((Z2 tptp.complex)) (@ (@ (@ tptp.if_real (= Z2 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A4 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z2) (@ tptp.cis A4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A4) (@ (@ tptp.ord_less_eq_real A4) tptp.pi))))))))
% 6.75/7.08 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cis (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_complex))))
% 6.75/7.08 (assert (forall ((Bs tptp.list_o)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_int (@ (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) _let_1) Bs)) (@ (@ tptp.power_power_int _let_1) (@ tptp.size_size_list_o Bs))))))
% 6.75/7.08 (assert (forall ((M7 tptp.set_nat) (N4 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N4) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N4))))
% 6.75/7.08 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit_ri7919022796975470100ot_int K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.75/7.08 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_ri7919022796975470100ot_int K)) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.75/7.08 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K2)) (@ tptp.bit_ri7919022796975470100ot_int L2))))))
% 6.75/7.08 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K2 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K2)) tptp.one_one_int))))
% 6.75/7.08 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.75/7.08 (assert (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int)))
% 6.75/7.08 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K2) (@ tptp.bit_ri7919022796975470100ot_int L2))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K2)) L2)))))
% 6.75/7.08 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_ri7919022796975470100ot_int K)) _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K) _let_1))))))
% 6.75/7.08 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int K)) (not (@ _let_1 K))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int)))
% 6.75/7.08 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) _let_1))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N) M))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.zero_zero_int)))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.75/7.08 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.75/7.08 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) K2))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K2) _let_1))))))))
% 6.75/7.08 (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 ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ _let_1 K)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.75/7.08 (assert (forall ((N tptp.nat) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) tptp.zero_zero_int) L) (@ (@ tptp.bit_se545348938243370406it_int N) L))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X2) X2)))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X2) (@ _let_1 Y2)) (= X2 Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X2) tptp.zero_zero_real)))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_real X2) Y2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) tptp.one_one_real) tptp.one_one_real))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X2) tptp.one_one_real) (= X2 tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y2)) (@ _let_1 Y2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y2)) (@ _let_1 Y2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y2)) (@ _let_1 Y2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y2)) (@ _let_1 Y2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ _let_1 X2))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N))) (= (@ _let_1 (@ _let_2 X2)) (@ _let_2 (@ _let_1 X2)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N) K)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.inverse_inverse_real X2)) (@ tptp.inverse_inverse_real (@ _let_1 X2))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N)) X2) (@ (@ tptp.root M) (@ (@ tptp.root N) X2)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real (@ _let_1 X2)) (@ _let_1 Y2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.times_times_real (@ _let_1 X2)) (@ _let_1 Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.root N) X2))))))
% 6.75/7.08 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N3) (@ (@ tptp.bit_se547839408752420682it_nat M3) tptp.one_one_nat)))))
% 6.75/7.08 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N3) (@ (@ tptp.bit_se547839408752420682it_nat M3) tptp.one_one_nat)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y2)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y2)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X2) K)) (@ (@ tptp.power_power_real (@ _let_1 X2)) K))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real (@ _let_1 X2)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X2)) (@ tptp.sgn_sgn_real X2)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N) M))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q2)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q2) (@ (@ tptp.minus_minus_nat N) M))))))
% 6.75/7.08 (assert (= tptp.bit_concat_bit (lambda ((N3 tptp.nat) (K2 tptp.int) (L2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N3) K2)) (@ (@ tptp.bit_se545348938243370406it_int N3) L2)))))
% 6.75/7.08 (assert (= tptp.bit_concat_bit (lambda ((N3 tptp.nat) (K2 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N3) K2)) (@ (@ tptp.bit_se545348938243370406it_int N3) L2)))))
% 6.75/7.08 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K2) (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int)))))
% 6.75/7.08 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K2) (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.root N) X2)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ (@ tptp.root N4) X2)) (@ (@ tptp.root N) X2)))))))
% 6.75/7.08 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y2) N))) (@ tptp.abs_abs_real Y2)))))
% 6.75/7.08 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K2) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) (@ (@ tptp.root N4) X2))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N4) X2)) (@ (@ tptp.root N) X2)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X2) N)) X2)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (= (@ (@ tptp.power_power_real Y2) N) X2) (= (@ (@ tptp.root N) X2) Y2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (Y2 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y2) N) X2) (= (@ (@ tptp.root N) X2) Y2)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X2) N)) X2))))
% 6.75/7.08 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.times_times_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 6.75/7.08 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N3 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.times_times_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) (@ (@ tptp.root N4) X2))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N)) X2)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N))) Y2))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (B tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N) B)) X2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) X2)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.75/7.08 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X2 tptp.real)) (= (@ P (@ (@ tptp.root N) X2)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N)) X2) (@ P Y))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.root N) X2) (@ (@ tptp.powr_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_height X2) Y2) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) X2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_1) (=> (= Y2 tptp.zero_zero_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) _let_1)))))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y2 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary2) (@ tptp.set_VEBT_VEBT2 TreeList2)))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) _let_1))))))))))))
% 6.75/7.08 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X7 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M3) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N3) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X7 M3)) (@ X7 N3)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N) (@ P M3))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N) (@ P M3))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (K tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K)))) (let ((_let_3 (@ tptp.pred_numeral K))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M) _let_3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.insert_nat _let_3) (@ _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))))
% 6.75/7.08 (assert (forall ((C tptp.nat) (Y2 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X2) Y2))) (let ((_let_2 (@ (@ tptp.ord_less_nat X2) Y2))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y2))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X2) C)) (@ (@ tptp.minus_minus_nat Y2) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.75/7.08 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) tptp.one_one_nat)))))
% 6.75/7.08 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X2) Y2) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_1) (=> (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y2 tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X2) Y2) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_1) (=> (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y2 tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ A I2)) (@ A J2))))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I2))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ B I4)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (=> (= (@ tptp.vEBT_T_m_i_n_t X2) Y2) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) X2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_1) (=> (= Y2 (@ _let_2 (@ (@ (@ tptp.if_nat A3) tptp.zero_zero_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) _let_1)))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (=> (= (@ tptp.vEBT_T_m_a_x_t X2) Y2) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) X2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_1) (=> (= Y2 (@ _let_2 (@ (@ (@ tptp.if_nat B2) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1)))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel))) (=> (= (@ tptp.vEBT_T_m_i_n_N_u_l_l X2) Y2) (=> (@ _let_2 X2) (=> (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (= (@ tptp.vEBT_VEBT_minNull X2) Y2) (=> (@ _let_2 X2) (=> (=> (= X2 _let_1) (=> Y2 (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X2 _let_1) (=> Y2 (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (@ tptp.vEBT_VEBT_minNull X2) (=> (@ _let_2 X2) (=> (=> (= X2 _let_1) (not (@ _let_2 _let_1))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X2)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X2) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 6.75/7.08 (assert (forall ((T tptp.vEBT_VEBT) (D2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D2) (@ (@ tptp.vEBT_invar_vebt T) D2))))
% 6.75/7.08 (assert (forall ((T tptp.vEBT_VEBT) (D2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D2) (@ (@ tptp.vEBT_VEBT_valid T) D2))))
% 6.75/7.08 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.75/7.08 (assert (forall ((Uu Bool) (Uv Bool) (D2 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D2) (= D2 tptp.one_one_nat))))
% 6.75/7.08 (assert (= tptp.code_Target_positive tptp.numeral_numeral_int))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.csqrt Z)) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.re (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 6.75/7.08 (assert (= tptp.csqrt (lambda ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z2))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z2))) (let ((_let_4 (@ tptp.im Z2))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_4 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.im Z))) (= (@ tptp.im (@ tptp.csqrt Z)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_1 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_1))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.75/7.08 (assert (= tptp.divide1717551699836669952omplex (lambda ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y))) (let ((_let_3 (@ tptp.re Y))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (@ tptp.times_times_real (@ tptp.re X)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ _let_5 _let_3)) (@ _let_6 _let_2))) _let_4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_6 _let_3)) (@ _let_5 _let_2))) _let_4)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.power_power_complex X2) N)) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_real (@ tptp.re X2)) N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.im X2))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X2)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X2)))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.csqrt Z))) (let ((_let_2 (@ tptp.re _let_1))) (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (and (= _let_2 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im _let_1))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.im (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X2))) (@ tptp.im X2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X2) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X2)) _let_1))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= Z tptp.zero_zero_complex) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)) tptp.zero_zero_real)))))
% 6.75/7.08 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z2)) _let_1)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X2))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X2)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X2)) _let_1))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (= Z tptp.zero_zero_complex)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y2))) (let ((_let_3 (@ tptp.re Y2))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X2)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.75/7.08 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.re W))) (=> (= (@ (@ tptp.power_power_complex W) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im W)))) (= (@ tptp.csqrt Z) W))))))
% 6.75/7.08 (assert (forall ((B tptp.complex)) (let ((_let_1 (@ tptp.re B))) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im B)))) (= (@ tptp.csqrt (@ (@ tptp.power_power_complex B) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) B)))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X2))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X2)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y2))) (let ((_let_3 (@ tptp.re Y2))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X2)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z)))) (@ (@ tptp.times_times_real (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.real_V1022390504157884413omplex Z))) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.re Z)) _let_2)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.im Z)) _let_2)) _let_1)) tptp.one_one_real))))))
% 6.75/7.08 (assert (= tptp.invers8013647133539491842omplex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (let ((_let_3 (@ tptp.re X))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real _let_3) _let_4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_4)))))))))
% 6.75/7.08 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 6.75/7.08 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 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 L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 6.75/7.08 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (= (@ tptp.cnj (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex (@ tptp.cnj X2)) N))))
% 6.75/7.08 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 6.75/7.08 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 6.75/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.divide1717551699836669952omplex A) B))) (and (= (@ _let_2 (@ tptp.re _let_3)) (@ _let_2 (@ tptp.re _let_1))) (= (@ _let_2 (@ tptp.im _let_3)) (@ _let_2 (@ tptp.im _let_1)))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re Z))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.minus_minus_complex Z) (@ tptp.cnj Z)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.im Z)))) tptp.imaginary_unit))))
% 6.75/7.08 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A4) (@ tptp.cnj B3))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((Z tptp.complex) (W tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex Z) (@ tptp.cnj W)))) (= (@ (@ tptp.plus_plus_complex _let_1) (@ (@ tptp.times_times_complex (@ tptp.cnj Z)) W)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re _let_1)))))))
% 6.75/7.08 (assert (= tptp.code_integer_of_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))) N)))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I4) N)))) (@ tptp.suc N))))
% 6.75/7.08 (assert (= tptp.abs_abs_Code_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K2)) K2))))
% 6.75/7.08 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.75/7.08 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ (@ tptp.ord_less_int Xa2) X2))))
% 6.75/7.08 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int Xa2) X2)))))
% 6.75/7.08 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 6.75/7.08 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 6.75/7.08 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 6.75/7.08 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A2))))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (= A2 _let_1)))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S3)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S3))))))
% 6.75/7.08 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N4)) N))))
% 6.75/7.08 (assert (forall ((S3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S3)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) S3))))
% 6.75/7.08 (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 ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C)))) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))) N))))
% 6.75/7.08 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.75/7.08 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 6.75/7.08 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.75/7.08 (assert (= tptp.code_int_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K2)))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L2 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 L2)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.code_int_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_int K))))
% 6.75/7.08 (assert (forall ((X2 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.divide6298287555418463151nteger X2) Xa2)) (@ (@ tptp.divide_divide_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa2)))))
% 6.75/7.08 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer K2)) (@ tptp.code_int_of_integer L2)))))
% 6.75/7.08 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa4)))))
% 6.75/7.08 (assert (= tptp.code_num_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_num _let_1) _let_1))) (@ (@ (@ tptp.if_num (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (= tptp.code_nat_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (= tptp.code_bit_cut_integer (lambda ((K2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K2) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K2)))))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.75/7.08 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 6.75/7.08 (assert (= tptp.code_bit_cut_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K2)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S6))) (= S6 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.75/7.08 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 6.75/7.08 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M5)))) M)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M5) N)))) M)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K2 tptp.nat)) K2)) (@ _let_1 N))))))
% 6.75/7.08 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K2) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L2)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K2)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L2) S6)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K2)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L2)) S6)))))) _let_1))))))))))))
% 6.75/7.08 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 6.75/7.08 (assert (= tptp.archim6058952711729229775r_real (lambda ((X tptp.real)) (@ tptp.the_int (lambda ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))))
% 6.75/7.08 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X tptp.rat)) (@ tptp.the_int (lambda ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))))
% 6.75/7.08 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N) K)) (@ _let_1 K)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N) _let_1) _let_1))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.75/7.08 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.75/7.08 (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))))))
% 6.75/7.08 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 6.75/7.08 (assert (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (not (forall ((S2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S2) (forall ((T4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T4) (not (= R (@ (@ tptp.plus_plus_rat S2) T4)))))))))))
% 6.75/7.08 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N) M)) K)))))
% 6.75/7.08 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.divide_divide_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 6.75/7.08 (assert (forall ((Q2 tptp.int) (P6 tptp.int)) (=> (@ (@ tptp.ord_less_int Q2) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P6) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P6)) (@ tptp.uminus_uminus_int Q2)))))))
% 6.75/7.08 (assert (= tptp.nat_prod_decode_aux (lambda ((K2 tptp.nat) (M3 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M3) K2)) (@ (@ tptp.product_Pair_nat_nat M3) (@ (@ tptp.minus_minus_nat K2) M3))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M3) _let_1)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X2))) (=> (= (@ (@ tptp.nat_prod_decode_aux X2) Xa2) Y2) (and (=> _let_2 (= Y2 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X2) Xa2)))) (=> (not _let_2) (= Y2 (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N) K)))))
% 6.75/7.08 (assert (forall ((R tptp.product_prod_int_int) (P6 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.normalize R) (@ (@ tptp.product_Pair_int_int P6) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.75/7.08 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N3 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.divide_divide_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_snd_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_fst_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 6.75/7.08 (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))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.divide_divide_nat M) N))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.modulo_modulo_nat M) N))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N)))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N))))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N)))))))
% 6.75/7.08 (assert (= tptp.adjust_mod (lambda ((L2 tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= R5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L2) R5)))))
% 6.75/7.08 (assert (= tptp.bezw (lambda ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X2) Xa2) Y2) (and (=> _let_3 (= Y2 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y2 (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Xa2))))))))))))))
% 6.75/7.08 (assert (forall ((Y2 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y2) (@ (@ tptp.modulo_modulo_nat X2) Y2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y2) (= (@ (@ tptp.bezw X2) Y2) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Y2)))))))))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X2) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_4 (= Y2 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y2 (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Xa2)))))))) (not _let_1)))))))))))
% 6.75/7.08 (assert (= tptp.normalize (lambda ((P4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P4))) (let ((_let_2 (@ tptp.product_fst_int_int P4))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 6.75/7.08 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int M) N)) (or (not (= M tptp.zero_zero_int)) (not (= N tptp.zero_zero_int))))))
% 6.75/7.08 (assert (forall ((N tptp.num) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int _let_1)) X2) (@ (@ tptp.gcd_gcd_int _let_1) X2)))))
% 6.75/7.08 (assert (forall ((X2 tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.gcd_gcd_int X2))) (= (@ _let_2 (@ tptp.uminus_uminus_int _let_1)) (@ _let_2 _let_1))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) A))))
% 6.75/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) B))))
% 6.75/7.08 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y2) (= (@ (@ tptp.gcd_gcd_int X2) Y2) (@ (@ tptp.gcd_gcd_int Y2) (@ (@ tptp.modulo_modulo_int X2) Y2))))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (@ tptp.suc X2))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X2))) (=> (= (@ (@ tptp.nat_prod_decode_aux X2) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_3 (= Y2 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X2) Xa2)))) (=> (not _let_3) (= Y2 (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 6.75/7.08 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N)) (or (not (= M tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.gcd_gcd_nat M) N)) (@ (@ tptp.gcd_gcd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) A))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) B))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N) M)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X4 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 X4))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X4))) (or (and (@ (@ tptp.ord_less_eq_nat _let_6) _let_7) (= (@ (@ tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (@ (@ tptp.ord_less_eq_nat _let_3) _let_5) (= (@ (@ tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D))) (and (@ _let_1 M) (@ _let_1 N))))))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K3) (@ P K3))) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) I3) (@ P I3))) (@ P K3)))) (@ P M)))))
% 6.75/7.08 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X2) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_2 (= Y2 X2)) (=> (not _let_2) (= Y2 (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2))))) (not _let_1)))))))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K))) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((K tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int K))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((N tptp.num) (K tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) K) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.neg_numeral_sub_int N) tptp.one)) K)))))
% 6.75/7.08 (assert (forall ((R tptp.rat) (P6 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.quotient_of R) (@ (@ tptp.product_Pair_int_int P6) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.75/7.08 (assert (forall ((R tptp.rat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.product_snd_int_int (@ tptp.quotient_of R)))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))
% 6.75/7.08 (assert (= tptp.ord_less_rat (lambda ((P4 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B3 tptp.int) (D tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A4) D)) (@ (@ tptp.times_times_int C3) B3)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P4)))))
% 6.75/7.08 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P4 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P4)))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) (@ tptp.numeral_numeral_int K))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat K)))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int)) (@ tptp.numeral_numeral_rat K))))
% 6.75/7.08 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int L))) (@ (@ tptp.divide_divide_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat L)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 6.75/7.08 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) X))) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))))
% 6.75/7.08 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa2) X2)))))
% 6.75/7.08 (assert (forall ((Z tptp.int)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X4) Y3))))))))
% 6.75/7.08 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.75/7.08 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N3 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N3) tptp.zero_zero_nat)))))
% 6.75/7.08 (assert (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X))) X2)))))
% 6.75/7.08 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.75/7.08 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))) Xa2) X2))))
% 6.75/7.08 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))) Xa2) X2))))
% 6.75/7.08 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0))) Xa2) X2)))))
% 6.75/7.08 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0))) Xa2) X2)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.pow X2))) (= (@ _let_1 (@ tptp.bit1 Y2)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y2))) X2)))))
% 6.75/7.08 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 6.75/7.08 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.75/7.08 (assert (= tptp.sqr (lambda ((X tptp.num)) (@ (@ tptp.times_times_num X) X))))
% 6.75/7.08 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.pow X2))) (= (@ _let_1 (@ tptp.bit0 Y2)) (@ tptp.sqr (@ _let_1 Y2))))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N) N)) (@ tptp.bit0 (@ tptp.num_of_nat N))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N))))))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 6.75/7.08 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y) V4)) (@ (@ tptp.plus_plus_nat U2) Z2)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))))
% 6.75/7.08 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y) V4)) (@ (@ tptp.plus_plus_nat U2) Z2)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))))
% 6.75/7.08 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B))) (let ((_let_2 (@ (@ tptp.fract A) B))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) _let_2) (@ (@ tptp.ord_less_rat _let_2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.divide_divide_int A) B))))
% 6.75/7.08 (assert (forall ((B tptp.int) (D2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D2))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D2)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.75/7.08 (assert (forall ((P (-> tptp.rat Bool)) (Q2 tptp.rat)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ P (@ (@ tptp.fract A3) B2)))) (@ P Q2))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.gcd_gcd_int A) B))) (= (@ (@ tptp.fract (@ (@ tptp.divide_divide_int A) _let_1)) (@ (@ tptp.divide_divide_int B) _let_1)) (@ (@ tptp.fract A) B)))))
% 6.75/7.08 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))))
% 6.75/7.08 (assert (= tptp.numeral_numeral_rat (lambda ((K2 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K2)) tptp.one_one_int))))
% 6.75/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ _let_1 A))))))
% 6.75/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.75/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B)))))
% 6.75/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int B) A)))))
% 6.75/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.75/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A)))))
% 6.75/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.75/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int B) A)))))
% 6.75/7.08 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) tptp.one_one_int) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))))
% 6.75/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 6.75/7.08 (assert (= tptp.times_times_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))))))
% 6.75/7.08 (assert (= tptp.minus_minus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0))))))
% 6.75/7.08 (assert (= tptp.plus_plus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.numeral_numeral_int Q4)))))) (@ (@ tptp.bit_take_bit_num _let_1) N))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.positive (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B)))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.75/7.08 (assert (forall ((R tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N3 tptp.nat)) (@ tptp.some_num tptp.one))) N))))
% 6.75/7.08 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y tptp.rat)) (@ tptp.positive (@ (@ tptp.minus_minus_rat Y) X)))))
% 6.75/7.08 (assert (= tptp.bit_take_bit_num (lambda ((N3 tptp.nat) (M3 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N3) (@ tptp.numeral_numeral_nat M3)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 6.75/7.08 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M))))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N) M)))))
% 6.75/7.08 (assert (forall ((R tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R)) M))))))
% 6.75/7.08 (assert (forall ((R tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R)) M)))))
% 6.75/7.08 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.75/7.08 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.75/7.08 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit0 M))) (= (@ (@ tptp.bit_and_not_num _let_1) tptp.one) (@ tptp.some_num _let_1)))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 6.75/7.08 (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 ((N3 tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N3) M)))) N))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) (@ tptp.some_num Q2)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int Q2)))))
% 6.75/7.08 (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 ((N3 tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N3) M))))) N))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N) M)))))
% 6.75/7.08 (assert (= tptp.bit_take_bit_num (lambda ((N3 tptp.nat) (M3 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A4 tptp.nat) (X tptp.num)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((O tptp.nat)) (@ (@ (@ (@ tptp.case_num_option_num (@ tptp.some_num tptp.one)) (lambda ((P4 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) P4)))) (lambda ((P4 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P4))))) X))) A4))) (@ (@ tptp.product_Pair_nat_num N3) M3)))))
% 6.75/7.08 (assert (= tptp.positive (lambda ((X tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (not (= Y2 tptp.none_num)))) (let ((_let_2 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X2) Xa2) Y2) (=> (=> _let_2 (=> (= Xa2 tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N2 tptp.num)) (= Xa2 (@ tptp.bit0 N2))) (not (= Y2 (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N2 tptp.num)) (= Xa2 (@ tptp.bit1 N2))) _let_1)) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num _let_1))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N2)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N2)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N2)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N2)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num (@ tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N2)) (not (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M4) N2)))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N2)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N2))))))))))))))))))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N))))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N)))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N)))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.75/7.08 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X2) Xa2) Y2) (=> (=> _let_1 (=> (= Xa2 tptp.one) (not (= Y2 tptp.none_num)))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N2)) (not (= Y2 (@ tptp.some_num (@ tptp.bit1 N2))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N2)) (not (= Y2 (@ tptp.some_num (@ tptp.bit0 N2))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num (@ tptp.bit1 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N2)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N2)) (not (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2))))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num (@ tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N2)) (not (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2))))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N2)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2)))))))))))))))))))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num (@ tptp.bit0 N)))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num (@ tptp.bit1 N)))))
% 6.75/7.08 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (not (= Y2 (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa2 tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y2 tptp.none_num)))) (let ((_let_5 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X2) Xa2) Y2) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N2 tptp.num)) (= Xa2 (@ tptp.bit0 N2))) _let_4)) (=> (=> _let_5 (=> (exists ((N2 tptp.num)) (= Xa2 (@ tptp.bit1 N2))) _let_1)) (=> (=> (exists ((M4 tptp.num)) (= X2 (@ tptp.bit0 M4))) (=> _let_2 _let_4)) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N2)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N2)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2)))))))) (=> (=> (exists ((M4 tptp.num)) (= X2 (@ tptp.bit1 M4))) _let_3) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N2)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2)))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N2)) (not (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2)))))))))))))))))))))))))
% 6.75/7.08 (assert (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))
% 6.75/7.08 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num tptp.one))))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.75/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N)) tptp.none_num)))
% 6.75/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.75/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.75/7.08 (assert (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))
% 6.75/7.08 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q2) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.75/7.08 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q2) tptp.zero_z5237406670263579293d_enat)))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat M) N)))))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.75/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.75/7.08 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) (@ tptp.pred_numeral K))))))
% 6.75/7.08 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K)) N)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N) Q2)) (@ (@ tptp.ord_min_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M) N)) Q2) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I)) (@ (@ tptp.minus_minus_nat N) I)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N)) I))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L tptp.int) (R tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N) K) L)) R) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N)) L) R)))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ (@ tptp.bit_concat_bit N) K) L)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N)) L)))))
% 6.75/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M5)))) M))))
% 6.75/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M5) N)))) M))))
% 6.75/7.08 (assert (forall ((K tptp.nat) (M tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K) M)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M))))
% 6.75/7.08 (assert (= tptp.quotient_of (lambda ((X tptp.rat)) (@ tptp.the_Pr4378521158711661632nt_int (lambda ((Pair tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Pair))) (let ((_let_2 (@ tptp.product_fst_int_int Pair))) (and (= X (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)))))))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.algebr932160517623751201me_int K))) (= (@ _let_1 (@ tptp.abs_abs_int L)) (@ _let_1 L)))))
% 6.75/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.algebr932160517623751201me_int (@ tptp.abs_abs_int K)) L) (@ (@ tptp.algebr932160517623751201me_int K) L))))
% 6.75/7.08 (assert (forall ((Q2 tptp.int) (P6 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int P6) Q2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2) (=> (@ (@ tptp.algebr932160517623751201me_int P6) Q2) (= (@ tptp.normalize _let_1) _let_1))))))
% 6.75/7.08 (assert (forall ((P (-> tptp.rat Bool)) (Q2 tptp.rat)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.algebr932160517623751201me_int A3) B2) (@ P (@ (@ tptp.fract A3) B2))))) (@ P Q2))))
% 6.75/7.08 (assert (forall ((Q2 tptp.rat)) (not (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= Q2 (@ (@ tptp.fract A3) B2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (not (@ (@ tptp.algebr932160517623751201me_int A3) B2))))))))
% 6.75/7.08 (assert (forall ((A tptp.int) (B tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X2))) (=> (@ (@ tptp.algebr932160517623751201me_int A) B) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ tptp.abs_abs_int X2) tptp.one_one_int)))))))
% 6.75/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.75/7.08 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.75/7.08 (assert (forall ((Q2 tptp.rat)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= Q2 (@ (@ tptp.fract A3) B2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (not (= A3 tptp.zero_zero_int)) (not (@ (@ tptp.algebr932160517623751201me_int A3) B2)))))) (= Q2 tptp.zero_zero_rat))))
% 6.75/7.08 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M3) N3))) M3)))))
% 6.75/7.08 (assert (forall ((R tptp.rat)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X4))) (let ((_let_2 (@ tptp.product_fst_int_int X4))) (and (= R (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1) (forall ((Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y4))) (let ((_let_2 (@ tptp.product_fst_int_int Y4))) (=> (and (= R (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)) (= Y4 X4)))))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X2)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X2) tptp.field_5140801741446780682s_real))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.algebr932160517623751201me_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.algebr934650988132801477me_nat M) N))))
% 6.75/7.09 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N) (@ (@ tptp.algebr932160517623751201me_int K) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ (@ tptp.algebr932160517623751201me_int (@ tptp.semiri1314217659103216013at_int N)) K))))
% 6.75/7.09 (assert (forall ((A tptp.nat) (B tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X2))) (=> (@ (@ tptp.algebr934650988132801477me_nat A) B) (=> (@ _let_1 A) (=> (@ _let_1 B) (= X2 tptp.one_one_nat)))))))
% 6.75/7.09 (assert (forall ((A tptp.nat) (D2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.algebr934650988132801477me_nat A) D2) (=> (@ (@ tptp.algebr934650988132801477me_nat B) C) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) D2)) (and (= A B) (= C D2)))))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc tptp.zero_zero_nat))))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X2) X4) (@ (@ tptp.ord_less_real X4) Y2))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X4) X2)))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X2) X4)))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) tptp.field_5140801741446780682s_real) (not (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (=> (= (@ tptp.abs_abs_real X2) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M4)) (@ tptp.semiri5074537144036343181t_real N2))) (not (@ (@ tptp.algebr934650988132801477me_nat M4) N2)))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 6.75/7.09 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X2) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= 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 ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y2 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num _let_1)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num (@ tptp.bit0 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N4))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L2) N4)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L2)) tptp.one_one_nat) N4))))))))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N4 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N4))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N4) M)) tptp.one_one_nat)) N4))))
% 6.75/7.09 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X2) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= 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 ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X2) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ tptp.bit1 N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ tptp.bit0 N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num (@ tptp.bit1 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num (@ tptp.bit0 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X2) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bit1 M4)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.bit0 tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N2 tptp.num)) (=> (= X2 (@ tptp.bit0 N2)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N2)) _let_1))))))))) (=> (forall ((N2 tptp.num)) (=> (= X2 (@ tptp.bit0 N2)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N2) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N2)) _let_1))))))))) (=> (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N2 tptp.num)) (=> (= X2 (@ tptp.bit1 N2)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N2)) _let_1))))))))) (not (forall ((N2 tptp.num)) (=> (= X2 (@ tptp.bit1 N2)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N2)) _let_1))))))))))))))))))))))))
% 6.75/7.09 (assert (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel))
% 6.75/7.09 (assert (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel))
% 6.75/7.09 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) Y2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y2 (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (= Y2 (not (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7))))))) (@ 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 ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))))
% 6.75/7.09 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList) Summary)) Deg4) (and (= Deg Deg4) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X7))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7))))))) (@ 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 ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima2)))))))
% 6.75/7.09 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X2) Xa2)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7))))))) (@ 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 ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (not (and (= Deg2 Xa2) (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X6) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7))))))) (@ 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 ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))))))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (= Y2 (= Xa2 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X2 _let_1) (=> (= Y2 (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7))))))) (@ 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 ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X6) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7))))))) (@ 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 ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7))))))) (@ 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 ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))))))))))))))
% 6.75/7.09 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.75/7.09 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 6.75/7.09 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.75/7.09 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I4 tptp.int) (J3 tptp.int)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))
% 6.75/7.09 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I4 tptp.int) (N3 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.semiri5074537144036343181t_real N3))) (not (= N3 tptp.zero_zero_nat))))))))
% 6.75/7.09 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.size_size_VEBT_VEBT) X13)) (@ tptp.size_size_VEBT_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.75/7.09 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.vEBT_size_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.vEBT_size_VEBT) X13)) (@ tptp.vEBT_size_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I) J)) K) _let_1)))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) M))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M) (@ _let_2 N)) (@ _let_2 _let_1)))))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N))))
% 6.75/7.09 (assert (forall ((Ns tptp.list_nat) (I tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.nth_nat Ns) I))))))
% 6.75/7.09 (assert (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I)))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M3) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (R tptp.rat)) (=> (@ tptp.cauchy X8) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M2) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N7) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M2)) (@ X8 N7)))) R))))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K4 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) M4) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M4)) (@ X8 N2)))) R3)))))))) (@ tptp.cauchy X8))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (@ tptp.cauchy (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N3)) (@ Y6 N3))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (@ tptp.cauchy (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N3)))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (@ tptp.cauchy (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N3)) (@ Y6 N3))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.rat)) (@ tptp.cauchy (lambda ((N3 tptp.nat)) X2))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (@ tptp.cauchy (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N3)) (@ Y6 N3))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (exists ((B2 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N7))) B2)))))))
% 6.75/7.09 (assert (= tptp.cauchy (lambda ((X7 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) M3) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X7 M3)) (@ X7 N3)))) R5)))))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X8)) (@ tptp.real2 Y6)) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N3) (@ (@ tptp.ord_less_eq_rat (@ X8 N3)) (@ (@ tptp.plus_plus_rat (@ Y6 N3)) R5))))))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (exists ((B2 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (exists ((K3 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N7) (@ (@ tptp.ord_less_rat B2) (@ tptp.abs_abs_rat (@ X8 N7))))))))))))
% 6.75/7.09 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 6.75/7.09 (assert (forall ((C tptp.rat)) (= (@ tptp.vanishes (lambda ((N3 tptp.nat)) C)) (= C tptp.zero_zero_rat))))
% 6.75/7.09 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (= (= (@ tptp.real2 X8) (@ tptp.real2 Y6)) (@ tptp.vanishes (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N3)) (@ Y6 N3)))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.real2 X8)))) (let ((_let_2 (@ tptp.vanishes X8))) (=> (@ tptp.cauchy X8) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (@ tptp.real2 (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N3))))))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (@ tptp.cauchy (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N3))))))))
% 6.75/7.09 (assert (forall ((P (-> tptp.real Bool)) (X2 tptp.real)) (=> (forall ((X9 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (@ P (@ tptp.real2 X9)))) (@ P X2))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X8) (@ tptp.vanishes (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N3)))))))
% 6.75/7.09 (assert (= tptp.semiri5074537144036343181t_real (lambda ((X tptp.nat)) (@ tptp.real2 (lambda ((N3 tptp.nat)) (@ tptp.semiri681578069525770553at_rat X))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X8) (=> (@ tptp.vanishes Y6) (@ tptp.vanishes (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N3)) (@ Y6 N3))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X8) (=> (@ tptp.vanishes Y6) (@ tptp.vanishes (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N3)) (@ Y6 N3))))))))
% 6.75/7.09 (assert (= tptp.zero_zero_real (@ tptp.real2 (lambda ((N3 tptp.nat)) tptp.zero_zero_rat))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.times_times_real (@ tptp.real2 X8)) (@ tptp.real2 Y6)) (@ tptp.real2 (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N3)) (@ Y6 N3)))))))))
% 6.75/7.09 (assert (= tptp.one_one_real (@ tptp.real2 (lambda ((N3 tptp.nat)) tptp.one_one_rat))))
% 6.75/7.09 (assert (= tptp.ring_1_of_int_real (lambda ((X tptp.int)) (@ tptp.real2 (lambda ((N3 tptp.nat)) (@ tptp.ring_1_of_int_rat X))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (=> (@ tptp.cauchy Y6) (=> (not (@ tptp.vanishes Y6)) (=> (@ tptp.vanishes (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N3)) (@ Y6 N3)))) (@ tptp.vanishes (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ tptp.inverse_inverse_rat (@ X8 N3))) (@ tptp.inverse_inverse_rat (@ Y6 N3))))))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X8)) (@ tptp.real2 (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N3))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 X8)) (@ tptp.real2 Y6)) (@ tptp.real2 (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N3)) (@ Y6 N3)))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.minus_minus_real (@ tptp.real2 X8)) (@ tptp.real2 Y6)) (@ tptp.real2 (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N3)) (@ Y6 N3)))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (exists ((A8 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A8) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N2))) A8)))) (=> (@ tptp.vanishes Y6) (@ tptp.vanishes (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N3)) (@ Y6 N3))))))))
% 6.75/7.09 (assert (= tptp.vanishes (lambda ((X7 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X7 N3))) R5)))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N2))) R3)))))) (@ tptp.vanishes X8))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (R tptp.rat)) (=> (@ tptp.vanishes X8) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N7) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N7))) R))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (exists ((B2 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (exists ((K3 tptp.nat)) (or (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N7) (@ (@ tptp.ord_less_rat B2) (@ tptp.uminus_uminus_rat (@ X8 N7))))) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N7) (@ (@ tptp.ord_less_rat B2) (@ X8 N7))))))))))))
% 6.75/7.09 (assert (= tptp.root (lambda ((N3 tptp.nat) (X tptp.real)) (@ (@ (@ tptp.if_real (= N3 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N3)))) X)))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (not (@ tptp.positive2 (@ tptp.real2 X8))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N3) (@ (@ tptp.ord_less_eq_rat (@ X8 N3)) R5))))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ tptp.positive2 X2) (=> (@ tptp.positive2 Y2) (@ tptp.positive2 (@ (@ tptp.plus_plus_real X2) Y2))))))
% 6.75/7.09 (assert (not (@ tptp.positive2 tptp.zero_zero_real)))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ tptp.positive2 X2) (=> (@ tptp.positive2 Y2) (@ tptp.positive2 (@ (@ tptp.times_times_real X2) Y2))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (not (@ tptp.positive2 X2)) (=> (not (= X2 tptp.zero_zero_real)) (@ tptp.positive2 (@ tptp.uminus_uminus_real X2))))))
% 6.75/7.09 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (@ tptp.positive2 (@ (@ tptp.minus_minus_real Y) X)))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (@ tptp.positive2 (@ tptp.real2 X8)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N3) (@ (@ tptp.ord_less_rat R5) (@ X8 N3)))))))))))
% 6.75/7.09 (assert (= (@ tptp.finite_card_char tptp.top_top_set_char) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (X2 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.minus_minus_real X2) H4))))))))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X2) H4))) (@ F X2)))))))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.plus_plus_real X2) H4))))))))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X2) H4))) (@ F X2)))))))))))
% 6.75/7.09 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 6.75/7.09 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 6.75/7.09 (assert (= tptp.comple4887499456419720421f_real (lambda ((X7 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X7))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S3)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S3)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 6.75/7.09 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) 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)) (@ F4 Z3)))))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) D2) (= (@ F X2) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.75/7.09 (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 ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real V) K) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (= (@ V (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ V A)) (@ V B))) _let_1)))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) D2) (@ (@ tptp.ord_less_eq_real (@ F X2)) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) D2) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X2)))) (= L tptp.zero_zero_real))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (X2 tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X2) S))))
% 6.75/7.09 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ G X)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G X2)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M)) _let_1)))))
% 6.75/7.09 (assert (forall ((Z tptp.real) (R tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z2 tptp.real)) (@ (@ tptp.powr_real Z2) R))) (@ (@ tptp.times_times_real R) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X2))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.75/7.09 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (R tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ G X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G X)) R))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))))
% 6.75/7.09 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (F (-> tptp.real tptp.real)) (R tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ G X2))) (let ((_let_3 (@ F X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G X)) (@ F X)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (A2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arsinh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A2))))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X2)))) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D4 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D4) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A2)))))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) A2)))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arccos) (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcsin) (@ tptp.inverse_inverse_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))
% 6.75/7.09 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X2 tptp.real) (N tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 6.75/7.09 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X2 tptp.real) (N tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X2 tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))
% 6.75/7.09 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.75/7.09 (assert (forall ((H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))))
% 6.75/7.09 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real H2) T4) (@ (@ tptp.ord_less_eq_real T4) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T4) (@ (@ tptp.ord_less_real T4) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.75/7.09 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X2 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X2 tptp.zero_zero_real)) (=> (forall ((M4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (exists ((T4 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T4))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))))))
% 6.75/7.09 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X2 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T4) (@ (@ tptp.ord_less_eq_real T4) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) B) (=> (not (= X2 C)) (exists ((T4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T4))) (let ((_let_2 (@ tptp.ord_less_real X2))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T4) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T4) (@ _let_1 X2))) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C)) N))))))))))))))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T4) (@ (@ tptp.ord_less_eq_real T4) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real C) T4) (@ (@ tptp.ord_less_real T4) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T4) (@ (@ tptp.ord_less_eq_real T4) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real A) T4) (@ (@ tptp.ord_less_real T4) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B4 tptp.real)) (=> (forall ((M4 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M2 tptp.nat) (T7 tptp.real)) (let ((_let_1 (@ tptp.suc M2))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M2))) (@ (@ tptp.minus_minus_real (@ (@ Diff M2) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M2) P4)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real U2) P4)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B4) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T7)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) P4)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real T7) P4)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B4) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T7) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real))))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X10 tptp.real)) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X10) _let_1)))))))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.75/7.09 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R2)) R2)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N3)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) (@ (@ tptp.power_power_real X4) N3)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R2)) R2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real X) (@ tptp.suc N3))))))) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N3)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) (@ (@ tptp.power_power_real X0) N3))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 6.75/7.09 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real) (Y2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.member_real X2) _let_1) (=> (@ (@ tptp.member_real Y2) _let_1) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (= (@ F X2) (@ F Y2)))))))))
% 6.75/7.09 (assert (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 6.75/7.09 (assert (forall ((C tptp.char)) (@ (@ tptp.ord_less_nat (@ tptp.comm_s629917340098488124ar_nat C)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.75/7.09 (assert (= (@ (@ tptp.image_char_nat tptp.comm_s629917340098488124ar_nat) tptp.top_top_set_char) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.75/7.09 (assert (forall ((B0 Bool) (B1 Bool) (B22 Bool) (B32 Bool) (B42 Bool) (B52 Bool) (B62 Bool) (B72 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.integer_of_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B0) B1) B22) B32) B42) B52) B62) B72)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger B72)) _let_1)) (@ tptp.zero_n356916108424825756nteger B62))) _let_1)) (@ tptp.zero_n356916108424825756nteger B52))) _let_1)) (@ tptp.zero_n356916108424825756nteger B42))) _let_1)) (@ tptp.zero_n356916108424825756nteger B32))) _let_1)) (@ tptp.zero_n356916108424825756nteger B22))) _let_1)) (@ tptp.zero_n356916108424825756nteger B1))) _let_1)) (@ tptp.zero_n356916108424825756nteger B0))))))
% 6.75/7.09 (assert (forall ((C tptp.char)) (= (@ tptp.comm_s629917340098488124ar_nat (@ tptp.ascii_of C)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 tptp.one)))) (@ tptp.comm_s629917340098488124ar_nat C)))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J))))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (J tptp.nat) (X2 tptp.nat) (Xs2 tptp.list_nat)) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat X2) Xs2)) (and (@ (@ tptp.ord_less_nat I) J) (= I X2) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J) Xs2)))))
% 6.75/7.09 (assert (= tptp.upt (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I4) J3)) (@ (@ tptp.cons_nat I4) (@ (@ tptp.upt (@ tptp.suc I4)) J3))) tptp.nil_nat))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M) (@ (@ tptp.upt I) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) M)) J))))
% 6.75/7.09 (assert (forall ((X2 tptp.list_nat) (Y2 tptp.nat)) (=> (= (@ tptp.nat_list_encode X2) Y2) (=> (=> (= X2 tptp.nil_nat) (not (= Y2 tptp.zero_zero_nat))) (not (forall ((X4 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X2 (@ (@ tptp.cons_nat X4) Xs3)) (not (= Y2 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X4) (@ tptp.nat_list_encode Xs3)))))))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X2) Xs2)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X2) (@ tptp.nat_list_encode Xs2)))))))
% 6.75/7.09 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I4)) Js) (@ (@ (@ tptp.upto_aux I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.75/7.09 (assert (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))))
% 6.75/7.09 (assert (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))))
% 6.75/7.09 (assert (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.75/7.09 (assert (forall ((I tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I) J))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J)) I))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X6 tptp.real)) (=> (and (not (= X6 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X6))) R3)) (@ (@ tptp.ord_less_real (@ F X6)) tptp.zero_zero_real)))))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (not (= L tptp.zero_zero_real)) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X6 tptp.real)) (=> (and (not (= X6 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X6))) R3)) (not (= (@ F X6) tptp.zero_zero_real))))))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X6 tptp.real)) (=> (and (not (= X6 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X6))) R3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X6))))))))))
% 6.75/7.09 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X)) (@ tptp.sin_real X)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.top_top_set_real)))
% 6.75/7.09 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.75/7.09 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.75/7.09 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat X) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 6.75/7.09 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (@ tptp.times_times_nat C)) tptp.at_top_nat) tptp.at_top_nat))))
% 6.75/7.09 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.root N3) (@ tptp.semiri5074537144036343181t_real N3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ (@ tptp.ord_less_real R3) (@ X8 N2)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.75/7.09 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.root N3) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 6.75/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) L)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N7)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X2)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X2) N3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.75/7.09 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real C)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real C)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.75/7.09 (assert (forall ((C tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real C))) (=> (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real _let_1)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X2) N3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) (@ tptp.semiri5074537144036343181t_real N3)))) N3))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) tptp.at_top_nat)))
% 6.75/7.09 (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 ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N3)) (@ A N3))))))))
% 6.75/7.09 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N3)) (@ A N3)))))))))
% 6.75/7.09 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J3)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((K3 (-> tptp.nat tptp.int))) (not (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K3 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 6.75/7.09 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ Theta J3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((K3 (-> tptp.nat tptp.int))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K3 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.75/7.09 (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 ((N3 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))) N3))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.75/7.09 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 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))) N3))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 6.75/7.09 (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 ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))))))))
% 6.75/7.09 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 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))) N3))))) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 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))) N3)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 6.75/7.09 (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 ((N3 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))) N3)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 6.75/7.09 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 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))) N3)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 6.75/7.09 (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 ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))))
% 6.75/7.09 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I4) K)))) tptp.at_top_nat))))
% 6.75/7.09 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N3 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N3) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.75/7.09 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 6.75/7.09 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real B) A)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))))))
% 6.75/7.09 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) K)) (@ tptp.exp_real X)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 6.75/7.09 (assert (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5984915006950818249n_real _let_1)))))
% 6.75/7.09 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) X4) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.75/7.09 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.at_top_real))
% 6.75/7.09 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X4) (@ P X4))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.75/7.09 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N6 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ P N3)))))))
% 6.75/7.09 (assert (forall ((F5 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F5) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N6)) F5)))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N))) tptp.at_top_real) F5))))))
% 6.75/7.09 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.75/7.09 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N))) tptp.at_bot_real) F5))))))
% 6.75/7.09 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) tptp.at_bot_real))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X2)) tptp.at_top_nat)))))
% 6.75/7.09 (assert (let ((_let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 6.75/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real A) B)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))))))
% 6.75/7.09 (assert (= tptp.positive2 (lambda ((X tptp.real)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N3) (@ (@ tptp.ord_less_rat R5) (@ (@ tptp.rep_real2 X) N3))))))))))
% 6.75/7.09 (assert (= tptp.inverse_inverse_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real2) tptp.real2) (lambda ((X7 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X7)) (lambda ((N3 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X7 N3)))) __flatten_var_0)))))
% 6.75/7.09 (assert (= tptp.uminus_uminus_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real2) tptp.real2) (lambda ((X7 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X7 N3))))))
% 6.75/7.09 (assert (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))
% 6.75/7.09 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 6.75/7.09 (assert (= tptp.times_times_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real2) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real2) tptp.real2)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N3)) (@ Y7 N3))))))
% 6.75/7.09 (assert (= tptp.plus_plus_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real2) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real2) tptp.real2)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N3)) (@ Y7 N3))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.sqrt)))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (@ tptp.root N))))
% 6.75/7.09 (assert (forall ((A tptp.real) (X2 tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (= (@ G (@ F Z3)) Z3)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X2)) tptp.top_top_set_real)) G)))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arcosh_real))))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (D4 tptp.real) (G (-> tptp.real tptp.real)) (X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D4) (@ (@ tptp.topolo2177554685111907308n_real (@ G X2)) tptp.top_top_set_real)) (=> (not (= D4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Y3) (=> (@ (@ tptp.ord_less_real Y3) B) (= (@ F (@ G Y3)) Y3)))) (=> (@ (@ tptp.topolo4422821103128117721l_real _let_1) G) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ tptp.inverse_inverse_real D4)) _let_1))))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arccos)))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arcsin)))))
% 6.75/7.09 (assert (forall ((B tptp.real) (X2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real B) X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X2)))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.artanh_real)))))
% 6.75/7.09 (assert (forall ((D2 tptp.real) (X2 tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X2))) D2) (= (@ G (@ F Z3)) Z3))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X2))) D2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X2)) tptp.top_top_set_real)) G))))))
% 6.75/7.09 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((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) (@ F4 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))) (@ F4 C2))))))))))))
% 6.75/7.09 (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 ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) F))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X4) (@ (@ tptp.ord_less_real X4) B)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) G))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X4) (@ (@ tptp.ord_less_real X4) B)) (@ (@ tptp.differ6690327859849518006l_real G) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C2) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C2) (@ (@ tptp.ord_less_real C2) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) F_c))))))))))))
% 6.75/7.09 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 6.75/7.09 (assert (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M3)) M3))))))
% 6.75/7.09 (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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((L4 tptp.real) (Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 6.75/7.09 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F4 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (= (@ F4 Z3) (lambda ((V4 tptp.real)) tptp.zero_zero_real))))))))))
% 6.75/7.09 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F4 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (not (forall ((Xi tptp.real)) (=> (@ (@ tptp.ord_less_real A) Xi) (=> (@ (@ tptp.ord_less_real Xi) B) (not (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ F4 Xi) (@ (@ tptp.minus_minus_real B) A)))))))))))))
% 6.75/7.09 (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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (= (@ F B) (@ F A)))))))
% 6.75/7.09 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F B)) (@ F A)))))))
% 6.75/7.09 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F A)) (@ F B)))))))
% 6.75/7.09 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A) X2) (=> (@ (@ tptp.ord_less_eq_real X2) B) (= (@ F X2) (@ F A)))))))))
% 6.75/7.09 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.inj_on_real_real (lambda ((Y tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N)))) tptp.top_top_set_real))))
% 6.75/7.09 (assert (forall ((B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.inj_on_real_real (@ tptp.log B)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.75/7.09 (assert (forall ((N4 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N4)))
% 6.75/7.09 (assert (forall ((N4 tptp.set_nat) (K tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.member_nat N2) N4) (@ (@ tptp.ord_less_eq_nat K) N2))) (@ (@ tptp.inj_on_nat_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat N3) K))) N4))))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (or (not (= X2 tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N)) (= (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.power_int_real X2) N))))))
% 6.75/7.09 (assert (@ (@ tptp.inj_on_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 6.75/7.09 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 6.75/7.09 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.75/7.09 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 6.75/7.09 (assert (forall ((F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (=> (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F4 X4))) (@ tptp.order_7092887310737990675l_real F)))))
% 6.75/7.09 (assert (forall ((X2 tptp.list_nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X2) Y2) (=> (@ _let_1 X2) (=> (=> (= X2 tptp.nil_nat) (=> (= Y2 tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X4 tptp.nat) (Xs3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X4) Xs3))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X4) (@ tptp.nat_list_encode Xs3))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))))
% 6.75/7.09 (assert (forall ((X2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X2) X2) (= (@ tptp.inverse_inverse_real (@ tptp.real2 X2)) (@ tptp.real2 (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X2)) (lambda ((N3 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X2 N3)))))))))
% 6.75/7.09 (assert (forall ((P (-> tptp.real Bool)) (X2 tptp.real)) (=> (forall ((Y3 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Y3) Y3) (@ P (@ tptp.real2 Y3)))) (@ P X2))))
% 6.75/7.09 (assert (@ (@ tptp.realrel (lambda ((N3 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N3 tptp.nat)) tptp.zero_zero_rat)))
% 6.75/7.09 (assert (@ (@ tptp.realrel (lambda ((N3 tptp.nat)) tptp.one_one_rat)) (lambda ((N3 tptp.nat)) tptp.one_one_rat)))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (@ (@ tptp.realrel X8) X8))))
% 6.75/7.09 (assert (forall ((X2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X2) X2) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X2)) (@ tptp.real2 (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X2 N3))))))))
% 6.75/7.09 (assert (forall ((Xa2 (-> tptp.nat tptp.rat)) (X2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa2) Xa2) (=> (@ (@ tptp.realrel X2) X2) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 Xa2)) (@ tptp.real2 X2)) (@ tptp.real2 (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ Xa2 N3)) (@ X2 N3)))))))))
% 6.75/7.09 (assert (forall ((Xa2 (-> tptp.nat tptp.rat)) (X2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa2) Xa2) (=> (@ (@ tptp.realrel X2) X2) (= (@ (@ tptp.times_times_real (@ tptp.real2 Xa2)) (@ tptp.real2 X2)) (@ tptp.real2 (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_rat (@ Xa2 N3)) (@ X2 N3)))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (=> (@ tptp.vanishes (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N3)) (@ Y6 N3)))) (@ (@ tptp.realrel X8) Y6))))))
% 6.75/7.09 (assert (= tptp.realrel (lambda ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (and (@ tptp.cauchy X7) (@ tptp.cauchy Y7) (@ tptp.vanishes (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X7 N3)) (@ Y7 N3))))))))
% 6.75/7.09 (assert (forall ((X2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X2) X2) (= (@ tptp.positive2 (@ tptp.real2 X2)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N3) (@ (@ tptp.ord_less_rat R5) (@ X2 N3)))))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y)))))) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N))))))
% 6.75/7.09 (assert (= tptp.cr_real (lambda ((X (-> tptp.nat tptp.rat)) (Y tptp.real)) (and (@ (@ tptp.realrel X) X) (= (@ tptp.real2 X) Y)))))
% 6.75/7.09 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o tptp.realrel) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) (lambda ((X7 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N3) (@ (@ tptp.ord_less_rat R5) (@ X7 N3))))))))) (lambda ((X7 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N3) (@ (@ tptp.ord_less_rat R5) (@ X7 N3))))))))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) tptp.ord_less_eq_nat) tptp.ord_less_eq_nat))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) tptp.ord_less_int) tptp.ord_less_int))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) tptp.ord_less_nat) tptp.ord_less_nat))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)))) tptp.times_times_nat) tptp.times_times_nat))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re8402795839162346335um_int (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4))) (@ (@ tptp.bNF_re1822329894187522285nt_int (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4))) (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)))) (lambda ((M3 tptp.num) (N3 tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M3)) (@ tptp.numeral_numeral_int N3)))) (lambda ((M3 tptp.num) (N3 tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M3)) (@ tptp.numeral_numeral_int N3)))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)))) tptp.divide_divide_int) tptp.divide_divide_int))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)))) tptp.divide_divide_nat) tptp.divide_divide_nat))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)))) tptp.plus_plus_nat) tptp.plus_plus_nat))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N3)) (@ Y7 N3)))) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N3)) (@ Y7 N3)))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel) (lambda ((X7 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X7 N3)))) (lambda ((X7 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X7 N3)))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N3)) (@ Y7 N3)))) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N3)) (@ Y7 N3)))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel) (lambda ((X7 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X7)) (lambda ((N3 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X7 N3)))) __flatten_var_0))) (lambda ((X7 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X7)) (lambda ((N3 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X7 N3)))) __flatten_var_0))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) (lambda ((X7 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N3) (@ (@ tptp.ord_less_rat R5) (@ X7 N3))))))))) tptp.positive2))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re1494630372529172596at_o_o tptp.pcr_rat) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X))))) tptp.positive))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re4521903465945308077real_o tptp.pcr_real) (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) tptp.realrel) (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4))))
% 6.75/7.09 (assert (= tptp.pcr_real tptp.cr_real))
% 6.75/7.09 (assert (@ (@ tptp.pcr_real (lambda ((N3 tptp.nat)) tptp.zero_zero_rat)) tptp.zero_zero_real))
% 6.75/7.09 (assert (@ (@ tptp.pcr_real (lambda ((N3 tptp.nat)) tptp.one_one_rat)) tptp.one_one_real))
% 6.75/7.09 (assert (= tptp.pcr_real (lambda ((X (-> tptp.nat tptp.rat)) (Y tptp.real)) (and (@ tptp.cauchy X) (= (@ tptp.real2 X) Y)))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real) (lambda ((X7 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X7 N3)))) tptp.uminus_uminus_real))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N3)) (@ Y7 N3)))) tptp.plus_plus_real))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N3)) (@ Y7 N3)))) tptp.times_times_real))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real) (lambda ((X7 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X7)) (lambda ((N3 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X7 N3)))) __flatten_var_0))) tptp.inverse_inverse_real))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))) tptp.times_times_int))
% 6.75/7.09 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) tptp.zero_zero_int))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) tptp.pcr_int) (lambda ((N3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N3) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int) (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X)))) tptp.uminus_uminus_int))
% 6.75/7.09 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) tptp.ord_less_int))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))) tptp.plus_plus_int))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0)))) tptp.minus_minus_int))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (exists ((Q3 tptp.rat)) (let ((_let_1 (@ tptp.field_7254667332652039916t_real Q3))) (and (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real _let_1) Y2)))))))
% 6.75/7.09 (assert (= tptp.field_7254667332652039916t_real (lambda ((X tptp.rat)) (@ tptp.real2 (lambda ((N3 tptp.nat)) X)))))
% 6.75/7.09 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.75/7.09 (assert (forall ((Y6 (-> tptp.nat tptp.rat)) (X2 tptp.real)) (=> (@ tptp.cauchy Y6) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.real2 Y6)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real X2) (@ tptp.field_7254667332652039916t_real (@ Y6 N2))))))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y2 tptp.real)) (=> (@ tptp.cauchy X8) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.field_7254667332652039916t_real (@ X8 N2))) Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X8)) Y2)))))
% 6.75/7.09 (assert (forall ((Y6 (-> tptp.nat tptp.rat)) (X2 tptp.real)) (=> (@ tptp.cauchy Y6) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.field_7254667332652039916t_real (@ Y6 N2)))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.real2 Y6))))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))))
% 6.75/7.09 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (U tptp.nat) (V tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X2) Y2)) (@ (@ tptp.product_Pair_nat_nat U) V)) (= (@ (@ tptp.plus_plus_nat X2) V) (@ (@ tptp.plus_plus_nat U) Y2)))))
% 6.75/7.09 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel) (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X)))) (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X)))))
% 6.75/7.09 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.75/7.09 (assert (= tptp.intrel (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (= (@ (@ tptp.plus_plus_nat X) V4) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0)))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))))
% 6.75/7.09 (assert (forall ((S3 tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat S3)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S3) N)))))
% 6.75/7.09 (assert (forall ((S3 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S3) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S3)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S3) N))))))
% 6.75/7.09 (assert (forall ((R tptp.real) (A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.rcis R) A)) N) (@ (@ tptp.rcis (@ (@ tptp.power_power_real R) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))))
% 6.75/7.09 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat))))
% 6.75/7.09 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (Q (-> tptp.nat Bool)) (M tptp.nat)) (=> (@ P N) (=> (@ Q M) (=> (not (@ P tptp.zero_zero_nat)) (=> (forall ((K3 tptp.nat)) (= (@ P (@ tptp.suc K3)) (@ Q K3))) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat Q)))))))))
% 6.75/7.09 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat (lambda ((M3 tptp.nat)) (@ P (@ tptp.suc M3))))))))))
% 6.75/7.09 (assert (= tptp.comple1385675409528146559p_real (lambda ((X7 tptp.set_real)) (@ tptp.ord_Least_real (lambda ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) X7) (@ (@ tptp.ord_less_eq_real X) Z2))))))))
% 6.75/7.09 (assert (= tptp.topolo896644834953643431omplex (@ tptp.comple8358262395181532106omplex (@ (@ tptp.image_5971271580939081552omplex (lambda ((E3 tptp.real)) (@ tptp.princi3496590319149328850omplex (@ tptp.collec8663557070575231912omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V3694042436643373181omplex X) Y)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.75/7.09 (assert (= tptp.topolo1511823702728130853y_real (@ tptp.comple2936214249959783750l_real (@ (@ tptp.image_2178119161166701260l_real (lambda ((E3 tptp.real)) (@ tptp.princi6114159922880469582l_real (@ tptp.collec3799799289383736868l_real (@ tptp.produc5414030515140494994real_o (lambda ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V975177566351809787t_real X) Y)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.75/7.09 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N6 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) M3) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ P (@ (@ tptp.product_Pair_nat_nat N3) M3))))))))))
% 6.75/7.09 (assert (forall ((M tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) M)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M)) (lambda ((R5 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) R5)))))))
% 6.75/7.09 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 6.75/7.09 (assert (forall ((X2 tptp.nat)) (= (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vimage_nat_nat tptp.suc) (@ tptp.nat_set_decode X2)))))
% 6.75/7.09 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.nat_set_encode (@ (@ tptp.vimage_nat_nat tptp.suc) A2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat_set_encode A2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.75/7.09 (assert (= tptp.positive2 (@ (@ (@ tptp.map_fu1856342031159181835at_o_o tptp.rep_real2) tptp.id_o) (lambda ((X7 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N3) (@ (@ tptp.ord_less_rat R5) (@ X7 N3)))))))))))
% 6.75/7.09 (assert (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X)))))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N)))) (lambda ((Uu3 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 6.75/7.09 (assert (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)) (lambda ((Uu3 tptp.nat)) (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N))))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o tptp.ratrel) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X))))) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X))))))
% 6.75/7.09 (assert (forall ((X2 tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X2) X2) (= (@ tptp.positive (@ tptp.abs_Rat X2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2)))))))
% 6.75/7.09 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.last_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) tptp.one_one_nat)))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (@ tptp.bNF_We3818239936649020644el_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (M7 tptp.nat)) (=> (@ (@ tptp.bfun_nat_real (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) M7)))) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) M4) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_real (@ F M4)) (@ F N2))))) (@ tptp.topolo7531315842566124627t_real F)))))
% 6.75/7.09 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_real (@ X8 M4)) (@ X8 N2)))) (@ tptp.topolo7531315842566124627t_real X8)))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ tptp.topolo7531315842566124627t_real (@ tptp.power_power_real X2))))))
% 6.75/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (M7 tptp.nat)) (=> (@ (@ tptp.bfun_nat_real (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) M7)))) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) M4) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F M4))))) (@ tptp.topolo7531315842566124627t_real F)))))
% 6.75/7.09 (assert (forall ((A tptp.nat) (B tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat S) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_less)))))
% 6.75/7.09 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X2))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 Y2)) (@ _let_1 Z))) tptp.fun_pair_less) (@ (@ tptp.ord_less_nat Y2) Z)))))
% 6.75/7.09 (assert (forall ((A tptp.nat) (B tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_less))))
% 6.75/7.09 (assert (forall ((A tptp.nat) (B tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat S) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_leq)))))
% 6.75/7.09 (assert (forall ((A tptp.nat) (B tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_leq))))
% 6.75/7.09 (assert (@ (@ (@ tptp.ordering_top_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) X))) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))) tptp.zero_zero_nat))
% 6.75/7.09 (assert (= tptp.euclid4777050414544973029ze_nat tptp.id_nat))
% 6.75/7.09 (assert (= tptp.euclid4774559944035922753ze_int (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)))
% 6.75/7.09 (assert (forall ((K tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.euclid3395696857347342551nt_int K)) tptp.one_one_int)))
% 6.75/7.09 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (= (@ tptp.euclid3395696857347342551nt_int K) (@ tptp.sgn_sgn_int K)))))
% 6.75/7.09 (assert (= tptp.euclid3398187327856392827nt_nat (lambda ((N3 tptp.nat)) tptp.one_one_nat)))
% 6.75/7.09 (assert (= tptp.euclid3395696857347342551nt_int (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.75/7.09 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((M3 tptp.extended_enat) (__flatten_var_0 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((N1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M1) N1))) false) M3))) true) __flatten_var_0))))
% 6.75/7.09 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((M3 tptp.extended_enat) (N3 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (@ tptp.ord_less_nat M1)) true) N3))) false) M3))))
% 6.75/7.09 (assert (@ tptp.transp_nat_rat tptp.realrel))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 6.75/7.09 (assert (forall ((K tptp.nat) (M tptp.nat)) (= (@ tptp.nat_prod_decode (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M)) (@ (@ tptp.nat_prod_decode_aux K) M))))
% 6.75/7.09 (assert (forall ((A0 tptp.nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (@ _let_1 A0) (=> (=> (@ _let_1 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (=> (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (=> (forall ((X6 tptp.nat) (Y4 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X6) Y4) (@ tptp.nat_prod_decode N2)) (@ P Y4))) (@ P _let_1))))) (@ P A0)))))))
% 6.75/7.09 (assert (= tptp.powr_real2 (lambda ((B3 tptp.real) (I4 tptp.real)) (let ((_let_1 (@ tptp.literal2 false))) (let ((_let_2 (@ _let_1 false))) (let ((_let_3 (@ _let_2 true))) (let ((_let_4 (@ (@ (@ (@ _let_3 false) true) true) true))) (let ((_let_5 (@ _let_1 true))) (let ((_let_6 (@ _let_5 true))) (let ((_let_7 (@ (@ (@ (@ _let_6 true) false) true) true))) (let ((_let_8 (@ tptp.literal2 true))) (let ((_let_9 (@ _let_8 false))) (let ((_let_10 (@ _let_9 true))) (let ((_let_11 (@ (@ (@ (@ _let_10 false) false) true) true))) (let ((_let_12 (@ _let_8 true))) (let ((_let_13 (@ _let_12 true))) (let ((_let_14 (@ _let_13 true))) (let ((_let_15 (@ (@ (@ _let_14 false) true) true))) (let ((_let_16 (@ _let_2 false))) (let ((_let_17 (@ _let_16 false))) (let ((_let_18 (@ (@ (@ _let_17 true) true) true))) (let ((_let_19 (@ _let_16 true))) (let ((_let_20 (@ (@ (@ _let_17 false) true) false))) (let ((_let_21 (@ (@ _let_5 false) false))) (let ((_let_22 (@ (@ (@ _let_21 true) true) true))) (let ((_let_23 (@ _let_13 false))) (let ((_let_24 (@ _let_9 false))) (let ((_let_25 (@ (@ (@ (@ _let_24 true) false) true) true))) (let ((_let_26 (@ (@ (@ _let_19 false) true) true))) (let ((_let_27 (@ (@ (@ _let_23 true) true) true))) (let ((_let_28 (@ (@ (@ (@ _let_3 true) false) true) true))) (let ((_let_29 (@ (@ (@ (@ _let_24 false) false) true) true))) (let ((_let_30 (@ (@ (@ _let_14 true) false) true))) (let ((_let_31 (@ tptp.power_power_real B3))) (let ((_let_32 (@ tptp.archim6058952711729229775r_real I4))) (let ((_let_33 (@ (@ (@ (@ (@ _let_12 false) false) true) true) true))) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real)) (@ (@ tptp.abort_real (@ _let_18 (@ _let_15 (@ _let_27 (@ _let_22 (@ _let_30 (@ _let_22 (@ _let_11 (@ _let_29 (@ _let_28 (@ _let_20 (@ _let_27 (@ _let_25 (@ _let_4 (@ _let_26 (@ _let_20 (@ _let_7 (@ _let_15 (@ _let_7 (@ _let_18 (@ _let_15 (@ _let_33 (@ _let_25 (@ _let_4 (@ _let_25 (@ (@ (@ (@ (@ _let_6 false) true) true) true) (@ _let_11 (@ _let_20 (@ (@ (@ (@ _let_21 false) true) true) (@ _let_29 (@ _let_33 (@ _let_11 tptp.zero_zero_literal)))))))))))))))))))))))))))))))) (lambda ((Uu3 tptp.product_unit)) (@ (@ tptp.powr_real2 B3) I4)))) (@ (@ (@ tptp.if_real (= (@ tptp.ring_1_of_int_real _let_32) I4)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) I4)) (@ _let_31 (@ tptp.nat2 _let_32))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_31 (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real I4))))))) (@ (@ tptp.abort_real (@ _let_18 (@ _let_15 (@ _let_27 (@ _let_22 (@ _let_30 (@ _let_22 (@ _let_11 (@ _let_29 (@ _let_28 (@ _let_20 (@ _let_27 (@ _let_25 (@ _let_4 (@ _let_26 (@ _let_20 (@ _let_7 (@ _let_15 (@ _let_7 (@ (@ (@ (@ (@ _let_10 true) false) true) false) (@ _let_25 (@ _let_7 (@ _let_4 (@ _let_11 (@ (@ (@ (@ _let_23 false) true) true) (@ _let_11 (@ _let_22 (@ _let_20 (@ _let_11 (@ (@ (@ (@ _let_19 true) true) true) (@ _let_18 (@ _let_15 (@ _let_7 (@ _let_11 (@ _let_7 (@ _let_4 tptp.zero_zero_literal)))))))))))))))))))))))))))))))))))) (lambda ((Uu3 tptp.product_unit)) (@ (@ tptp.powr_real2 B3) I4)))))))))))))))))))))))))))))))))))))))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.75/7.09 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.extended_enat2 Nat) (@ tptp.extended_enat2 Nat2)) (= Nat Nat2))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ (@ tptp.plus_plus_nat M) N)))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) (@ tptp.extended_enat2 tptp.zero_zero_nat)) N)))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (let ((_let_1 (@ tptp.extended_enat2 tptp.zero_zero_nat))) (= (@ (@ tptp.minus_3235023915231533773d_enat _let_1) N) _let_1))))
% 6.75/7.09 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ tptp.extended_enat2 A)) (@ tptp.extended_enat2 B)) (@ tptp.extended_enat2 (@ (@ tptp.minus_minus_nat A) B)))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat M) N)))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ (@ tptp.ord_max_nat M) N)))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ (@ tptp.ord_min_nat M) N)))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 (@ tptp.suc M))) N) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M)) N))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat) (M tptp.nat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat N) (@ tptp.extended_enat2 M)) (exists ((K3 tptp.nat)) (= N (@ tptp.extended_enat2 K3))))))
% 6.75/7.09 (assert (forall ((A2 tptp.set_Extended_enat) (N tptp.nat)) (=> (forall ((Y3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y3) A2) (@ (@ tptp.ord_le2932123472753598470d_enat Y3) (@ tptp.extended_enat2 N)))) (@ tptp.finite4001608067531595151d_enat A2))))
% 6.75/7.09 (assert (forall ((X2 tptp.nat)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.extended_enat2 X2)) (= X2 tptp.one_one_nat))))
% 6.75/7.09 (assert (forall ((X2 tptp.nat)) (= (= (@ tptp.extended_enat2 X2) tptp.one_on7984719198319812577d_enat) (= X2 tptp.one_one_nat))))
% 6.75/7.09 (assert (= tptp.one_on7984719198319812577d_enat (@ tptp.extended_enat2 tptp.one_one_nat)))
% 6.75/7.09 (assert (= tptp.semiri4216267220026989637d_enat tptp.extended_enat2))
% 6.75/7.09 (assert (= tptp.numera1916890842035813515d_enat (lambda ((K2 tptp.num)) (@ tptp.extended_enat2 (@ tptp.numeral_numeral_nat K2)))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat) (M tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N) (@ tptp.extended_enat2 M)) (exists ((K3 tptp.nat)) (= N (@ tptp.extended_enat2 K3))))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat) (M tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N) (@ tptp.extended_enat2 M)) (not (forall ((K3 tptp.nat)) (=> (= N (@ tptp.extended_enat2 K3)) (not (@ (@ tptp.ord_less_nat K3) M))))))))
% 6.75/7.09 (assert (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 tptp.zero_zero_nat)))
% 6.75/7.09 (assert (forall ((X2 tptp.nat)) (= (= (@ tptp.extended_enat2 X2) tptp.zero_z5237406670263579293d_enat) (= X2 tptp.zero_zero_nat))))
% 6.75/7.09 (assert (forall ((X2 tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 X2)) (= X2 tptp.zero_zero_nat))))
% 6.75/7.09 (assert (forall ((X2 tptp.extended_enat) (Y2 tptp.extended_enat) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X2) Y2)) (@ tptp.extended_enat2 N)) (exists ((Y8 tptp.nat) (X10 tptp.nat)) (and (= X2 (@ tptp.extended_enat2 X10)) (= Y2 (@ tptp.extended_enat2 Y8)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X10) Y8)) N))))))
% 6.75/7.09 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1)))))
% 6.75/7.09 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (L tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat L) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg) _let_1))))) (let ((_let_3 (@ (@ tptp.vEBT_Node Info) Deg))) (= (@ (@ tptp.vEBT_VEBT_elim_dead (@ (@ _let_3 TreeList) Summary)) (@ tptp.extended_enat2 L)) (@ (@ _let_3 (@ (@ tptp.take_VEBT_VEBT _let_2) (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg) _let_1))))))) TreeList))) (@ (@ tptp.vEBT_VEBT_elim_dead Summary) (@ tptp.extended_enat2 _let_2)))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.extended_enat) (Y2 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_elim_dead X2) Xa2) Y2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_1) (not (= Y2 _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Node Info2) Deg2))) (=> (= X2 (@ (@ _let_1 TreeList2) Summary2)) (=> (= Xa2 tptp.extend5688581933313929465d_enat) (not (= Y2 (@ (@ _let_1 (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList2)) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) tptp.extend5688581933313929465d_enat)))))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (forall ((L4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat L4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))) (=> (= Xa2 (@ tptp.extended_enat2 L4)) (not (= Y2 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) (@ (@ tptp.take_VEBT_VEBT _let_2) (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList2))) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) (@ tptp.extended_enat2 _let_2)))))))))))))))))
% 6.75/7.09 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Node Info) Deg))) (= (@ (@ tptp.vEBT_VEBT_elim_dead (@ (@ _let_1 TreeList) Summary)) tptp.extend5688581933313929465d_enat) (@ (@ _let_1 (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg) _let_1))))))) TreeList)) (@ (@ tptp.vEBT_VEBT_elim_dead Summary) tptp.extend5688581933313929465d_enat))))))
% 6.75/7.09 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) tptp.extend5688581933313929465d_enat) _let_1)))))
% 6.75/7.09 (assert (forall ((X2 tptp.extended_enat)) (= (not (= X2 tptp.extend5688581933313929465d_enat)) (exists ((I4 tptp.nat)) (= X2 (@ tptp.extended_enat2 I4))))))
% 6.75/7.09 (assert (forall ((X2 tptp.extended_enat)) (= (forall ((Y tptp.nat)) (not (= X2 (@ tptp.extended_enat2 Y)))) (= X2 tptp.extend5688581933313929465d_enat))))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat Q2) tptp.extend5688581933313929465d_enat) (not (= Q2 tptp.extend5688581933313929465d_enat)))))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.extend5688581933313929465d_enat) Q2))))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.extend5688581933313929465d_enat) Q2) tptp.extend5688581933313929465d_enat)))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat Q2) tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat)))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat Q2) tptp.extend5688581933313929465d_enat)))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat tptp.extend5688581933313929465d_enat) Q2) (= Q2 tptp.extend5688581933313929465d_enat))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.extend5688581933313929465d_enat) N) tptp.extend5688581933313929465d_enat)))
% 6.75/7.09 (assert (= (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat)))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.extend5688581933313929465d_enat) Q2) tptp.extend5688581933313929465d_enat)))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.extend5688581933313929465d_enat) Q2) Q2)))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q2) tptp.extend5688581933313929465d_enat) Q2)))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (=> (not (= N tptp.extend5688581933313929465d_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) N) tptp.zero_z5237406670263579293d_enat))))
% 6.75/7.09 (assert (forall ((X2 tptp.extended_enat) (Y2 tptp.extended_enat)) (=> (not (= X2 tptp.extend5688581933313929465d_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X2) Y2)) X2) Y2))))
% 6.75/7.09 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ tptp.extended_enat2 A)) tptp.extend5688581933313929465d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 N)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))))
% 6.75/7.09 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_enat2 M)) tptp.extend5688581933313929465d_enat))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))))
% 6.75/7.09 (assert (= tptp.comple4398354569131411667d_enat (lambda ((A6 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= A6 tptp.bot_bo7653980558646680370d_enat)) tptp.zero_z5237406670263579293d_enat) (@ (@ (@ tptp.if_Extended_enat (@ tptp.finite4001608067531595151d_enat A6)) (@ tptp.lattic921264341876707157d_enat A6)) tptp.extend5688581933313929465d_enat)))))
% 6.75/7.09 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 B)) (@ _let_1 C)) (or (= A tptp.extend5688581933313929465d_enat) (@ (@ tptp.ord_le2932123472753598470d_enat B) C))))))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat Q2) tptp.extend5688581933313929465d_enat)))
% 6.75/7.09 (assert (= tptp.comple2295165028678016749d_enat (lambda ((A6 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= A6 tptp.bot_bo7653980558646680370d_enat)) tptp.extend5688581933313929465d_enat) (@ tptp.ord_Le1955565732374568822d_enat (lambda ((X tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X) A6)))))))
% 6.75/7.09 (assert (forall ((K tptp.num)) (not (= (@ tptp.numera1916890842035813515d_enat K) tptp.extend5688581933313929465d_enat))))
% 6.75/7.09 (assert (not (= tptp.extend5688581933313929465d_enat tptp.one_on7984719198319812577d_enat)))
% 6.75/7.09 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (or (= A tptp.extend5688581933313929465d_enat) (= B C))))))
% 6.75/7.09 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N) tptp.extend5688581933313929465d_enat) (or (= M tptp.extend5688581933313929465d_enat) (= N tptp.extend5688581933313929465d_enat)))))
% 6.75/7.09 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_1 B)) (@ _let_1 C)) (and (not (= A tptp.extend5688581933313929465d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat B) C))))))
% 6.75/7.09 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat A) B) tptp.extend5688581933313929465d_enat) (or (and (= A tptp.extend5688581933313929465d_enat) (not (= B tptp.zero_z5237406670263579293d_enat))) (and (= B tptp.extend5688581933313929465d_enat) (not (= A tptp.zero_z5237406670263579293d_enat)))))))
% 6.75/7.09 (assert (not (= tptp.extend5688581933313929465d_enat tptp.zero_z5237406670263579293d_enat)))
% 6.75/7.09 (assert (= tptp.top_to3028658606643905974d_enat tptp.extend5688581933313929465d_enat))
% 6.75/7.09 (assert (forall ((X2 tptp.produc7272778201969148633d_enat)) (=> (forall ((A3 Bool) (B2 Bool) (Uu2 tptp.extended_enat)) (not (= X2 (@ (@ tptp.produc581526299967858633d_enat (@ (@ tptp.vEBT_Leaf A3) B2)) Uu2)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ tptp.produc581526299967858633d_enat (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) tptp.extend5688581933313929465d_enat)))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (L4 tptp.nat)) (not (= X2 (@ (@ tptp.produc581526299967858633d_enat (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (@ tptp.extended_enat2 L4))))))))))
% 6.75/7.09 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 M)))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.extend5688581933313929465d_enat) (not (forall ((K3 tptp.nat)) (not (= N (@ tptp.extended_enat2 K3))))))))
% 6.75/7.09 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M)) tptp.extend5688581933313929465d_enat)))
% 6.75/7.09 (assert (= (lambda ((P2 (-> tptp.extended_enat Bool))) (exists ((X5 tptp.extended_enat)) (@ P2 X5))) (lambda ((P3 (-> tptp.extended_enat Bool))) (or (@ P3 tptp.extend5688581933313929465d_enat) (exists ((X tptp.nat)) (@ P3 (@ tptp.extended_enat2 X)))))))
% 6.75/7.09 (assert (forall ((Y2 tptp.extended_enat) (Ya tptp.extended_enat) (Yb tptp.extended_enat)) (let ((_let_1 (not (= Yb tptp.extend5688581933313929465d_enat)))) (let ((_let_2 (= Ya tptp.extend5688581933313929465d_enat))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (= Y2 tptp.extend5688581933313929465d_enat))) (=> (=> (exists ((Nat3 tptp.nat)) (= Y2 (@ tptp.extended_enat2 Nat3))) (=> (exists ((Nata tptp.nat)) (= Ya (@ tptp.extended_enat2 Nata))) (forall ((Natb tptp.nat)) (not (= Yb (@ tptp.extended_enat2 Natb)))))) (=> (=> (exists ((Nat3 tptp.nat)) (= Y2 (@ tptp.extended_enat2 Nat3))) (=> (exists ((Nata tptp.nat)) (= Ya (@ tptp.extended_enat2 Nata))) _let_1)) (=> (=> (exists ((Nat3 tptp.nat)) (= Y2 (@ tptp.extended_enat2 Nat3))) (=> _let_2 (forall ((Nata tptp.nat)) (not (= Yb (@ tptp.extended_enat2 Nata)))))) (=> (=> (exists ((Nat3 tptp.nat)) (= Y2 (@ tptp.extended_enat2 Nat3))) _let_3) (=> (=> _let_4 (=> (exists ((Nat3 tptp.nat)) (= Ya (@ tptp.extended_enat2 Nat3))) (forall ((Nata tptp.nat)) (not (= Yb (@ tptp.extended_enat2 Nata)))))) (=> (=> _let_4 (=> (exists ((Nat3 tptp.nat)) (= Ya (@ tptp.extended_enat2 Nat3))) _let_1)) (=> (=> _let_4 (=> _let_2 (forall ((Nat3 tptp.nat)) (not (= Yb (@ tptp.extended_enat2 Nat3)))))) (not (=> _let_4 _let_3)))))))))))))))
% 6.75/7.09 (assert (forall ((Y2 tptp.extended_enat) (Ya tptp.extended_enat)) (let ((_let_1 (not (= Ya tptp.extend5688581933313929465d_enat)))) (let ((_let_2 (= Y2 tptp.extend5688581933313929465d_enat))) (=> (=> (exists ((Nat3 tptp.nat)) (= Y2 (@ tptp.extended_enat2 Nat3))) (forall ((Nata tptp.nat)) (not (= Ya (@ tptp.extended_enat2 Nata))))) (=> (=> (exists ((Nat3 tptp.nat)) (= Y2 (@ tptp.extended_enat2 Nat3))) _let_1) (=> (=> _let_2 (forall ((Nat3 tptp.nat)) (not (= Ya (@ tptp.extended_enat2 Nat3))))) (not (=> _let_2 _let_1)))))))))
% 6.75/7.09 (assert (forall ((Y2 tptp.extended_enat)) (=> (forall ((Nat3 tptp.nat)) (not (= Y2 (@ tptp.extended_enat2 Nat3)))) (= Y2 tptp.extend5688581933313929465d_enat))))
% 6.75/7.09 (assert (forall ((Nat tptp.nat)) (not (= (@ tptp.extended_enat2 Nat) tptp.extend5688581933313929465d_enat))))
% 6.75/7.09 (assert (forall ((Nat tptp.nat)) (not (= tptp.extend5688581933313929465d_enat (@ tptp.extended_enat2 Nat)))))
% 6.75/7.09 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le2932123472753598470d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 M)))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_le2932123472753598470d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 N)))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) N) tptp.extend5688581933313929465d_enat))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (= (@ (@ tptp.times_7803423173614009249d_enat N) tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat))))
% 6.75/7.09 (assert (= tptp.plus_p3455044024723400733d_enat (lambda ((M3 tptp.extended_enat) (N3 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P4 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.plus_plus_nat O) P4)))) tptp.extend5688581933313929465d_enat) N3))) tptp.extend5688581933313929465d_enat) M3))))
% 6.75/7.09 (assert (= tptp.minus_3235023915231533773d_enat (lambda ((A4 tptp.extended_enat) (B3 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((X tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((Y tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.minus_minus_nat X) Y)))) tptp.zero_z5237406670263579293d_enat) B3))) tptp.extend5688581933313929465d_enat) A4))))
% 6.75/7.09 (assert (= tptp.times_7803423173614009249d_enat (lambda ((M3 tptp.extended_enat) (N3 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P4 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat O) P4)))) (@ (@ (@ tptp.if_Extended_enat (= O tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) N3))) (@ (@ (@ tptp.if_Extended_enat (= N3 tptp.zero_z5237406670263579293d_enat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M3))))
% 6.75/7.09 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.extended_enat) (Y2 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_elim_dead X2) Xa2) Y2) (=> (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat X2) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Node Info2) Deg2))) (let ((_let_2 (@ (@ _let_1 TreeList2) Summary2))) (=> (= X2 _let_2) (=> (= Xa2 tptp.extend5688581933313929465d_enat) (=> (= Y2 (@ (@ _let_1 (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList2)) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) tptp.extend5688581933313929465d_enat))) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat _let_2) tptp.extend5688581933313929465d_enat))))))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (forall ((L4 tptp.nat)) (let ((_let_1 (@ tptp.extended_enat2 L4))) (let ((_let_2 (@ (@ tptp.vEBT_Node Info2) Deg2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat L4) (@ (@ tptp.power_power_nat _let_3) (@ (@ tptp.divide_divide_nat Deg2) _let_3))))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ _let_2 (@ (@ tptp.take_VEBT_VEBT _let_4) (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList2))) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) (@ tptp.extended_enat2 _let_4)))) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat (@ (@ _let_2 TreeList2) Summary2)) _let_1)))))))))))))))))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (= (@ tptp.extended_the_enat (@ tptp.extended_enat2 N)) N)))
% 6.75/7.09 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (= (@ tptp.extended_eSuc (@ tptp.lattic921264341876707157d_enat A2)) (@ tptp.lattic921264341876707157d_enat (@ (@ tptp.image_80655429650038917d_enat tptp.extended_eSuc) A2)))))))
% 6.75/7.09 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ tptp.extended_eSuc M) (@ tptp.extended_eSuc N)) (= M N))))
% 6.75/7.09 (assert (= (@ tptp.extended_eSuc tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat) (M tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_eSuc N)) (@ tptp.extended_eSuc M)) (@ (@ tptp.ord_le72135733267957522d_enat N) M))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat) (M tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_eSuc N)) (@ tptp.extended_eSuc M)) (@ (@ tptp.ord_le2932123472753598470d_enat N) M))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat) (M tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ tptp.extended_eSuc N)) (@ tptp.extended_eSuc M)) (@ (@ tptp.minus_3235023915231533773d_enat N) M))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat N) (@ tptp.extended_eSuc tptp.zero_z5237406670263579293d_enat)) (= N tptp.zero_z5237406670263579293d_enat))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ tptp.extended_eSuc N)) tptp.one_on7984719198319812577d_enat) N)))
% 6.75/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.extended_eSuc (@ tptp.numera1916890842035813515d_enat K)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num K) tptp.one)))))
% 6.75/7.09 (assert (forall ((M tptp.nat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.extended_enat2 M))) (= (@ (@ tptp.ord_le72135733267957522d_enat _let_1) (@ tptp.extended_eSuc N)) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) N)))))
% 6.75/7.09 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M) N) (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_eSuc M)) N))))
% 6.75/7.09 (assert (@ tptp.order_4130057895858720880d_enat tptp.extended_eSuc))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat N) (@ tptp.extended_eSuc N))))
% 6.75/7.09 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_eSuc M)) N) (@ (@ tptp.plus_p3455044024723400733d_enat N) (@ (@ tptp.times_7803423173614009249d_enat M) N)))))
% 6.75/7.09 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat M))) (= (@ _let_1 (@ tptp.extended_eSuc N)) (@ (@ tptp.plus_p3455044024723400733d_enat M) (@ _let_1 N))))))
% 6.75/7.09 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat M))) (= (@ _let_1 (@ tptp.extended_eSuc N)) (@ tptp.extended_eSuc (@ _let_1 N))))))
% 6.75/7.09 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.extended_eSuc M)) N) (@ tptp.extended_eSuc (@ (@ tptp.plus_p3455044024723400733d_enat M) N)))))
% 6.75/7.09 (assert (forall ((X2 tptp.extended_enat) (Y2 tptp.extended_enat)) (= (@ tptp.extended_eSuc (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y2)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.extended_eSuc X2)) (@ tptp.extended_eSuc Y2)))))
% 6.75/7.09 (assert (= tptp.extended_eSuc (lambda ((N3 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat N3) tptp.one_on7984719198319812577d_enat))))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) Q2) (@ tptp.extended_eSuc Q2))))
% 6.75/7.09 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat Q2) tptp.one_on7984719198319812577d_enat) (@ tptp.extended_eSuc Q2))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.extended_eSuc N))))
% 6.75/7.09 (assert (= tptp.one_on7984719198319812577d_enat (@ tptp.extended_eSuc tptp.zero_z5237406670263579293d_enat)))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (not (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_eSuc N)))))
% 6.75/7.09 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_eSuc N)) tptp.zero_z5237406670263579293d_enat))))
% 6.75/7.09 (assert (forall ((N tptp.nat)) (= (@ tptp.extended_eSuc (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ tptp.suc N)))))
% 6.75/7.09 (assert (forall ((X2 tptp.extended_enat) (Y2 tptp.nat)) (= (= (@ tptp.extended_eSuc X2) (@ tptp.extended_enat2 Y2)) (exists ((N3 tptp.nat)) (and (= Y2 (@ tptp.suc N3)) (= X2 (@ tptp.extended_enat2 N3)))))))
% 6.75/7.09 (assert (forall ((Y2 tptp.nat) (X2 tptp.extended_enat)) (= (= (@ tptp.extended_enat2 Y2) (@ tptp.extended_eSuc X2)) (exists ((N3 tptp.nat)) (and (= Y2 (@ tptp.suc N3)) (= (@ tptp.extended_enat2 N3) X2))))))
% 6.75/7.09 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (= (@ tptp.extended_eSuc (@ tptp.comple4398354569131411667d_enat A2)) (@ tptp.comple4398354569131411667d_enat (@ (@ tptp.image_80655429650038917d_enat tptp.extended_eSuc) A2))))))
% 6.75/7.09 (assert (= tptp.extended_eSuc (@ (@ tptp.extend3600170679010898289d_enat (lambda ((N3 tptp.nat)) (@ tptp.extended_enat2 (@ tptp.suc N3)))) tptp.extend5688581933313929465d_enat)))
% 6.75/7.09 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y2)) tptp.less_than) (@ (@ tptp.ord_less_nat X2) Y2))))
% 6.75/7.09 (assert (@ (@ (@ (@ tptp.quotie3684837364556693515t_real tptp.realrel) tptp.real2) tptp.rep_real2) tptp.cr_real))
% 6.75/7.09 (assert (@ (@ tptp.semila9081495762789891438tr_nat tptp.ord_max_nat) tptp.zero_zero_nat))
% 6.75/7.09 (assert (= tptp.ord_less_eq_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))))))
% 6.75/7.09 (assert (= tptp.ord_less_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))))))
% 6.75/7.09 (assert (= tptp.code_sub (lambda ((Xa4 tptp.num) (X tptp.num)) (@ tptp.code_integer_of_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int Xa4)) (@ tptp.numeral_numeral_int X))))))
% 6.75/7.09 (assert (= (@ (@ tptp.code_sub tptp.one) tptp.one) tptp.zero_z3403309356797280102nteger))
% 6.75/7.09 (assert (forall ((X2 tptp.num) (Xa2 tptp.num)) (= (@ tptp.code_int_of_integer (@ (@ tptp.code_sub X2) Xa2)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Xa2)))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.code_sub (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_dup (@ (@ tptp.code_sub M) N))) tptp.one_one_Code_integer))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.code_sub (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_dup (@ (@ tptp.code_sub M) N))) tptp.one_one_Code_integer))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.code_sub (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.code_dup (@ (@ tptp.code_sub M) N)))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.code_sub (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.code_dup (@ (@ tptp.code_sub M) N)))))
% 6.75/7.09 (assert (forall ((N tptp.num)) (= (@ (@ tptp.code_sub tptp.one) (@ tptp.bit0 N)) (@ tptp.code_Neg (@ tptp.bitM N)))))
% 6.75/7.09 (assert (forall ((M tptp.num)) (= (@ (@ tptp.code_sub (@ tptp.bit0 M)) tptp.one) (@ tptp.code_Pos (@ tptp.bitM M)))))
% 6.75/7.09 (assert (forall ((N tptp.num)) (= (@ tptp.code_dup (@ tptp.code_Neg N)) (@ tptp.code_Neg (@ tptp.bit0 N)))))
% 6.75/7.09 (assert (forall ((N tptp.num)) (= (@ tptp.code_dup (@ tptp.code_Pos N)) (@ tptp.code_Pos (@ tptp.bit0 N)))))
% 6.75/7.09 (assert (forall ((L tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.code_Neg L)))))
% 6.75/7.09 (assert (forall ((K tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_Neg K)) tptp.zero_z3403309356797280102nteger)))
% 6.75/7.09 (assert (forall ((L tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.code_Pos L))))
% 6.75/7.09 (assert (forall ((K tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_Pos K)) tptp.zero_z3403309356797280102nteger))))
% 6.75/7.09 (assert (forall ((K tptp.num) (L tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_Pos K)) (@ tptp.code_Neg L)))))
% 6.75/7.09 (assert (forall ((K tptp.num) (L tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_Neg K)) (@ tptp.code_Pos L))))
% 6.75/7.09 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_Pos K)) (@ tptp.code_Pos L)) (@ (@ tptp.ord_less_num K) L))))
% 6.75/7.09 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_Neg K)) (@ tptp.code_Neg L)) (@ (@ tptp.ord_less_num L) K))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_Neg M)) (@ tptp.code_Neg N)) (@ tptp.code_Neg (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.09 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.bit1 K))) (= (@ tptp.numera6620942414471956472nteger _let_1) (@ tptp.code_Pos _let_1)))))
% 6.75/7.09 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.bit0 K))) (= (@ tptp.numera6620942414471956472nteger _let_1) (@ tptp.code_Pos _let_1)))))
% 6.75/7.09 (assert (= (@ tptp.numera6620942414471956472nteger tptp.one) (@ tptp.code_Pos tptp.one)))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_Neg M)) (@ tptp.code_Neg N)) (@ tptp.code_Pos (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_Neg M)) (@ tptp.code_Pos N)) (@ tptp.code_Neg (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_Pos M)) (@ tptp.code_Neg N)) (@ tptp.code_Neg (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.09 (assert (= tptp.one_one_Code_integer (@ tptp.code_Pos tptp.one)))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_Pos M)) (@ tptp.code_Pos N)) (@ tptp.code_Pos (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_Pos M)) (@ tptp.code_Pos N)) (@ tptp.code_Pos (@ (@ tptp.times_times_num M) N)))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_Neg M)) (@ tptp.code_Pos N)) (@ tptp.code_Neg (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_Pos M)) (@ tptp.code_Neg N)) (@ tptp.code_Pos (@ (@ tptp.plus_plus_num M) N)))))
% 6.75/7.09 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_Pos K)) (@ tptp.code_Pos L)) (@ (@ tptp.ord_less_eq_num K) L))))
% 6.75/7.09 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_Neg K)) (@ tptp.code_Neg L)) (@ (@ tptp.ord_less_eq_num L) K))))
% 6.75/7.09 (assert (forall ((M tptp.num)) (= (@ (@ tptp.code_sub (@ tptp.bit1 M)) tptp.one) (@ tptp.code_Pos (@ tptp.bit0 M)))))
% 6.75/7.09 (assert (forall ((N tptp.num)) (= (@ (@ tptp.code_sub tptp.one) (@ tptp.bit1 N)) (@ tptp.code_Neg (@ tptp.bit0 N)))))
% 6.75/7.09 (assert (@ (@ tptp.monoid_nat tptp.ord_max_nat) tptp.zero_zero_nat))
% 6.75/7.09 (assert (= tptp.nat_sum_decode (lambda ((N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N3) _let_1))) (@ (@ (@ tptp.if_Sum_sum_nat_nat (@ (@ tptp.dvd_dvd_nat _let_1) N3)) (@ tptp.sum_Inl_nat_nat _let_2)) (@ tptp.sum_Inr_nat_nat _let_2)))))))
% 6.75/7.09 (assert (forall ((A0 tptp.nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.accp_nat tptp.nth_item_rel))) (=> (@ _let_1 A0) (=> (=> (@ _let_1 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (=> (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.accp_nat tptp.nth_item_rel) _let_1) (=> (forall ((A8 tptp.nat) (Aa tptp.nat)) (=> (= (@ tptp.nat_sum_decode N2) (@ tptp.sum_Inl_nat_nat A8)) (=> (= (@ tptp.nat_sum_decode A8) (@ tptp.sum_Inl_nat_nat Aa)) (@ P Aa)))) (=> (forall ((A8 tptp.nat) (B10 tptp.nat)) (=> (= (@ tptp.nat_sum_decode N2) (@ tptp.sum_Inl_nat_nat A8)) (=> (= (@ tptp.nat_sum_decode A8) (@ tptp.sum_Inr_nat_nat B10)) (@ P B10)))) (=> (forall ((B10 tptp.nat) (Ba tptp.nat) (X6 tptp.nat) (Y4 tptp.nat)) (=> (= (@ tptp.nat_sum_decode N2) (@ tptp.sum_Inr_nat_nat B10)) (=> (= (@ tptp.nat_sum_decode B10) (@ tptp.sum_Inr_nat_nat Ba)) (=> (= (@ (@ tptp.product_Pair_nat_nat X6) Y4) (@ tptp.nat_prod_decode Ba)) (@ P X6))))) (=> (forall ((B10 tptp.nat) (Ba tptp.nat) (X6 tptp.nat) (Y4 tptp.nat)) (=> (= (@ tptp.nat_sum_decode N2) (@ tptp.sum_Inr_nat_nat B10)) (=> (= (@ tptp.nat_sum_decode B10) (@ tptp.sum_Inr_nat_nat Ba)) (=> (= (@ (@ tptp.product_Pair_nat_nat X6) Y4) (@ tptp.nat_prod_decode Ba)) (@ P Y4))))) (@ P _let_1)))))))) (@ P A0)))))))
% 6.75/7.09 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y2) (@ _let_1 (@ tptp.nat_sum_encode (@ tptp.sum_Inl_nat_nat Y2)))))))
% 6.75/7.09 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y2) (@ _let_1 (@ tptp.nat_sum_encode (@ tptp.sum_Inr_nat_nat Y2)))))))
% 6.75/7.09 (assert (= tptp.nat_sum_encode (@ (@ tptp.sum_ca6763686470577984908at_nat (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (lambda ((B3 tptp.nat)) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3))))))
% 6.75/7.09 (assert (= tptp.extend5688581933313929465d_enat (@ tptp.extended_Abs_enat tptp.none_nat)))
% 6.75/7.09 (assert (forall ((X2 tptp.extended_enat)) (not (forall ((Y3 tptp.option_nat)) (=> (= X2 (@ tptp.extended_Abs_enat Y3)) (not (@ (@ tptp.member_option_nat Y3) tptp.top_to8920198386146353926on_nat)))))))
% 6.75/7.09 (assert (forall ((P (-> tptp.extended_enat Bool)) (X2 tptp.extended_enat)) (=> (forall ((Y3 tptp.option_nat)) (=> (@ (@ tptp.member_option_nat Y3) tptp.top_to8920198386146353926on_nat) (@ P (@ tptp.extended_Abs_enat Y3)))) (@ P X2))))
% 6.75/7.09 (assert (forall ((X2 tptp.option_nat) (Y2 tptp.option_nat)) (=> (@ (@ tptp.member_option_nat X2) tptp.top_to8920198386146353926on_nat) (=> (@ (@ tptp.member_option_nat Y2) tptp.top_to8920198386146353926on_nat) (= (= (@ tptp.extended_Abs_enat X2) (@ tptp.extended_Abs_enat Y2)) (= X2 Y2))))))
% 6.75/7.09 (assert (= tptp.extended_enat2 (lambda ((N3 tptp.nat)) (@ tptp.extended_Abs_enat (@ tptp.some_nat N3)))))
% 6.75/7.09 (assert (forall ((Y2 tptp.option_nat)) (=> (@ (@ tptp.member_option_nat Y2) tptp.top_to8920198386146353926on_nat) (= (@ tptp.extended_Rep_enat (@ tptp.extended_Abs_enat Y2)) Y2))))
% 6.75/7.09 (assert (forall ((Y2 tptp.option_nat) (P (-> tptp.option_nat Bool))) (=> (@ (@ tptp.member_option_nat Y2) tptp.top_to8920198386146353926on_nat) (=> (forall ((X4 tptp.extended_enat)) (@ P (@ tptp.extended_Rep_enat X4))) (@ P Y2)))))
% 6.75/7.09 (assert (forall ((Y2 tptp.option_nat)) (=> (@ (@ tptp.member_option_nat Y2) tptp.top_to8920198386146353926on_nat) (not (forall ((X4 tptp.extended_enat)) (not (= Y2 (@ tptp.extended_Rep_enat X4))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.extended_enat)) (@ (@ tptp.member_option_nat (@ tptp.extended_Rep_enat X2)) tptp.top_to8920198386146353926on_nat)))
% 6.75/7.09 (assert (forall ((X2 tptp.extended_enat) (Y2 tptp.extended_enat)) (= (= (@ tptp.extended_Rep_enat X2) (@ tptp.extended_Rep_enat Y2)) (= X2 Y2))))
% 6.75/7.09 (assert (forall ((X2 tptp.extended_enat)) (= (@ tptp.extended_Abs_enat (@ tptp.extended_Rep_enat X2)) X2)))
% 6.75/7.09 (assert (@ (@ (@ tptp.type_d7649664348572268762on_nat tptp.extended_Rep_enat) tptp.extended_Abs_enat) tptp.top_to8920198386146353926on_nat))
% 6.75/7.09 (assert (= tptp.pcr_real (@ (@ tptp.relcom2856161143838007533t_real (@ (@ tptp.bNF_re4702136315717946289at_rat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)))) tptp.cr_real)))
% 6.75/7.09 (assert (= (@ tptp.domainp_nat_rat_real tptp.pcr_real) (lambda ((X (-> tptp.nat tptp.rat))) (exists ((Y (-> tptp.nat tptp.rat))) (and (@ (@ (@ (@ tptp.bNF_re4702136315717946289at_rat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4))) X) Y) (@ (@ tptp.realrel Y) Y))))))
% 6.75/7.09 (assert (= tptp.gcd_lcm_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A4)) (@ tptp.abs_abs_int B3))) (@ (@ tptp.gcd_gcd_int A4) B3)))))
% 6.75/7.09 (assert (= (@ tptp.domainp_nat_rat_real tptp.pcr_real) tptp.cauchy))
% 6.75/7.09 (assert (= (@ tptp.domainp_nat_rat_real tptp.pcr_real) (lambda ((X (-> tptp.nat tptp.rat))) (@ (@ tptp.realrel X) X))))
% 6.75/7.09 (assert (forall ((M tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (=> (not (= N tptp.zero_zero_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_lcm_int M) N))))))
% 6.75/7.09 (assert (forall ((P5 (-> (-> tptp.nat tptp.rat) Bool))) (=> (@ tptp.left_t2768085380646472630at_rat (@ (@ tptp.bNF_re4702136315717946289at_rat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)))) (=> (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o (@ (@ tptp.bNF_re4702136315717946289at_rat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)))) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) P5) (lambda ((X (-> tptp.nat tptp.rat))) (@ (@ tptp.realrel X) X))) (= (@ tptp.domainp_nat_rat_real tptp.pcr_real) P5)))))
% 6.75/7.09 (assert (= tptp.gcd_lcm_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat X) Y)) (@ (@ tptp.gcd_gcd_nat X) Y)))))
% 6.75/7.09 (assert (= tptp.times_times_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.gcd_gcd_nat M3) N3)) (@ (@ tptp.gcd_lcm_nat M3) N3)))))
% 6.75/7.09 (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) (@ _let_1 (@ (@ tptp.gcd_lcm_nat M) N)))))))
% 6.75/7.09 (assert (forall ((Y2 tptp.set_nat_rat) (P (-> tptp.set_nat_rat Bool))) (=> (@ (@ tptp.member_set_nat_rat Y2) (@ tptp.collect_set_nat_rat (lambda ((C3 tptp.set_nat_rat)) (exists ((X (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X))) (and (@ _let_1 X) (= C3 (@ tptp.collect_nat_rat _let_1)))))))) (=> (forall ((X4 tptp.real)) (@ P (@ tptp.rep_real X4))) (@ P Y2)))))
% 6.75/7.09 (assert (forall ((Y2 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat Y2) (@ tptp.collect_set_nat_rat (lambda ((C3 tptp.set_nat_rat)) (exists ((X (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X))) (and (@ _let_1 X) (= C3 (@ tptp.collect_nat_rat _let_1)))))))) (not (forall ((X4 tptp.real)) (not (= Y2 (@ tptp.rep_real X4))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (= (@ tptp.rep_real X2) (@ tptp.rep_real Y2)) (= X2 Y2))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (@ (@ tptp.member_set_nat_rat (@ tptp.rep_real X2)) (@ tptp.collect_set_nat_rat (lambda ((C3 tptp.set_nat_rat)) (exists ((X (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X))) (and (@ _let_1 X) (= C3 (@ tptp.collect_nat_rat _let_1))))))))))
% 6.75/7.09 (assert (forall ((Y2 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat Y2) (@ tptp.collect_set_nat_rat (lambda ((C3 tptp.set_nat_rat)) (exists ((X (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X))) (and (@ _let_1 X) (= C3 (@ tptp.collect_nat_rat _let_1)))))))) (= (@ tptp.rep_real (@ tptp.abs_real Y2)) Y2))))
% 6.75/7.09 (assert (= tptp.rep_real2 (@ tptp.quot_r1730120044975580712at_rat tptp.rep_real)))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (= (@ tptp.abs_real (@ tptp.rep_real X2)) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.set_nat_rat) (Y2 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X2) (@ tptp.collect_set_nat_rat (lambda ((C3 tptp.set_nat_rat)) (exists ((X (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X))) (and (@ _let_1 X) (= C3 (@ tptp.collect_nat_rat _let_1)))))))) (=> (@ (@ tptp.member_set_nat_rat Y2) (@ tptp.collect_set_nat_rat (lambda ((C3 tptp.set_nat_rat)) (exists ((X (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X))) (and (@ _let_1 X) (= C3 (@ tptp.collect_nat_rat _let_1)))))))) (= (= (@ tptp.abs_real X2) (@ tptp.abs_real Y2)) (= X2 Y2))))))
% 6.75/7.09 (assert (forall ((P (-> tptp.real Bool)) (X2 tptp.real)) (=> (forall ((Y3 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat Y3) (@ tptp.collect_set_nat_rat (lambda ((C3 tptp.set_nat_rat)) (exists ((X (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X))) (and (@ _let_1 X) (= C3 (@ tptp.collect_nat_rat _let_1)))))))) (@ P (@ tptp.abs_real Y3)))) (@ P X2))))
% 6.75/7.09 (assert (forall ((X2 tptp.real)) (not (forall ((Y3 tptp.set_nat_rat)) (=> (= X2 (@ tptp.abs_real Y3)) (not (@ (@ tptp.member_set_nat_rat Y3) (@ tptp.collect_set_nat_rat (lambda ((C3 tptp.set_nat_rat)) (exists ((X (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X))) (and (@ _let_1 X) (= C3 (@ tptp.collect_nat_rat _let_1))))))))))))))
% 6.75/7.09 (assert (= tptp.real2 (@ (@ tptp.quot_a3129823074075660125t_real tptp.realrel) tptp.abs_real)))
% 6.75/7.09 (assert (@ (@ (@ tptp.type_d8072115097938612567at_rat tptp.rep_real) tptp.abs_real) (@ tptp.collect_set_nat_rat (lambda ((C3 tptp.set_nat_rat)) (exists ((X (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X))) (and (@ _let_1 X) (= C3 (@ tptp.collect_nat_rat _let_1)))))))))
% 6.75/7.09 (assert (forall ((DT (-> tptp.nat Bool)) (DS (-> tptp.rat Bool)) (P22 (-> (-> tptp.nat tptp.rat) Bool))) (=> (= (@ tptp.domainp_nat_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) DT) (=> (= (@ tptp.domainp_rat_rat (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4))) DS) (=> (@ tptp.left_unique_nat_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (=> (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o (@ (@ tptp.bNF_re4702136315717946289at_rat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)))) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) P22) (lambda ((X (-> tptp.nat tptp.rat))) (@ (@ tptp.realrel X) X))) (= (@ tptp.domainp_nat_rat_real tptp.pcr_real) (@ (@ tptp.inf_inf_nat_rat_o (@ (@ tptp.basic_208271146493774413at_rat DT) DS)) P22))))))))
% 6.75/7.09 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ (@ tptp.if_int false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ (@ tptp.if_int true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ (@ tptp.if_num false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ (@ tptp.if_num true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ (@ tptp.if_real false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ (@ tptp.if_real true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X7 tptp.real)) (@ P X7)))))
% 6.75/7.09 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.extended_enat) (Y2 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.extended_enat) (Y2 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.set_int) (Y2 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.set_int) (Y2 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.list_int) (Y2 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.list_int) (Y2 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.list_nat) (Y2 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.list_nat) (Y2 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 (-> tptp.int tptp.int)) (Y2 (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 (-> tptp.int tptp.int)) (Y2 (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 (-> tptp.nat tptp.rat)) (Y2 (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 (-> tptp.nat tptp.rat)) (Y2 (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.option_nat) (Y2 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.option_nat) (Y2 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.option_num) (Y2 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.option_num) (Y2 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.sum_sum_nat_nat) (Y2 tptp.sum_sum_nat_nat)) (= (@ (@ (@ tptp.if_Sum_sum_nat_nat false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.sum_sum_nat_nat) (Y2 tptp.sum_sum_nat_nat)) (= (@ (@ (@ tptp.if_Sum_sum_nat_nat true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.product_prod_int_int) (Y2 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.product_prod_int_int) (Y2 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X2) Y2) X2)))
% 6.75/7.09 (assert (forall ((X2 (-> tptp.nat tptp.int tptp.int)) (Y2 (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int false) X2) Y2) Y2)))
% 6.75/7.09 (assert (forall ((X2 (/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 31854 Alarm clock ( read result; case "$result" in
% 299.86/300.14 unsat)
% 299.86/300.14 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.86/300.14 ;;
% 299.86/300.14 sat)
% 299.86/300.14 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.86/300.14 ;;
% 299.86/300.14 esac; exit 1 )
% 299.86/300.15 Alarm clock
% 299.86/300.15 % cvc5---1.0.5 exiting
% 299.86/300.15 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------